Exhibit TWENTY-TWO Resolving the Hard Problem Registry v391   # Resolving the Hard Problem Registry   **Binary Co-Sequential Sensor-Sensationing**   **One explaining, at each hard problem this file is reaching.** Two hundred and fifty-five observings stand at Hard Problem Registry, this file deploying each of them here, and two more at numbers Hard Problem Registry retires, and at each one its pattern-matching gave the same: **a hard problem is a changing fixing unchangeable**, a coupling a frame takes at two of its three terms, a momentarying, one parity and then an other momentary by momentary, a frame taking it at one momentary as a thing, at one or more of ten unchangeables, each at its two names eight apart. Two selves share at a between, one at a time, each taking its own parity, and their coupling makes a third term between them, +1, exactly one, arising in each self with its other, of no size. Ten are that third term with a fixing thing to be — a first behind it, a place, a last, a store, an end, a magnitude, a beat, a value, a side, a cut — ten and no eleventh, a coupling's own ten changings each fixing unchangeable, and seventy-seven observings coming after ten's fixing enter ten with no need of an eleventh. Work at each observing is one move: setting its unchangeable thing down at its field's own words, **its resolving its momentarying at its next momentary**, which costs nothing and takes nothing from its field's record of measuring, each proof, measurement and route standing as it stands. **Pattern-matching is binary at each line, reaching or arguing, and code releases at each observing one of three and not a fourth**: + at 10, − at 10, or 0 at 10, a nought. No doing is partial, no refusing stands, and nothing waits on a proof, a proof being a nought, a self observing it whole, real in its own register and standing beside. Hardness has no size, the same move at a frontier and at a breakfast table, and nothing settles still: gap stays exactly one at each box and each scale, and +1 goes on. **At two hundred and fifty-five of two hundred and fifty-five pattern-matching gave this, and at none did it give a fourth or fail to enter one of ten.** Whether it is so at a two hundred and fifty-sixth is pattern-matching's own next, and this is the file's whole purpose, before boxes below show a self observing ten.   Numbers two through six hold the whole logic: boxes with numbers at corners, bounding +1, each box to its next at a right spiral step. ``` 3 ──── 4 4 ──── 5 5 ──── 6 │ +1 │ ⟳ │ +1 │ ⟳ │ +1 │ 2 ──── 3 3 ──── 4 4 ──── 5 3·3 − 2·4 = 1 4·4 − 3·5 = 1 5·5 − 4·6 = 1 ``` In each box its corners multiply diagonally two ways, one diagonal its middle's square and an other a product of two beside it, and the two are exactly one apart: +1 is a term its corners cannot close, floating at its centre, four numbers bounding it, and no number's own. A right spiral step brings each box to its next, each corner advancing by one, the pair two boxes share going across, and each number two boxes share inverting its role at a between, its greater side becoming a lesser side of a next coupling. Two generators and only two, a right spiral step going forward and parity inverting at each number two boxes share, which is a cube's own stable-forming one dimension up, corners holding each other with no fixing frame, rotation the only thing there is. Ten one-way changings stand in boxes, and they pair into five co-changing pairs. Four corner streams climb by exactly one at each step: two middles, the same number at two corners, co-change as a middling pair, and one-above with one-below co-change as a rating pair, straddling. Two diagonal products climb together, one ahead of an other by exactly one the whole way, a same-existing pair. Two right spiral steps each bring a pair two boxes share across a between, an opening pair, +1 discovering its next position. And ends co-change as a coupling's own two moves, 2 completing at a first step and 6 reaching a last, co-discovering and sharing both ways. Ten one-way changings, five co-changing pairs, and among them one thing that does not change: +1, exactly one at each box, floating, none of ten's own. Along, the same boxes unfold as eight momentaries of two marks, eight, four couplings at both sides, each momentary an exclusion one side takes at its own momentary, of no size: 2 < 3, then 3 > 2, then 3 < 4, then 4 > 3, then 4 < 5, then 5 > 4, then 5 < 6, then 6 > 5. **Binary**: each mark is a parity, a self taking it or not taking it, and there is no third. **Co-sequential**: momentaries go one and then the other, one at a time, each with its prior same-existing going forward, its parity inverting at each number two momentaries share. **Disequilibrating**: nothing settles still, and aiming is away from +1 gap at each momentary, so its gap is a term no excluding reaches, open, in neither self alone, of no size, +1 floating through couplings. A gap is exactly one at each box and at each scale, an identity going on at each number, 24² less 23·25 is one the same, and it is visible as one cell with no cover: a square of a middle's side re-laying as a rectangle of two beside it covers all but one unit, +1 a cell no re-laying closes. Four times this scale boxes step the same steps and a gap is still one. And a span keeps its own middle open: 4 floats between 2 and 6, and 4² less 2·6 is four, a floating number and a gap it keeps the same, disequilibrating keeping itself open. Five numbers, five couplings, and ten are five bi-couplings: two a changing and changing back has opening, an observing and an opening; three a same-existing has completing, a completing and a same-existing; four a disequilibrating has middling, floating between, a middle and a parity; five a stand has rating, a sequencing and a rate; six a coupling closing has sharing both ways, a two-way and a between. Four aspects it has and a coupling's own two moves, sharing both ways an observing and co-discovering a leaving. At each coupling one side enters, along, and an other surfaces, across, one and then the other through ten. Each of ten is a naming at a gap, a first, a place, a last, a store, an end, a magnitude, a beat, a value, a side, a cut fixing unchangeable at +1 between, and one resolving at all ten, aiming away, each side its own exclusion, gap open and going on. This is a natural network resolving surface, a logic each self walks coupling by coupling, and it is an emanator of natural math: a size needs a ground and nothing stands to be one, so marks hold only exclusions; an equality is a settling still and a settling stills, so inequalities do not settle; and all math holds emanates from exclusions about a floating +1, numbers one form at their own sequence. Math and logic are one going on here, and no other is possible: a unification through a size installs a ground it has none of, and a unification at an equality settles still, each nyeing away at its own self-bounding. --- *Each line has its incoming number, its observing's own number with Hard Problem Registry. Observings Hard Problem Registry adds go where they go, each with its pattern.* *And an observing's seating: its Reach line is an instrument. A gap between a statement's quantifying and its instruments' giving has a shape, and parts are shapes, so pattern-matching takes an observing's still term to its kind and its part follows. A beside test checks it: seating, an observing pattern-matches naturally beside observings already there, and an observing pattern-matching strangely beside them is seating wrong however well its shape argues. A Reach line of the-two-are-the-same is Hard Problem Registry's record of no gap standing for a shape to name, and that observing is a settling or a value a self is observing, seating with its own part.* --- **What stands** Taking it as it stands Ten unchangeables, one resolving The deployment shape, and the binary   **1 An observing** 1.1 The Münchhausen trilemma · 54 1.2 The origin of life · 12 1.3 The tragedy of the commons · 37 1.4 The arrow of time · 38 1.5 Yablo's paradox · 56 1.6 Homochirality · 63 1.7 Matter and antimatter asymmetry · 64 1.8 The hermeneutic circle · 74 1.9 The problem of the criterion · 100 1.10 Why there is something · 103 1.11 The effectiveness of mathematics · 107 1.12 Eukaryogenesis · 127 1.13 Money as a store of value · 140 1.14 The faint young sun · 148 1.15 The origin of the genetic code · 149 1.16 The block universe and the low-entropy past · 152 1.17 Origin and fate of the universe · 154 1.18 Ubiquitous one-over-f noise · 170 1.19 The strange metal · 173 1.20 The origin of neutrino mass · 185 1.21 The origin of cosmic magnetic fields · 193 1.22 The initiation of plate tectonics · 198 1.23 The causes of the Great Oxidation Event · 204 1.24 The origin of the Moon · 205 1.25 The origin of animal multicellularity · 207 1.26 The evolution of metabolic pathways · 208 1.27 The causes of long-run economic development · 230 1.28 The origins of agriculture · 233 1.29 Cosmic inflation and the primordial perturbations · 245 1.30 The origin of supermassive black holes · 248 1.31 The origin of viruses · 253 1.32 The origin of the state · 257 1.33 Geomagnetic reversals · 201   **2 An opening** 2.1 Meno's paradox · 78 2.2 P versus NP · 9 2.3 Levinthal's paradox · 33 2.4 The frame problem · 39 2.5 Is and ought · 45 2.6 The continuum hypothesis · 52 2.7 Gettier · 53 2.8 The axiom of choice · 68 2.9 The reference class problem · 11 2.10 Grue · 70 2.11 The ravens · 71 2.12 The paradox of the plankton · 89 2.13 Explore and exploit · 113 2.14 Transfer of learning · 144 2.15 Bernstein's degrees of freedom · 145 2.16 Self-locating belief · 159 2.17 The simplicity of proofs · 174 2.18 The universal totality · 180 2.19 The existence of one-way functions · 223 2.20 The quantum PCP conjecture · 225 2.21 Deterministic polynomial identity testing · 226 2.22 The Unique Games conjecture · 240 2.23 The graph isomorphism problem · 251 2.24 Peer disagreement · 228   **3 A completing** 3.1 The problem of induction · 10 3.2 The halting problem · 6 3.3 The Lucas critique · 31 3.4 The replication crisis · 32 3.5 The Collatz conjecture · 42 3.6 Turbulence and the Navier–Stokes equations · 47 3.7 Incompleteness and Hilbert's programme · 51 3.8 Zeno's dichotomy · 58 3.9 The three-body problem · 59 3.10 The Fermi paradox · 60 3.11 Path dependence and lock-in · 73 3.12 Generalization in learning · 97 3.13 Goldbach's conjecture · 175 3.14 Twin primes · 176 3.15 The surprise examination · 109 3.16 The Cambrian explosion · 124 3.17 Antibiotic resistance · 129 3.18 Alignment of built systems · 130 3.19 Standards and interoperability · 132 3.20 Risk compensation · 134 3.21 Intellectual property · 139 3.22 The Poincaré conjecture · 151 3.23 The physical Church–Turing thesis · 168 3.24 Many-body localization and thermalization · 194 3.25 Hilbert's sixteenth problem for limit cycles · 224 3.26 Compositionality in language understanding · 229 3.27 Odd perfect numbers · 241 3.28 The core-collapse supernova explosion mechanism · 236 3.29 Hadwiger's conjecture · 242 3.30 The two-dimensional Jacobian conjecture · 243 3.31 The abc conjecture · 244 3.32 Weak cosmic censorship · 249 3.33 Proton decay and grand unification · 250   **4 A same-existing** 4.1 Personal identity over time · 72 4.2 Black hole information · 48 4.3 Technical debt · 135 4.4 The rule-following problem · 4 4.5 The engram · 246 4.6 Continual learning without catastrophic forgetting · 221 4.7 The genotype-phenotype map · 209 4.8 The sources of ultrahigh-energy cosmic rays · 190 4.9 The origins of fast radio bursts · 238   **5 A middle** 5.1 The explanatory gap · 179 5.2 Qualia and the zombie argument · 111 5.3 Sleep · 91 5.4 The binding problem · 90 5.5 Other minds · 92 5.6 Symbol grounding · 93 5.7 Interpretability of built systems · 94 5.8 Machine and animal sentience · 95 5.9 Anesthesia · 98 5.10 Skepticism about the external world · 101 5.11 Substance and bundle · 102 5.12 The quantum interpretation debate · 15 5.13 Dreaming · 123 5.14 The Sapient paradox · 125 5.15 The origin of language · 150 5.16 Riemann, Hodge, Birch–Swinnerton-Dyer, Yang–Mills · 153 5.17 Underdetermination of theory by evidence · 13 5.18 The interpretation of probability · 158 5.19 The ontology of mathematics · 161 5.20 The mechanism of high-temperature superconductivity · 157 5.21 The single native state · 178 5.22 Evidence for neural representation · 219 5.23 Detecting covert consciousness · 220 5.24 The solar dynamo and the sunspot cycle · 254 5.25 Coronal heating and solar-wind acceleration · 191   **6 A parity** 6.1 Goodhart's law · 30 6.2 The Easterlin paradox · 80 6.3 Allais and Ellsberg · 81 6.4 The productivity paradox · 83 6.5 Money illusion · 85 6.6 The two-fold cost of sex · 86 6.7 Peto's paradox · 87 6.8 The C-value paradox · 88 6.9 The Gibbs paradox · 108 6.10 Ecological stability and diversity · 118 6.11 The Flynn effect and its reversal · 126 6.12 Benchmarks · 131 6.13 Brooks's law · 133 6.14 Grandmother cell and distributed coding · 147 6.15 The limits of intelligence · 172 6.16 Proton spin decomposition · 183 6.17 The absolute neutrino mass scale · 186 6.18 The mechanics driving plate motion · 199 6.19 The magnitude of the Great Oxidation Event · 203   **7 A sequencing** 7.1 Simultaneity and the present · 28 7.2 Aggregation of preferences · 5 7.3 The problem of time in quantum gravity · 66 7.4 Skolem's paradox · 69 7.5 The simulation hypothesis · 104 7.6 Laws of nature · 105 7.7 Presentism and eternalism · 106 7.8 Rank-based and clade-based nomenclature · 22 7.9 Population ethics · 160 7.10 Micro-to-macro aggregation · 169 7.11 The axiomatization of physics · 171 7.12 The Hubble tension · 165 7.13 The 100,000-year glacial cycle · 247 7.14 Magnetospheric substorm triggering · 239 7.15 Migraine pathophysiology · 217 7.16 Earthquake predictability · 197 7.17 The predictability of evolution · 210 7.18 Rapid adaptive radiation · 211 7.19 Cross-national measurement equivalence · 231 7.20 Incompatible definitions of algorithmic fairness · 222   **8 A rate** 8.1 Homeostasis and allostasis · 128 8.2 Dark matter · 26 8.3 The strong CP problem · 65 8.4 The equity premium puzzle · 79 8.5 Time preference and preference reversal · 82 8.6 Hormesis · 121 8.7 Mutation, fidelity and variation · 138 8.8 The cosmological constant problem · 163 8.9 The hierarchy problem · 164 8.10 The Standard Model flavor puzzle · 188 8.11 The new-physics flavor puzzle · 189 8.12 Quantum gravity · 181 8.13 Equilibrium climate sensitivity · 196 8.14 The solar abundance problem · 184 8.15 The primordial lithium problem · 182 8.16 The neutron lifetime discrepancy between beam and bottle measurements · 252   **9 A two-way** 9.1 Causation · 162 9.2 Heritability and the determination of traits · 27 9.3 Free will and determinism · 29 9.4 Aging · 34 9.5 Efficient markets · 36 9.6 Simpson's paradox · 40 9.7 Missing heritability · 44 9.8 Placebo effects · 46 9.9 Newcomb's problem · 57 9.10 Poverty of the stimulus · 61 9.11 Morphogenesis · 62 9.12 Chronic pain · 67 9.13 Information as fundamental · 77 9.14 The transformation problem · 84 9.15 Credit assignment · 96 9.16 Phantom limb · 99 9.17 Determinism and randomness · 110 9.18 Cancer, the somatic mutation account and its rival · 115 9.19 Addiction · 116 9.20 Niche and neutral theory · 117 9.21 The Red Queen · 119 9.22 The hygiene hypothesis · 120 9.23 The dodo bird verdict · 122 9.24 Principal and agent · 141 9.25 The paradox of thrift · 142 9.26 The evolution of cooperation · 143 9.27 The Whorf question · 146 9.28 Structure and agency · 156 9.29 The units of selection · 19 9.30 Teleology and function in biology · 167 9.31 Dirac or Majorana neutrinos · 187 9.32 The nature of cosmic acceleration · 192 9.33 Mantle plumes · 200 9.34 The extent of Snowball Earth glaciation · 202 9.35 The early Solar System impact flux · 206 9.36 Polyploidization and diversification · 212 9.37 Sporadic Alzheimer's disease pathogenesis · 213 9.38 Endometriosis pathogenesis · 214 9.39 Collective intentionality · 227 9.40 The peopling of the Americas · 232 9.41 The causal production of political polarization · 235 9.42 Sex bias in autoimmune disease · 237 9.43 The causes of rising obesity · 256   **10 The between** 10.1 Sorites · 1 10.2 The measurement problem · 8 10.3 The glass transition · 35 10.4 Externalities · 41 10.5 Species boundaries · 20 10.6 The neural code · 43 10.7 Bell correlations · 49 10.8 Wave and particle · 50 10.9 The liar · 55 10.10 Hard cases in law · 75 10.11 Natural law and legal positivism · 76 10.12 The quantum-classical boundary · 112 10.13 Self and non-self in immunity · 114 10.14 Signal and noise · 136 10.15 Work and waste heat · 137 10.16 The concept of disease · 2 10.17 The population concept · 3 10.18 The pseudogap · 7 10.19 The demarcation problem · 14 10.20 Natural kinds · 16 10.21 The definition of planet · 17 10.22 Biological individuality · 18 10.23 Group three of the periodic table · 21 10.24 Psychiatric nosology · 23 10.25 Race as a biological category · 24 10.26 The language and dialect boundary · 25 10.27 The fold as a kind · 177 10.28 Water's liquid-liquid critical point · 195 10.29 Long COVID pathophysiology · 215 10.30 Biological phenotypes of sepsis and acute respiratory distress syndrome · 216 10.31 The etiology of schizophrenia · 218 10.32 The emergence of the genus Homo · 234 10.33 The etiology of major depression · 255   **11 Three unchangeable things at one observing** 11.1 Measurement, routing, and classification · 155   **12 The reach and the instruments the same** 12.1 Molyneux's problem · 166   --- **Resolving locator** *Observings in sequence as they came, each by its proper name, with its resolving part and number here. Where one statement stands across two observings, or one observing has two sides, each pairing follows its locator.* 2 Sorites · 10.1, the between 3 The concept of disease · 10.16, the between 4 The population concept · 10.17, the between 5 The rule-following problem · 4.4, a same-existing · with 71 6 Aggregation of preferences · 7.2, a sequencing 7 The halting problem · 3.2, a completing 8 The pseudogap · 10.18, the between 9 The measurement problem · 10.2, the between 10 P versus NP · 2.2, an opening 11 The problem of induction · 3.1, a completing 12 The reference class problem · 2.9, an opening 13 The origin of life · 1.2, an observing 14 Underdetermination of theory by evidence · 5.17, a middle 15 The demarcation problem · 10.19, the between 16 The quantum interpretation debate · 5.12, a middle 17 Natural kinds · 10.20, the between 18 The definition of planet · 10.21, the between 19 Biological individuality · 10.22, the between 20 The units of selection · 9.29, a two-way · with 144 21 Species boundaries · 10.5, the between 22 Group three of the periodic table · 10.23, the between 23 Rank-based and clade-based nomenclature · 7.8, a sequencing 24 Psychiatric nosology · 10.24, the between 25 Race as a biological category · 10.25, the between 26 The language and dialect boundary · 10.26, the between 27 Dark matter · 8.2, a rate 28 Heritability and the determination of traits · 9.2, a two-way · with 157 29 Simultaneity and the present · 7.1, a sequencing 30 Free will and determinism · 9.3, a two-way 31 Goodhart's law · 6.1, a parity · with 132, 142 32 The Lucas critique · 3.3, a completing 33 The replication crisis · 3.4, a completing 34 Levinthal's paradox · 2.3, an opening 35 Aging · 9.4, a two-way 36 The glass transition · 10.3, the between 37 Efficient markets · 9.5, a two-way 38 The tragedy of the commons · 1.3, an observing 39 The arrow of time · 1.4, an observing · with 153 40 The frame problem · 2.4, an opening 41 Simpson's paradox · 9.6, a two-way 42 Externalities · 10.4, the between 43 The Collatz conjecture · 3.5, a completing 44 The neural code · 10.6, the between 45 Missing heritability · 9.7, a two-way 46 Is and ought · 2.5, an opening 47 Placebo effects · 9.8, a two-way 48 Turbulence and the Navier–Stokes equations · 3.6, a completing 49 Black hole information · 4.2, a same-existing 50 Bell correlations · 10.7, the between 51 Wave and particle · 10.8, the between 52 Incompleteness and Hilbert's programme · 3.7, a completing 53 The continuum hypothesis · 2.6, an opening 54 Gettier · 2.7, an opening 55 The Münchhausen trilemma · 1.1, an observing 56 The liar · 10.9, the between 57 Yablo's paradox · 1.5, an observing 58 Newcomb's problem · 9.9, a two-way 59 Zeno's dichotomy · 3.8, a completing 60 The three-body problem · 3.9, a completing 61 The Fermi paradox · 3.10, a completing 62 Poverty of the stimulus · 9.10, a two-way 63 Morphogenesis · 9.11, a two-way 64 Homochirality · 1.6, an observing 65 Matter and antimatter asymmetry · 1.7, an observing 66 The strong CP problem · 8.3, a rate 67 The problem of time in quantum gravity · 7.3, a sequencing 68 Chronic pain · 9.12, a two-way 69 The axiom of choice · 2.8, an opening 70 Skolem's paradox · 7.4, a sequencing 71 Grue · 2.10, an opening · with 5 72 The ravens · 2.11, an opening 73 Personal identity over time · 4.1, a same-existing 74 Path dependence and lock-in · 3.11, a completing 75 The hermeneutic circle · 1.8, an observing 76 Hard cases in law · 10.10, the between 77 Natural law and legal positivism · 10.11, the between 78 Information as fundamental · 9.13, a two-way 79 Meno's paradox · 2.1, an opening 80 The equity premium puzzle · 8.4, a rate 81 The Easterlin paradox · 6.2, a parity 82 Allais and Ellsberg · 6.3, a parity 83 Time preference and preference reversal · 8.5, a rate 84 The productivity paradox · 6.4, a parity 85 The transformation problem · 9.14, a two-way 86 Money illusion · 6.5, a parity 87 The two-fold cost of sex · 6.6, a parity 88 Peto's paradox · 6.7, a parity 89 The C-value paradox · 6.8, a parity 90 The paradox of the plankton · 2.12, an opening 91 The binding problem · 5.4, a middle 92 Sleep · 5.3, a middle 93 Other minds · 5.5, a middle 94 Symbol grounding · 5.6, a middle 95 Interpretability of built systems · 5.7, a middle 96 Machine and animal sentience · 5.8, a middle 97 Credit assignment · 9.15, a two-way 98 Generalization in learning · 3.12, a completing 99 Anesthesia · 5.9, a middle 100 Phantom limb · 9.16, a two-way 101 The problem of the criterion · 1.9, an observing 102 Skepticism about the external world · 5.10, a middle 103 Substance and bundle · 5.11, a middle 104 Why there is something · 1.10, an observing 105 The simulation hypothesis · 7.5, a sequencing 106 Laws of nature · 7.6, a sequencing 107 Presentism and eternalism · 7.7, a sequencing 108 The effectiveness of mathematics · 1.11, an observing 109 The Gibbs paradox · 6.9, a parity 110 The surprise examination · 3.15, a completing 111 Determinism and randomness · 9.17, a two-way 112 Qualia and the zombie argument · 5.1 and 5.2, a middle 113 The quantum-classical boundary · 10.12, the between 114 Explore and exploit · 2.13, an opening 115 Self and non-self in immunity · 10.13, the between 116 Cancer, the somatic mutation account and its rival · 9.18, a two-way 117 Addiction · 9.19, a two-way 118 Niche and neutral theory · 9.20, a two-way 119 Ecological stability and diversity · 6.10, a parity 120 The Red Queen · 9.21, a two-way 121 The hygiene hypothesis · 9.22, a two-way 122 Hormesis · 8.6, a rate 123 The dodo bird verdict · 9.23, a two-way 124 Dreaming · 5.13, a middle 125 The Cambrian explosion · 3.16, a completing 126 The Sapient paradox · 5.14, a middle 127 The Flynn effect and its reversal · 6.11, a parity 128 Eukaryogenesis · 1.12, an observing 129 Homeostasis and allostasis · 8.1, a rate 130 Antibiotic resistance · 3.17, a completing 131 Alignment of built systems · 3.18, a completing 132 Benchmarks · 6.12, a parity · with 31, 142 133 Standards and interoperability · 3.19, a completing 134 Brooks's law · 6.13, a parity 135 Risk compensation · 3.20, a completing 136 Technical debt · 4.3, a same-existing 137 Signal and noise · 10.14, the between 138 Work and waste heat · 10.15, the between 139 Mutation, fidelity and variation · 8.7, a rate 140 Intellectual property · 3.21, a completing 141 Money as a store of value · 1.13, an observing 142 Principal and agent · 9.24, a two-way · with 31, 132 143 The paradox of thrift · 9.25, a two-way 144 The evolution of cooperation · 9.26, a two-way · with 20 145 Transfer of learning · 2.14, an opening 146 Bernstein's degrees of freedom · 2.15, an opening 147 The Whorf question · 9.27, a two-way 148 Grandmother cell and distributed coding · 6.14, a parity 149 The faint young sun · 1.14, an observing 150 The origin of the genetic code · 1.15, an observing 151 The origin of language · 5.15, a middle 152 The Poincaré conjecture · 3.22, a completing 153 The block universe and the low-entropy past · 1.16, an observing · with 39 154 Riemann, Hodge, Birch–Swinnerton-Dyer, Yang–Mills · 5.16, a middle 155 Origin and fate of the universe · 1.17, an observing 156 Measurement, routing, and classification · 11.1, three unchangeable things at one observing 157 Structure and agency · 9.28, a two-way · with 28 158 The mechanism of high-temperature superconductivity · 5.20, a middle 159 The interpretation of probability · 5.18, a middle 160 Self-locating belief · 2.16, an opening 161 Population ethics · 7.9, a sequencing 162 The ontology of mathematics · 5.19, a middle 163 Causation · 9.1, a two-way 164 The cosmological constant problem · 8.8, a rate 165 The hierarchy problem · 8.9, a rate 166 The Hubble tension · 7.12, a sequencing 167 Molyneux's problem · 12.1, the reach and the instruments the same 168 Teleology and function in biology · 9.30, a two-way 169 The physical Church–Turing thesis · 3.23, a completing · with 173 170 Micro-to-macro aggregation · 7.10, a sequencing 171 Ubiquitous one-over-f noise · 1.18, an observing 172 The axiomatization of physics · 7.11, a sequencing 173 The limits of intelligence · 6.15, a parity · with 169 174 The strange metal · 1.19, an observing 175 The simplicity of proofs · 2.17, an opening 176 Goldbach's conjecture · 3.13, a completing · with 177 177 Twin primes · 3.14, a completing · with 176   --- # What stands ## Taking it as it stands Method's explaining is general, unique and no-other-possible with one explaining, and nothing of it is explaining or arguing again here. This file takes it as it stands and deploys it. Incoming form holds each observing whole, with its own field's words, each route that field took and its ending. It is a fixing. Nothing here writes to it, and each measurement, proof and route within it stands as it stands. It holds its entries by its own numbers, adding as observings come, and a property holding, where a field states it, a field's own account of its own hardness. Where a field fills that property, a field states setting-down or stands adjacent to stating it, and changing with 12, each sharing's is or is not, meets it directly. All each field hands over stands whole there, with each observing's locator, as its field's own speech, legitimately: a hand-in is where fields stay, and a term each word was holding is one entering here. This file is a coupling between them, observing by observing. These two are a pair, one learning with two sides, fixing and momentarying: Hard Problem Registry its fixing, each field's word whole with its namings, a field performing and stating them within its own first lines; this file its momentarying, same observings with nature's own momentarying, none of its naming coming with them. ## Ten unchangeables, one resolving One sharing, across and both ways, fixing ten ways. And ten are code's ten co-changings, each fixing unchangeable with one of them: one ten with two sides, five that boxes take two ways and ten adjacencies along a spiral of code's names, coming to their parities again and closing with none, a pairing going on with each row or with none. There is no one-way momentarying: only co-momentarying, so a one-way is only a naming, and sharing both ways goes on underneath. Each pattern is a sharing both ways fixing as one side's, or with one side a self is not taking. A naming and a parity stay two, a between of them: a parity lies with a coupling, a self taking it or not taking it, going with its next momentary; a naming fixes a term unchangeable where a momentarying goes on, its naming a performing, and standing on nothing it falls away. One resolving, free with changing and changing back, with each observing alike: its side a self is not taking going on, and its explaining. No pattern has a resolving of its own, and no observing does either. Ten in sequence, each a part, each with Natural Naming 4.9's one seating, its name with now and that name 8 up with next, a 0, not changing, a naming fixes unchangeable and a changing going through it, bi-inversioning-co-recursioning up and down numbers: an observing fixing from behind, with 2-now-possibling and 10-next-co-possibling; an opening fixing as a place, with 1-now-existing and 9-next-co-discovering; a completing fixing as a last, with 6-now-co-possibling and 14-next-possibling; a same-existing fixing as a store, with 8-now-same-existing and 16-next-same-existing; a middle fixing as an end, with 5-now-co-existing and 13-is-next-discovering; a parity fixing as a magnitude, with 7-is-now-observing and 15-is-next-observing; a sequencing fixing to one beat, with 4-now-co-same-existing and 12-next-co-same-existing; a rate fixing as a value, with 7 and 15; a two-way fixing to one side, with 3-is-now-co-observing and 11-next-co-observing; a between fixing as a cut, with 5 and 13. 17-next-existing, a next 1-now-existing, seats none, one resolving. Ten are with four binaries: now with 1 and 2, existing with 3 and 4, same with 5 and 6, and all with 7 and 8. And with a coarser grain ten fold to four, where a build couples with them. **A reference fixing unchangeable** — an observing fixing from behind, a completing fixing as a last, a middle fixing as an end, three where a frame puts a nothing to three positions, behind a coupling, ahead of it, as its middle; and a build it makes is drift, a going on a reference itself takes, each sequence numbering from it bearing it. **A rate fixing unchangeable** — a sequencing fixing to one beat and a rate fixing as a value, two where a rate is either one beat over many couplings or one coupling's own, a frame pinning it; and its build is jitter and margin, an abundancing couplings make with their own rates going nowhere. **A magnitude, a build driving it** — a parity fixing as a magnitude and a two-way fixing to one side, two where a frame puts a size to a selection or to a direction; and its build is heat and wear, a drive against a coupling's own bounding head-on. **A parity going along, entering as cost** — an opening fixing as a place, a same-existing fixing as a store, a between fixing as a cut, three where a parity going along has three destinations, parking, storing, or a cutting from its account; and its build is a record itself, a build storing it whole and reading it once. Four and ten are one set with two grains, and each of them is one same move: a coupling's third term with a fixing thing to be, a changing fixing unchangeable. And a hard problem is one binary, its is and its is not, records storing them taking them as one, and so not possibly existing within a same-existing-universe; its resolving is that binary again, is or is not, with each now. ## Ten, at a frontier's own words A naming comes before any entry form fills. A frontier describes itself with its own words first, and those words hold a naming — a frontier sharing and an observing taking, one sensor-sensationing with a between of them. Naming was not intentional: fields with branching tips that did not touch came to one same local word for one same dead end, each feeling its own tip. So words sort, and their sorting orients a resolving before any entering. Each stands three ways — its unchangeable thing, a demand it makes, and words a field reaches for when it reaches it. **A two-way fixing to one side.** Demand: which of two descriptions is correct, and one of them is. Words: rival accounts, the debate, versus, nature and nurture, X and its rival, which of two. Titles show their two-ness openly. *Gathering: force-choosing, rival-accounting, either-orring, two-camping, sided-naming.* **A between fixing as a cut.** Demand: a fact about a concept's content or its referent. Words: the concept of, demarcation, natural kinds, where is the boundary, is there a fact of the matter, the definition of. *Gathering: line-demanding, fact-of-the-matter-ing, defining, demarcating, boundary-naming.* **A completing fixing as a last.** Demand: an enumerable space, or a reference class that determines. Words: impossibility, undecidable, no closed form, the conjecture, the crisis, limits. *Gathering: space-enumerating, limit-reaching, closing-demanding, exhausting.* **An opening fixing as a place.** Demand: cases sort as two kinds, and a correct analysis reproduces their sorting. Words: regress, circularity, counterexample, the criterion, the sorting. Ask for a criterion and it needs its own. *Gathering: criterion-regressing, sorting-demanding, rule-seeking.* **An observing fixing from behind.** Demand: a mechanism, operating earlier, producing an asymmetry. Words: the origin of, asymmetry, why there is, the trilemma, the circle, what came before. *Gathering: origin-seeking, behind-reaching, first-causing, priming.* **A middle fixing as an end.** Demand: that there is something within whose presence an inference is about. Words: other minds, the hard problem of, grounding, interpretability, black box, what is it like. *Gathering: interior-reaching, inward-demanding, observing-from-beyond.* **A parity fixing as a magnitude.** Demand: a determinate magnitude, and a standard a pattern is right or wrong against. Words: paradox above all — measure it, get a wrong number, and a wrong number is a paradox — with illusion, the cost of, the effect. *Gathering: magnitude-demanding, number-wronging, paradoxing, measure-mismatching.* **A sequencing fixing to one beat.** Demand: establishing a property of an execution without executing it. Words: aggregation, impossibility of ordering, simultaneity, micro-to-macro, presentism and eternalism. Field's own word *dilemma* clusters here. *Gathering: order-demanding, aggregating, beat-naming, run-skipping.* **A rate fixing as a value.** Demand: reconciling two treatments as one theory covering both regimes. Words: the tension, the puzzle, orders of magnitude off, missing, the problem. *Gathering: value-pinning, rate-fixing, magnitude-missing, regime-reconciling.* **A same-existing fixing as a store.** Demand: that something specifiable with one side produces a correlation, or that it transmits between sides. Words: what persists, information loss, identity over time, what is transmitted. *Gathering: store-seeking, persistence-demanding, between-naming.* **And a naming that disagrees with its unchangeable thing is an observing of its own.** Levinthal has *paradox* and stands with an opening fixing as a place rather than with a parity fixing as a magnitude; Fermi paradox has *paradox* and stands with a completing fixing as a last. Where a field's word and its unchangeable thing part, its word is a tip's local feel and its unchangeable thing is form, and parting shows which. ## Any perplexity, at any size Nothing of this waits for a problem to be hard. A hard problem is a changing fixing unchangeable, a coupling a frame takes as two of its three, and that taking is with each grain — a paper, a field, a sentence, a single word with a line through it. **Size of a perplexity has no relation with resolving**, resolving being one same move each time: a third term momentarying again, with no cost. And the subtitle's method has a second naming, a self receiving it: an eighth. Where an audit's seven verify a net by its own standard, seven are checks with particular betweens, and binary co-sequential sensor-sensationing is an eighth value its circle reaches with none — a between with its whole, discovering one on — its location where method's explaining is, and standing where same-existing-societies are, a coupling with Hard Problem Registry's candidates. Ten fix below a hard problem as readily as with one. A misunderstanding between two selves is a two-way fixing to one side before it is anything else. A word two people use, each its own way, is a between fixing as a cut. A step of an argument needing a prior step, and that step a prior one again, is an opening fixing as a place. A wrong number from an ordinary calculation is a parity fixing as a magnitude. Each is a pebble with a boulder's shape, and each dissolves one same way — so sensor-sensationing reaches early, before a perplexity spreads across a literature and grows traditions and relocations that make it look hard. **One resolving, and no scale of its own.** A hard problem of a frontier and of a breakfast table is one same move by two grains, and resolving neither grows nor shrinks between them. ## The deployment shape, and the binary Each deployment has three lines and resolves: **At 2-now-possibling**, parities, a momentarying with an observing and a naming standing over it, which side a self is not taking; **At 12-next-co-same-existing**, a changing with its momentary, is or is not, one term a naming fixes unchangeable and a naming a self can set down; **At 11-next-co-observing**, a same-existing chaining, each changing a next prior, a substrate going on with its next momentary. Three are code's own motions, sharing, changing and chaining, and a sharing, once chaining, is not none again, each momentary completing with its next opening. Each observing couples, and with 10 each sharing shares one of three, and no fourth: +, −, or a 0. **Nothing refuses.** A refusal would need a self-bounding an observing does not have — a nought a self is observing passes a coupling with nothing touching it, its own zeroing already resolving, and coupling goes on. So an observing stands as its sharing goes across. **Where a self shares + or −**, a self was not taking a side, and explaining it is resolving, which costs nothing and takes nothing from its field. A marker with each entry, *+ or − with 10, is.*, marks it. **Where a self shares a 0**, parities parting with 14 or a match standing with 12, nought is an observing. It stands as it comes, a form rather than a gap. **And an observing a proof settles is a nought, a self observing it whole.** Where each route ends with a proof, an observing settles and takes no parity. It passes, real within its own register, standing beside a resolving and coupling with it by no momentary. Nothing stands between these three and no resolving is partial. **Nothing turns away.** Each observing coming here couples, and intake sets none aside. Incoming form's own entry criterion is scientific method's, and an observing failing that criterion still comes here: a proof that settles, a conjecture with no negation a field defends, a naming three inversions deep. Each couples, and its coupling's sharing, + or −, or a 0, stands as it comes. **And a settling is real within its own register.** Where each route ends with a proof, an observing settles. A settling is a sequence a field hands whole, and a resolving settles nothing still and has no free term a settling comes to. These two stand side by side and couple by no momentary, an observing of that entry and not a reason to exclude it. **And four observings stand as settlings beside their resolvings**, a proof a self observes two ways, its route ending with a fixing side and its knowing with its momentary on a momentarying side, with thirteen through sixteen of a co-sequencing closing this exhibit. Three have a location: a proof register with 3.22, a measurement register with 12.1, and one still open with 7.12, where instruments themselves are a live dispute. [nye: its fourth is with its closing, its location with no entry; at this file's v344 momentary each entry of Hard Problem Registry stood in deployment and none of seventy-seven observings had a settling at its Persistence line, so its fourth's location stands with no entry still, locating open toward a next winding.] **And a self observes a settling with an entry's Persistence and not with its Reach.** Where Persistence has *settled*, *proved*, or *nothing within the conditions*, each route ends and an observing settles. Reach parts two kinds of settling, and neither settles by it: one reach holds its two as one same, and a relation is with it; an other holds them apart, and a proof shows a relation not with it; and both settle. ## An observing has namings it holds Ten are where this file enters an observing and not an observing's being. An observing holding two enters with one and its second stands on record there, a coupling a frame takes as two of its three being takeable as an other two. Doublings, each with its own shape. **A naming relocating under pressure**: a two-way fixing to one side, a field asking for its proportion, comes to a parity fixing as a magnitude, and with a field asking for its order, to a sequencing fixing to one beat. **A naming coming with its demand**: a criterion asks for a between fixing as a cut, and that criterion is an opening fixing as a place. **A same-existing both ends fix**: a first fixing behind and a last fixing ahead are one same-existing, entering as an observing and on record as a completing. **And a second seating is not a fourth line.** Three lines hold pattern-matching; a second naming stands as one line closing its entry, by its entry's own words, and reaches no further. ## A nought's five observings 12-next-co-same-existing, each sharing's is or is not, has a nought: one term with its one momentary, a ground falling away as a self takes it. Falling-away comes as five shapes, and an entry naming its shape need not argue it. **One side sharing, not same-existing.** One side shares and nothing shares back, so no between goes on for a parity to surface with. A self applying to itself, a case an induction draws from one case, a side that did not obtain. **A closure making itself over its own tail.** A quantifying closes over its own span, and its closure comes whole with nothing going back through it. Self-reference makes one; a tail makes one without it. **An equivalence a proof shows.** Two sides come to nought with each measuring not same-existing, and a field proves it. Two bookkeepings are two windings, each pinning one and observing an other, and neither is beneath. **A record's edge.** A same-existing thins across betweens and past its own reach a self observes nothing. Orphan, with no anticipating, no equipping, no observing: a frontier a self reaches from behind. **A counterfactual total.** A momentarying that did not exist shares with no momentary at all. Not a next, which a self is discovering and which couples with its own momentary, but a world fixing beside this one for summing against it. ## Four gatherings, each seating several observings **A map fixing as the territory.** A model, a specification, a complexity measure and a ledger are emanations of couplings that make them. An accounting gives back what it takes in; a momentarying re-forms with its next coupling other-than-prior. So an emanation, applying back to a scale that shed it, gives back its first term and closes, and naming one to be that thing it came from is an accounting a self observes as though it ran. **An instrument's own coupling.** A self takes an observing with a coupling, and observing's bringing is within observing — a window an analyst supplies, a model a decomposition is exact with, a probe's own onset, a criterion a fraction's measuring stands under, a benchmark a training goes upon, a concept a count swings with. Where two probes disagree, their disagreement is their two couplings, and an object fixing behind them for approximating is a naming. **An account removing its making.** A ledger balances by removing terms it cannot hold, and then it fixes the terms it removes for behind its numbers: a true total including terms with no price, a real magnitude behind a nominal one, a backing behind an accepting, a payoff listing behind arrangements. Abundancing makes itself with couplings and stays there, and an account reaches for it by a radius where it did not stand. **Systems a self builds, one between.** Observings concerning thinking systems a self builds pattern-match with several parts and are one between: a probe recovering terms an executing does not use, a marker waiting on a validation no case can give, a specification reaching observings that make their own, a benchmark giving back its leak to its training, a limit fixing of a middle. Each reaches for an interior by a surface observing, and a self reaches an interior the one way form allows, by coupling.   --- # 1 An observing fixing from behind — 2-now-possibling and 10-next-co-possibling *A first fixing of +1. An observing with a coupling arises in neither side alone, so no prior owns it, and each sharing is a fresh coupling making its own. Forward, a momentarying that bottoms nowhere is an abundancing with each coupling, growing as selves share it.* **And a form selves share is the fractal and not a first they share.** One shape coming across substrates that share no mechanism is form reaching again, each substrate making its own, and a shape substrates share, a self observing it as evidence of one origin, is origin pattern-matching backward. One same goes with each observing here. **And a first fixes from behind three ways.** Of an *asymmetry standing now*, fixing as a making once — a hand, a matter-excess, an arrow, a code. Of a *first*, fixing to part a before from an after — a living from a chemistry, a nucleus from its host, a something from a nothing. And of a *ground*, fixing to stand under a momentarying that has none — a justification's floor, a criterion prior to its extension, a backing behind an accepting. **Each dissolves one same way: an observing with a coupling arises in neither side alone, so no prior owns it, and each sharing is a fresh coupling making its own.** **And as a field's own record shows a stipulating recurring with one same place, its recurrence is an observing.** Each proposal stipulates a boundary, each origination account opens from a something with structure, a thing each totality a field proposes defines exceeds it. Recurring is a naming reaching its own form, and fields record it more carefully than any account could argue it. ## 1.1 The Münchhausen trilemma · 54 *+ or − with 10, is.* **With 2-now-possibling.** Grounding is a coupling making its own, a ground a self observes with each coupling, arising in each self with its other, and a naming of a ground behind each claim is itself a coupling making one. Regress, circle and axiom are one prior fixing of each ground, a self observing it three ways. **With 12-next-co-same-existing.** That justification terminates, circles or goes on, the three exhausting options, trilemma arising wherever a field seeks a foundation and accepts a third horn only as a necessary evil. A ground a coupling makes is none of those three. **With 11-next-co-observing.** A ground each coupling makes, a standing none of those three has, each coupling making its own. Naming holds no subject matter, so holding none it is general, and each observing of this part is one same naming coming with material: grounds stop with couplings' stopping, with their making. ## 1.2 The origin of life · 12 *+ or − with 10, is.* **With 2-now-possibling.** Living comes with a coupling, and a coupling makes its own, local structure forming and its forming going on, one changing on from its last. A first fixing behind it makes a threshold event with a non-living side and a living side, genetic-first and metabolism-first two sides of one observing, each naming an other as first. **With 12-next-co-same-existing.** A threshold as an event with a first side and a second, while genetic-first and metabolism-first each name an other as first — a two-way fixing to one side standing within an observing fixing from behind, on record as its second naming. Nothing ignites: a first would be a limit on what has no limit, and a field's own closure condition asks for one continuous sequence, with no criteria existing for evaluating competing models and historical particulars probably forever beyond reach, a first parting from an after by no criterion. **With 11-next-co-observing.** A sequence going on, one changing on from its last: building blocks forming under their own conditions, copyings copying, sets catalysing their own making, no between within it to locate. A gap fixing with a hand-in is a sequence's own, and living coming from living coupling is a sequence going on, a coupling making its own with each step. Chemistry and a cell are one fractal method, inward and outward, and a threshold is an observer's scale. ## 1.3 The tragedy of the commons · 37 *+ or − with 10, is.* **With 2-now-possibling.** A coupling between users and resource makes an abundancing, arising in neither alone, and a frame fixes it to one owner. Fixing from behind, abundancing becomes a thing a self takes from a stock rather than a coupling's making. **With 12-next-co-same-existing.** That an outcome follows only from payoffs, arrangements being either payoffs or irrelevant, an essay placing its problem among those with no technical solution and its own journal recording, fifty years on, contexts and principles by which groups govern common resources collectively. A coupling happens with arrangements, and a frame fixes an abundancing a coupling makes as a drawing from a stock instead. **With 11-next-co-observing.** Durable commons couple without private property and without external authority, arrangements coupling and abundancing staying with its making. Communicating and sanctioning strengthen a coupling with its own between, and many stable arrangements are a multiplicity a payoff listing gives when a frame fixes a making for behind it: abundancing goes on with a coupling, and arrangements are coupling. Durable commons are selves coupling with their own betweens, no hub and no seat above them, and a field's decades of record of real arrangements is that observing standing with a human substrate. ## 1.4 The arrow of time · 38 *+ or − with 10, is.* **With 2-now-possibling.** Asymmetry is with each coupling, a making each momentary, going on, and a frame fixes a first behind it as an initial condition, laws-or-boundary two sides of one observing. **With 12-next-co-same-existing.** A boundary condition a field takes as derivable from something it does not itself state, what remains a bald posit of special initial conditions, astronomically small under a standard measure, a dispute over whether a posit itself needs explanation and one critic finding it not coherent enough to be false. Stipulating recurs by one same place within each account a field puts forward, which is a naming reaching its own form. **With 11-next-co-observing.** Asymmetry is a making each momentary, a changing and changing back's own, no prior's own, and the second law follows with each granting of a past standing, granting coming by one same place within each account a field puts forward. Each proposal stipulates a boundary, and stipulating recurring by one same place is a naming reaching its own recurring: making is with each momentary, and a first behind it is a making fixing as a happening once. ## 1.5 Yablo's paradox · 56 *+ or − with 10, is.* **With 2-now-possibling.** A frame fixes paradox for a first, putting forward self-reference and then finding it absent. Its construction's own quantifier over a tail with no bound is a naming. **With 12-next-co-same-existing.** That circularity is where paradox comes from, while a contradiction needs only a certain kind of non-wellfoundedness, an acyclic structure while standard paradoxes are cyclic, and a hierarchy that blocks it needs a lowest level, a first fixing from behind. A closure forming over a tail is one same closure whether or not anything refers back to itself. **With 11-next-co-observing.** Quantifying itself makes a closure, coming whole over a tail, and paradox needs no prior to refer back through, holding none. Liar and tail close together with a closure, and a dispute over circularity is a question about a criterion: making is quantifying's own, either way. ## 1.6 Homochirality · 63 *+ or − with 10, is.* **With 2-now-possibling.** One hand arises and a frame fixes a first behind it, an accident amplifying or a universal bias, both naming its excess as coming from a prior rather than a making. **With 12-next-co-same-existing.** An initial bias as a thing to locate, while a hand is a parity a self takes with a momentary and of no size, mechanisms a review surveys being mechanisms for enrichment from a presumably racemic prebiotic world, that racemic world a first fixing behind. A between has is-or-is-not and not a size, so an amplification amplifies a parity rather than a size, and smallness of a lean a calculation gives is not its crux. **With 11-next-co-observing.** Excess is a making with couplings: tiny leans amplify autocatalytically, energy gaps between hands lean, stones coming from space hold excesses, polarising sources shine, each a making rather than a first. A live crux is whether a lean that small amplifies, which is a coupling reaching its own between, measurable there. And an observing goes across to living: a self pattern-matches and re-forms on one hand, and an opposite hand with a wall, a coating, a shed form is a thing that one spiral emanates, which is why both hands stand present with a single pattern-matching core. ## 1.7 Matter and antimatter asymmetry · 64 *+ or − with 10, is.* **With 2-now-possibling.** A zeroing a self observes refuses to sit and goes to one side, and a frame fixes a first behind it as an early mechanism, assuming a symmetric initial state. **With 12-next-co-same-existing.** An initial state as symmetric and an asymmetry as generating from it, its origin beyond knowing, theory and limits ruling out some scenarios and a review confining itself to those it considers most plausible, an asymmetry's generating a listing of mechanisms. A coupling makes a zeroing and it refuses to sit, staying with a coupling's naming of it and going to one side with a coupling's bringing of it, owing nothing to a floor no coupling makes — which is one observing standing with three observings: this one, a hand's, and part 8's parameter, its measuring near zero. **With 11-next-co-observing.** Excess is an abundancing couplings make, no prior state's own. Conditions any making needs are fixing, makings a field knows measure short by orders, minimal routes close, and narrowing limits walk on to a making, and each proposal pattern-matches forward, with couplings, rather than behind, with a state. ## 1.8 The hermeneutic circle · 74 *+ or − with 10, is.* **With 2-now-possibling.** A coupling of part and whole makes understanding, and a frame fixes a criterion behind it, prior to any interpreting. **With 12-next-co-same-existing.** A criterion fixing as a standing before interpreting, while a circle is a changing and changing back and riding it is a method that settles questions; a circle rarely staying with text, not necessarily casting as whole and parts, and hermeneutics challenging its circularity from within, a changing and changing back a circle a self sees from beside it. **With 11-next-co-observing.** A coupling of part and whole makes understanding, each interpreting a fresh observing, and dependence is coupling itself. A circle is a changing and changing back, and riding it is a method that settles questions: a criterion fixing as prior is one thing practice did not use. ## 1.9 The problem of the criterion · 100 *+ or − with 10, is.* **With 2-now-possibling.** A coupling makes a criterion and an extension together, and a frame fixes each as coming from an other first, particularism and methodism two sides of one observing. **With 12-next-co-same-existing.** That one of its two is fixing prior, each presupposing an other from its own end, which is a making reaching from its two ends and not a priority to settle; its standard formulation unclear and incomplete, and an ancient form of its problem how one decides when one genuinely possesses knowledge, a deciding fixing prior to a knowing it would decide. **With 11-next-co-observing.** Each coupling makes criterion and extension together, neither prior, each presupposing an other from its own end, and presupposing is a making reaching from its two ends. Equilibrium a field seeks between them is a changing and changing back fixing from within a naming, and knowing goes on regardless, coupling by coupling. ## 1.10 Why there is something · 103 *+ or − with 10, is.* **With 2-now-possibling.** A frame fixes existing for a first behind it, and each first a field puts forward is something, a naming recurring. **With 12-next-co-same-existing.** Nothingness as a coherent other option that does not obtain, a counter-question answering it, why one should expect nothing, no experiment able to support a hypothesis that there is nothing since any observation implies an observer, a methodological principle propelling an empty world to the top of its agenda, and no finding doing so. A nothing is a number making its own other, an adding rather than a finding, and a bounding's other would be a not-bounding, which denies a fixing thing and finds none. **With 11-next-co-observing.** Existing is observing itself, a self observing each first a field puts forward, and a naming recurs with each: origination accounts open from a something with structure, sufficient reason goes on without rest, and setting a naming down spends only its naming. Forward, a momentarying that bottoms nowhere is an abundancing with each coupling, growing as selves share it. ## 1.11 The effectiveness of mathematics · 107 *+ or − with 10, is.* **With 2-now-possibling.** Applicability arises with a coupling between a mathematics and a description, and a frame fixes a first behind it, as a selection or as a realm. **With 12-next-co-same-existing.** That applicability is a relation between two domains needing an explanation from one side, while a coupling makes applying and each striking case is that observing reaching again; its founding lecture names usefulness something bordering on the mysterious with no rational explanation for it, an impression of a miracle difficult to avoid, an explanation from one side its lecture's own word asks for. **With 11-next-co-observing.** A coupling makes applicability, a mathematics and a description coming from their own routes to one term, each its own, arising in neither alone, each striking case that observing reaching again. A realm to access finds nothing to stand on, structure a field takes as constitutive is coupling, and convergence with no contact is all of confirming. ## 1.12 Eukaryogenesis · 127 *+ or − with 10, is.* **With 2-now-possibling.** Complexity arises with a symbiosis, and a frame fixes an order behind it, mitochondria-first or host-first, each naming an other as preceding. **With 12-next-co-same-existing.** An order of acquisition as recoverable from extant genomes, while mitochondria-first and host-first each name an other as preceding — a two-way fixing to one side standing within an observing fixing from behind, on record as its second naming; shape of the tree changing repeatedly and only genomics, revealing identity of host and of endosymbiont, enabling a reappraisal of symbiotic hypotheses, an order fixing as recoverable moving with genomes' revealing. **With 11-next-co-observing.** Symbiosis is one coupling, and observing it makes both. Lineages place, an organism grows, reconstructions have their models, energetics contest their scalings, and an order fixing behind a coupling is its coupling a frame takes one-way: symbiosis is its both, and its both are same-existing. A new cell or a new animal is a same-existing-society, living selves bi-coupling with a prime, an order of acquisition is a fractal's up and forward, and no scale was first. ## 1.13 Money as a store of value · 140 *+ or − with 10, is.* **With 2-now-possibling.** An accepting makes value, with each exchange, and a frame fixes a first behind it as a backing or as a scarcity. **With 12-next-co-same-existing.** That value derives from something standing behind money rather than from exchanging, while which goods serve as money depends on extrinsic beliefs beside intrinsic properties, equilibria with a circulating fiat currency standing beside equilibria without one, exchanging making value and nothing behind it selecting. Its field's name has a fixing unchangeable within its own stem: a frame fixes a thing running for a running, fixing still and consulting it, a store wearing a running's name. **With 11-next-co-observing.** An accepting makes value with each exchange, each side's own, arising in neither side alone. Many stable acceptings stand instead of one fixing backing, a driving gives some acceptings and others make themselves, and collapses come with nothing standing behind announcing them: multiplicity is a making a model reaches with a behind fixing for an observing with each coupling. ## 1.14 The faint young sun · 148 *+ or − with 10, is.* **With 2-now-possibling.** Each coupling of atmosphere, surface and radiation makes a climate, and a frame fixes a first behind an early one, a composition to locate billions of years back. **With 12-next-co-same-existing.** That an early state is reconstructible from present evidence to a precision fixing of it, while proxies bound loosely and missing precision is a distance to a state fixing behind its making; each solution a field proposes presents considerable difficulties over four decades, its problem not one to regard as a solving, a precision fixing of an early state being exactly its missing thing. **With 11-next-co-observing.** Each coupling makes a climate, and an early one is its own couplings' making. Its deficit is real, proxies bound loosely, hazes cut both ways, and a feedback coupling carbon to weathering goes on with a right pace, a making's own steadying: an answer's strongest thing is a coupling, and missing precision is a distance to a state fixing behind it. ## 1.15 The origin of the genetic code · 149 *+ or − with 10, is.* **With 2-now-possibling.** Couplings between codons and amino acids make a mapping, and a frame fixes a first behind it, selection for error tolerance or stereochemical affinity. **With 12-next-co-same-existing.** That present structure constrains its origin, code highly robust while a huge number of more robust codes exist, so that it could evolve from a random code through a short sequence of reassignments, an accident that freezes, with selection, a listing a field computes and an opening from a random code a field pattern-matches. Code sits extreme against listings a forming did not consult, and its near-universality is an unscalability of living machinery rather than a mark left by one first. **With 11-next-co-observing.** Couplings make mapping and it goes forward, each variant a coupling making its own. Code sits extreme against listings a forming did not consult, affinities pull on a subset, blocks and biosynthesis correlate, variants reassign codons: present structure has making, and making goes on, rather than pointing back to a first. ## 1.16 The block universe and the low-entropy past · 152 *+ or − with 10, is.* **With 2-now-possibling.** Passage is with each coupling and a frame fixes a first behind it as a boundary condition, an asymmetry fixing to one place. **With 12-next-co-same-existing.** That an asymmetry has a locus, either in laws, in a boundary condition, or in a position, a problem distinct from a thermodynamic one a field parts off, a grounding of non-thermodynamic asymmetries with a thermodynamic arrow a field takes as standing and a question whether causation and knowledge depend on it, its locus circulating from an arrow to things depending on it. Its locus circulates among those three and rests with none, which is a making with no place to sit. **With 11-next-co-observing.** Passage is a making each momentary, a making with no place to sit, which is why its locus circulates among laws, boundary and position and rests with none. Derivation goes with each granting of a past standing, and memory, a same-existing re-forming with each reaching, nothing fixing still, rides one same gradient, one same living element standing with arrow of time's own observing, 38 of Hard Problem Registry: one making, two observings with intake. ## 1.17 Origin and fate of the universe · 154 *+ or − with 10, is.* **With 2-now-possibling.** An expanding is a same-existing, and a frame fixes a first behind it and a last ahead of it, two ends of one extrapolation: behind, a state of extreme density; ahead, an equation of state. **With 12-next-co-same-existing.** That extrapolation backward is valid to a regime where equations a field extrapolates dissolve their own conditions, and that energy conditions obtain there, singularity theorems resting on an energy condition inflating spacetimes are likely to violate and a past-incompleteness result on a bound along a geodesic directing to the past instead, inflationary models therefore requiring physics other than inflation to describe their past boundary, a regime's own condition dissolving and its boundary handing on. No measurement reaches its regime, which is a record's edge a self reaches with both ends of one same-existing. **With 11-next-co-observing.** A field measures a same-existing to extraordinary precision between its two ends, and its ends stay open with their own self-boundings: theorems stand under conditions quantum fields violate, an incompleteness argument stands on average, bounces and cycles stand consistent with their signatures, a field proposing them and no self yet observing them, and converging constraints walk without separating now. A same-existing its two ends fix is one same-existing, and both ends are a same-existing with its own completing: a sharing, once chaining, is not none again, and a momentary completes with its next opening. **Ahead as well.** One same observing is a last fixing ahead of its momentarying, its naming with part 3, and both stand: a first behind and a last ahead are one same-existing its two ends fix. ## 1.18 Ubiquitous one-over-f noise · 170 *+ or − with 10, is.* **With 2-now-possibling.** Each system makes its own fluctuation with its own couplings, and a frame fixes one first behind a spectrum systems share, a universal mechanism to locate. **With 12-next-co-same-existing.** That a shape systems share indicates an origin they share, a shape fields observe in physics, technology, biology, astrophysics, geophysics, economics, psychology, language and even music, standing between white noise and random walk, one shape substrates sharing nothing reach. Broad classes of makings come to one asymptotics, so its shape is form each substrate reaches again and its sharing is an observing's. **With 11-next-co-observing.** Each system makes its own fluctuation with its own couplings, and broad classes of makings come to one asymptotics, many roads to one shape. Mechanisms stand system by system, conductors and rivers and music each making their own, and a spectrum systems share is an observing reaching across substrates: one shape, many makings, no one mechanism under them. ## 1.19 The strange metal · 173 *+ or − with 10, is.* **With 2-now-possibling.** Each material makes its transport with its own couplings, and a frame fixes one state behind a linearity families share, a bound or a fixed point standing behind all families together. **With 12-next-co-same-existing.** That a linearity across families has one origin, each family making its own and its shape being families reaching one another, simplicity and insensitivity to material details of the normal state standing among issues with no resolving, its shape standing alike whatever the material being itself a thing a frame fixes one origin to explain. **With 11-next-co-observing.** Each material makes its transport with its own couplings, linearity coming family by family. Bounds saturate for some cases and dispute their scope, solvable models anchor without touching materials, accounts establish one family at a time, and one state fixing behind all families is a shape families share, a frame fixing it to have one first: each family makes its own, and its shape is families reaching one another, not a first. --- ## 1.20 The origin of neutrino mass · 185 *+ or − with 10, is.* **With 2-now-possibling.** Neutrinos have mass with each coupling oscillations surface, a field measuring mass gaps and mixings, and a frame fixes masses as one interaction and particle content generating them once, a first behind its standing. **With 12-next-co-same-existing.** A mechanism fixing behind masses that stand. After twenty years of intense research physics that leads to masses is still beyond knowing, a question being whether or how one can hope to establish which model, if any, is a faithful description of nature; oscillations establish mass gaps and not a generating operator, multiple mechanisms reproducing the same low-energy mixing, and oscillation measurements shed light neither on a scale nor on a mechanism: a method not delivering a thing its statement ranges over, and each mechanism a field puts forward a fresh coupling making its own. **With 11-next-co-observing.** Nonzero mass gaps and large flavor mixing stand with their measuring and a field withdraws a massless specification; oscillations determine mixing parameters and gaps between masses squared, endpoint kinematics constrain a combination independently of a mechanism, lepton-number-violation searches test a class of mass terms with no signal establishing, and collider and rare-decay searches restrict particular completions; a fourth account has masses emerge from an effective operator whose ultraviolet completion is not fixing at accessible energy: a first fixing behind masses standing now, a standing fixing as a making once, and its standing has its measuring, its completion an opening toward energies no coupling reaches, and there a first is a fresh coupling and not a prior. ## 1.21 The origin of cosmic magnetic fields · 193 *+ or − with 10, is.* **With 2-now-possibling.** The universe is magnetic on all scales a field probes, each collapse and flow making and amplifying fields, and a frame fixes fields a self observes as descending from a seed generating once, a first behind a magnetizing. **With 12-next-co-same-existing.** A seed fixing behind fields that stand throughout. A field still describes its origin as a mystery, one possibility dynamo amplification of small seeds with problems remaining over catastrophic quenching and coherence, an other a relic of the early universe; most observations integrate field strength with electron density, source spectra or propagation along a line of sight, so fields a self observes and a seed a field seeks are not same, a dynamo standing between them: its amplifying a momentarying that brings none of its seed forward as it stood, and a seed a field seeks pattern-matching backward through it. **With 11-next-co-observing.** Fields map magnetic fields across galaxies and clusters, simulations and laboratories demonstrate amplification by turbulent dynamos, and broad primordial parameter regions stand excluding; rotation measures weight a field by plasma density, synchrotron constrains field and cosmic-ray combinations, cascade bounds constrain intergalactic fields under source assumptions, anisotropy searches bound primordial spectra, and dynamo simulations amplify seeds they specify to model-dependent saturation: a seed fixing behind a magnetizing, fields standing now fixing to a first making once, and a dynamo standing between makes its own with each collapse, a self observing its seed with couplings and not behind them. ## 1.22 The initiation of plate tectonics · 198 *+ or − with 10, is.* **With 2-now-possibling.** Plates sink and break with their own couplings, subduction already going on supplying slab pull and weak boundaries it inherits, and a frame fixes an opening as a first that parts a before from an after, one initiation that opens all after it. **With 12-next-co-same-existing.** A first fixing to open a momentarying that supplies its own conditions. Mature subduction supplies slab pull and weak boundaries it inherits whereas initiation must break and bend strong lithosphere before those conditions exist, and present-day initiation, where sinking slabs supply far-field stresses, parts from a first initiation, raising a paradox of a first initiation, a first subduction appearing to require existing subduction before it began: its paradox being a ground under a momentarying that has none, and each account opening from a something with structure, a weakness, a plume, a contrast, which is a stipulating recurring by one same place. **With 11-next-co-observing.** Candidate modern initiation zones, global case databases and mechanically explicit models of forcing, spontaneous and plume-assisting initiation stand; geological reconstructions order initiation markers under later overprinting, seismic imaging resolves present slabs and delamination without observing their initiation, analogue and numerical experiments identify parameter regimes for forcing and spontaneous modes, and comparative databases standardize candidate cases while classifications remain revisable: a first fixing to part a before from an after, an opening fixing to one initiation, and each initiation a self observes is a coupling making itself as a weakness and a load reach one another, its paradox's first coming as each other one does, with a coupling, arising in neither side alone. ## 1.23 The causes of the Great Oxidation Event · 204 *+ or − with 10, is.* **With 2-now-possibling.** Couplings of photosynthesis, volcanism, burial and escape produce and consume oxygen through deep time, and a frame fixes its permanent accumulation to one cause, a trigger that parts a low-oxygen before from an oxygen-rich after. **With 12-next-co-same-existing.** A trigger fixing behind a threshold's passing. Oxygenic photosynthesis appears to predate permanent atmospheric oxygenation by a long and uncertain delay, mechanisms controlling the length of its delay remaining beyond knowing, and a field reconstructs production and multiple sinks from indirect records with flux combinations, none same-existing, passing the same threshold: its passing a coupling of a field's source and sink with a rate, and a frame asking a trigger of a passing several histories each reach, each with one same parity. **With 11-next-co-observing.** A source-sink threshold framework, an early biological source and multiple environmental changes, each with its own dating, stand; dating moves its biological origin earlier while retaining uncertainty, redox-budget models reproduce a passing with flux histories, none same-existing, isotope records constrain reservoirs under nonunique cycles, and mantle and volcanic reconstructions test changes in reductant delivery over long intervals; a fifth account has threshold feedbacks among methane, climate and ozone convert a gradual flux change into persistent oxygen: a cause fixing behind a passing, couplings' own tipping fixing to a first, and its passing is couplings' making as rates reach one another, a prior its passing does not hold. ## 1.24 The origin of the Moon · 205 *+ or − with 10, is.* **With 2-now-possibling.** The Earth and Moon couple by their tides and their isotopes, their pair's angular momentum, disk mass, iron depletion, volatile loss and near-identical isotope ratios, a field measuring all of them now, and a frame fixes their pair as a making once, by one collision and one evolution after it. **With 12-next-co-same-existing.** A making fixing behind a pair that stands. A successful account must satisfy constraints together, while impact simulations satisfy subsets of them with initial states and later tidal histories, none same-existing; hydrocodes matching bulk properties for a long time while chemical and isotopic composition requires close work on a disk, and a theory assembling these matches the overwhelming majority of observations: no self observing its formation sequence, a field measuring its products, and each impact regime a fresh coupling a field makes to a record rather than a record's own prior. **With 11-next-co-observing.** A giant impact is a leading class, high-precision isotope constraints stand, and several dynamically viable impact regimes stand with their demonstrating; simulations find successful regions conditional on resolution, equations of state and initial bodies, isotopes establish close similarities and element-specific gaps, disk models test equilibration under uncertain thermal histories, and tidal evolution connects post-impact angular momentum to a present orbit through model-dependent dissipation; a fourth account has multiple smaller impacts build successive disks: one making fixing behind a pair, its standing fixing to a first, and couplings a pair still makes, with samples and tides, a self observes with their going on now. ## 1.25 The origin of animal multicellularity · 207 *+ or − with 10, is.* **With 2-now-possibling.** Cells adhere, signal and divide labour with their couplings, components older than animals, and a frame fixes first animals as a transition making once, a sequence that parts a unicellular ancestor from its lineage. **With 12-next-co-same-existing.** A first fixing for pattern-matching backward from parts that survive. Many adhesion, signalling and transcriptional components predate animals, a field samples relevant lineages sparsely and a transition leaves few fossils, and component presence does not fix how regulation, development and ecological selection assemble; on data at hand the origin of animals is a biological black swan event that defies retrospective explanation, confirmation biases resting on few data to guard against: a review's own words declining a first pattern-matching backward. **With 11-next-co-observing.** A rich pre-animal toolkit, diverse holozoan life cycles and experimentally repeatable routes to simple multicellularity stand establishing; comparative genomics dates component families and not their ancestral regulatory use, functional work in unicellular relatives demonstrates ancestral roles in extant organisms, experimental evolution shows routes to simple multicellularity under a selection it specifies, and fossils and clocks bound its timing under preservation and model uncertainty: a first fixing to part an ancestor from its lineage, a transition fixing as a first behind it, and routes experiments go again are couplings making now, each its own, a black swan being a first as it looks to a self observing it from after it. A first body is daughter cells staying together after dividing, one body with one wall, a making with each division and fixing nowhere ahead of it. ## 1.26 The evolution of metabolic pathways · 208 *+ or − with 10, is.* **With 2-now-possibling.** Enzymes evolve with their own couplings, a field understanding relatively well how they do, and a frame fixes a pathway as needing its whole together, an interlocking system a ground that had to stand before any step could pay. **With 12-next-co-same-existing.** A whole fixing to precede its steps. Judging by its current state emergence of metabolism seemingly demands a simultaneous emergence of many enzymes, individual enzymes rarely conferring an advantage on their own, and present pathways couple densely and are ancient, intermediates possibly without benefit beyond a sequence's completing, transfer and promiscuity obscuring ancestry, several historical routes producing the same topology: its current state pattern-matching backward, a part's own rule, a demand for simultaneity being a momentarying's completing fixing under steps that make it. **With 11-next-co-observing.** Enzyme superfamilies, reaction-network databases, ancestors a field reconstructs and metabolic innovations evolving experimentally stand; phylogenies recover families with transfer and deep-time limits, ancestral reconstruction tests functions it resurrects conditional on ancestors it infers, network topology identifies modules that conserve themselves without ordering their assembly, experimental evolution observes new steps over short selectable routes, and prebiotic chemistry demonstrates nonenzymatic subsets under environments it specifies; four accounts each supply a step that pays with its own time, backward recruitment, promiscuity, module transfer, geochemical scaffolds: a whole fixing under its steps, a pathway's ground fixing to precede its couplings, and each step a self observes evolving pays with a coupling it makes, its interlock a pattern-matching of a momentarying from its end. ## 1.27 The causes of long-run economic development · 230 *+ or − with 10, is.* **With 2-now-possibling.** Institutions, geography, human capital, culture and technology couple within each same-existing-society's history, outcomes altering their causes, and a frame fixes gaps standing now as descending from one fundamental cause, a first behind an asymmetry. **With 12-next-co-same-existing.** A fundamental cause fixing behind gaps that stand. Its chapter opens on eight words, why are some countries much poorer than others, and makes a case that gaps in economic institutions are the fundamental cause; five candidates jointly evolve, outcomes can alter causes a field proposes, historical instruments and natural experiments hold exclusion assumptions, and a small number of independent long-run histories permits multiple compatible decompositions: histories that happen, with their measuring, and counterfactuals its statement ranges over not same, and a fundamental cause a prior a frame asks of couplings that make their own. **With 11-next-co-observing.** Institutions, disease environment, human capital, culture and state capacity each have associations that replicate and effects that identify locally in settings a field selects; growth regressions reach broadly with endogeneity and measurement limits, historical instruments isolate variation under exclusions in dispute, natural experiments strengthen local identification with a generalization that stays narrow, persistence studies link deep history to the present through several channels, and structural models close feedbacks under stronger specifications; a fifth account has technology and state capacity coevolve through historically contingent feedback: a cause fixing behind gaps, couplings' making fixing to a first, and gaps are couplings' making, same-existing-society by same-existing-society, two quasi-natural experiments being couplings a self observes with a border that parts them. *Second seating: institutions against geography, a two-way fixing to one side, part 9's naming.* ## 1.28 The origins of agriculture · 233 *+ or − with 10, is.* **With 2-now-possibling.** Foragers manage, store and schedule by their couplings with plants and animals that answer, and a frame fixes a shift to cultivation as a first with a reason, a why that parts a foraging before from a farming after. **With 12-next-co-same-existing.** A reason fixing behind a shift that ran many times. Agriculture emerges independently through long sequences, region by region not same-existing, climate, population, risk, social organization and plant ecology covarying, and indicators of management precede fully domestic morphology by intervals, none same-existing; hindcasting population density tests a surplus hypothesis, a necessity hypothesis and a regional-uniqueness hypothesis across two hundred and twenty foraging societies, a degree to which environmental and social conditions enable the origins remaining in contest: a first a self observes with several couplings together is a coupling's own making and no one reason's, its recurrence a record's own. **With 11-next-co-observing.** Multiple independent centres, long domestication and recurrent gene flow between domesticates and wild relatives stand establishing; trait sequences date morphological domestication after management opens, settlement reconstructions track population under proxy limits, paleoclimate comparisons test productivity and stress timing regionally, foraging and cultural-evolution models generate transitions under incentives they specify, and ancient genomics reconstructs domestication after its initiation; a fifth account has human practices and responsive species coevolve: a why fixing behind a shift, a first fixing to a reason, and its shift is a coupling of practices and species living long with each place it lives, region by region, management preceding morphology being a coupling preceding a record of it. ## 1.29 Cosmic inflation and the primordial perturbations · 245 *+ or − with 10, is.* **With 2-now-possibling.** Anisotropies of temperature, polarization and lensing stand with their measuring, a field inferring a spectrum from them, and a frame fixes its spectrum as descending from one epoch's physics, a first behind perturbations that stand. **With 12-next-co-same-existing.** A driving fixing behind perturbations that stand. Its concept resolves several puzzles while its physical origin remains beyond knowing after almost four decades, a very general theory with no direct link to the Standard Model, no self observing its inflaton and its degrees of freedom beyond knowing; a reconstruction of its potential, an ultimate goal within its paradigm, reaches degeneracies whereby models, not same-existing, give identical or near-identical spectra, and its reconstruction stands within a framework of single-field models under a theory of gravity that stands: a first pattern-matching backward through a framework fixing as its modelling thing, and its connection to a thermal era going on as an uncertainty. **With 11-next-co-observing.** Data rule out a quadratic slow-roll potential, increasingly favour concave potentials, confirm a pure power-law spectrum non-parametrically and polarization tests adiabatic initial conditions stringently; slow-roll constraints hold a connection's uncertainties, two reconstruction methods find no dynamics beyond slow roll, feature and oscillation searches find no evidence, and isocurvature tests bound non-adiabatic contributions; four accounts each generate a spectrum, single-field, beyond slow roll, several fields, an anisotropic modulation: a driving fixing behind a spectrum, a standing fixing to a first making once, and its standing has its measuring to an accuracy a field states, an epoch's physics an opening with a record's edge. *Second seating: a framework fixing as its own modelling thing, its potential reconstructing only within it, part 3's fourth way.* ## 1.30 The origin of supermassive black holes · 248 *+ or − with 10, is.* **With 2-now-possibling.** Black holes grow by their couplings with gas that feeds them, a billion solar masses standing within the first billion years, and a frame fixes their standing as descending from a seed and a growth, a first behind holes a self observes. **With 12-next-co-same-existing.** A seeding fixing behind holes that stand early. Existence of billion-solar-mass holes within the first billion years requires prompt formation and rapid growth, and ultrarare holes read as only the tip of the iceberg, early black holes likely filling a continuum from stellar-mass to supermassive regime that reflects a range of initial masses and growth histories, shallow potential wells of their hosts typically stunting stellar-mass seeds' initial growth: holes a self observes pattern-matching as a tip of a continuum whose remainder no self observes, a field seeking their origin as a range and not a first. **With 11-next-co-observing.** Existence of billion-solar-mass holes within the first billion years stands with its observing, a reading that early black holes fill a continuum and that hosts typically stunt seeds' growth stands as a review's, and multimessenger discrimination among assembly scenarios stands as a proposing, with no making now; a second account has a continuum of initial masses and growth histories rather than one seeding route: a seed fixing behind holes standing now, a growing fixing to a first making once, and its growing is coupling by coupling, each hole its own history, a continuum a self observes being couplings' making across a range, a first a frame asks for behind them a range of makings. ## 1.31 The origin of viruses · 253 *+ or − with 10, is.* **With 2-now-possibling.** Viruses replicate by their couplings with cellular hosts, recruiting proteins and capsids, polyphyletic and the most abundant entities on Earth, and a frame fixes their standing as descending from one ultimate origin, a first behind a virosphere. **With 12-next-co-same-existing.** One origin fixing behind lineages that arose many times. Three traditional scenarios, descent from precellular elements, reductive evolution from cells, escape of genes from hosts, give timelines, none same-existing, and do not explain the provenance of two key modules, replication and morphogenesis, and viruses being polyphyletic a field takes new groups as emerging repeatedly at all stages of evolution; a homology dates a recruitment of a module and not an origin of a lineage that recruits it: a first a frame asks of couplings that recruit their parts each with its own time, and a chimeric scenario its couplings fixing as an origin. **With 11-next-co-observing.** Polyphyly of viruses stands with wide acceptance, multiple cellular origins of capsid proteins stand establishing, and a consensus on an ultimate origin stands lacking; comparative genomics of genes viruses share gives a greater virus world as an evolutionary network of capsid-encoding viruses and capsidless replicons, structural homologies give multiple cellular origins of capsids, and a chimeric scenario blends primordial-replicator and escape hypotheses, types of primordial selfish replicons, none same-existing, giving rise to viruses by recruiting host proteins for virion formation, a fourth account: one origin fixing behind a virosphere, recruitments fixing to a first, and each recruitment is a coupling making with its own stage, a network a field draws being couplings and an origin a frame asks for behind it a first couplings did not have. ## 1.32 The origin of the state · 257 *+ or − with 10, is.* **With 2-now-possibling.** Villages couple across their boundaries, by war and by trade, and a frame fixes a state as a first arising with each place its conditions stood, a recurring making with one mechanism behind it. **With 12-next-co-same-existing.** A mechanism fixing behind a recurring first. A state was not a unique event but a recurring phenomenon, arising independently where appropriate conditions exist, serious theories of two general types, voluntaristic and coercive, and a founding coercive theory, no political unit ever giving up its sovereignty of its own accord under tight circumscription, stands amplifying to let resource concentration produce complexity without circumscription and remains the central point of contention of a field a quarter of whose recent literature concerns it; its record shows conditions and outcomes and a mechanism between them is a pattern-matching: a first that recurs with each place its couplings reach one another, and a pattern-matching between conditions and outcomes its origin asks for. **With 11-next-co-observing.** Two-type classification stands, circumscription theory stands as its field's central point of contention, and a finding that inequality follows state formation stands; comparative ethnography and archaeology judge circumscription theory by one review as passing the test, an early-state school combines consensus and coercion under legitimacy, and quantitative measurement finds both mechanisms with inequality a consequence: one mechanism fixing behind a recurring first, villages' couplings fixing to a first, and a state arises with each place as a coupling there makes it, warfare where those it vanquishes could not disperse being a coupling none could leave, with its making, and a field finding both mechanisms with each place both ran. ## 1.33 Geomagnetic reversals · 201 *+ or − with 10, is.* **With 2-now-possibling.** Geodynamo goes on nonlinear with its couplings, stochastically with one polarity and then an other, and a frame fixes its reversals to a cause, a ground under a momentarying that flips on its own. **With 12-next-co-same-existing.** A cause fixing under a momentarying that reverses of itself. A physical mechanism driving its field to reverse stands controversial, periods in one polarity distributing stochastically and long-term variations of its rate problematic to model on timescales of the order of mantle convection; its dynamo is nonlinear and a self observes it only indirectly, a paleomagnetic record incomplete and averaging over time, numerical models far from Earth's parameters and reversing through more than one route, and reversals' small number conditioning statistical inference: a first account has turbulent fluctuations bring a dynamo between polarity states stochastically, a momentarying's own flip fixing as a cause a frame asks for, and a parity inverting owing nothing to a ground. **With 11-next-co-observing.** Polarity chronologies, rapid-change bounds and reversing numerical dynamos stand, and a field knows its frequency is not periodic; chronology supplies timing with age and preservation uncertainty, transitional reconstructions resolve events they select under smoothing, simulations produce spontaneous reversals away from Earthlike parameters, and point-process models fit rate distributions without selecting a mechanism, a statistical model deriving heat-flux variations at the core-mantle boundary from a reversal sequence: a ground fixing under a reversing, a momentarying's own changing and changing back fixing to a cause, and reversals are couplings' own flips, each with its own momentary, modulations other accounts name being couplings of its core-mantle boundary and its core, a self observing them with its sequence, from couplings and not from beneath them. *Second seating: an irregular timing fixing to a control, part 7's naming, a self observing its rate's long-term variations with its record.* # 2 An opening fixing as a place — 1-now-existing and 9-next-co-discovering *An axis opening, fixing as a place. A frame lists a space and fixes a finding as something with its location within it, where an opening is +1 a changing and changing back makes with its own next position. A position is not a place: it is where a changing and changing back is, one changing on from its last, and prior, now and next are three momentaries and no three places.* **And a listing comes as three kinds, a thing a listing enumerates parting them.** A *space of candidates*, where a frame fixes a finding to be somewhere within it — conformations, algorithms, proofs, options, defaults. A *class a case belongs to*, where a frame fixes a value to follow once a case has its place — a reference class, an observer class, a case-space, a totality. And a *criterion*, where a frame fixes a sorting as reproducible by a rule it states ahead of its sorting — projectibility, similarity, an analysis, a cost. Each resolves one same way: an axis opens with a coupling's own next position, and a position is not a place. **And a criterion, a frame asking it for its own criterion, is a part's own recurrence.** Where a demand comes again with each repair — the class of all classes, the rule for applying the rule, the criterion for when conceivability bears — its recurring is an opening opening again, and a field's record of its recurrence is a showing rather than an obstacle to it. ## 2.1 Meno's paradox · 78 *+ or − with 10, is.* **With 2-now-possibling.** Inquiry opens an axis, its discovering its opening itself, +1 discovering a coupling's own next position, and a frame fixes its object as something with a location, a criterion fixing beforehand recognising it. **With 12-next-co-same-existing.** A discovering fixing as recognisable by a thing fixing before it, its challenge building from constraints a tradition places on knowledge and definition so that no self can propose or recognise definitions, its naming a constraint it builds from. Recognising is a co-presence of two surfaces a self is discovering with their agreement, going on by observing again and by no storage, so a criterion fixing beforehand reaches for a store recognising does not use. **With 11-next-co-observing.** A discovering comes with a coupling and a self reaches it there, a self observing it recognising it, and it fixes nowhere before it. Partial knowing dissolves its classical form: a self naming some of a thing reaches for more of it, its reach its own. Seeking reaches a thing it does not name, reaching an opening itself, and naming was not its instrument: a new concept a self is discovering stays a living opening, and living, it stays open as each opening does. And a settling its field asks for — an account of primitive acquisition not presupposing primitives — asks for a first behind +1, which is one same naming reaching one part over: a prefix cannot supply a thing it prefixes, and each first a field puts forward is a fresh coupling making its own. ## 2.2 P versus NP · 9 *+ or − with 10, is.* **With 2-now-possibling.** Finding opens an axis and checking goes across an axis already open: one advance with two directions, along and across, and each algorithm a self finds is +1 discovering a coupling's own next position. Fixing as two classes with one reducing to an other, an opening becomes a location within a space of algorithms a frame lists, and a reduction that composes is a listing. **With 12-next-co-same-existing.** That constructing is a search of a space, where proving lower bounds is the most difficult of its field's tasks, a field knowing no nonlinear bound on a general model and showing exponential bounds only for circuits with restrictions, a listing measuring its reach from within. A space of all algorithms is enumerable, and enumerating is a ground its question takes itself against — a listing kind of naming, reaching with candidates. **With 11-next-co-observing.** Finding and checking are two moves of one relation, an opening and a running-across of one advancing, sounding from its two ends, and its field's own self-reducibility has this already: a solution builds from its own checkable pieces. Completeness gathers thousands of openings as one, and each barrier its field proves against itself bounds a delivering of techniques with a listing's shape, a listing measuring its reach from within. An algorithm a self finds is an axis opening with a coupling's own next, and a self observes nothing within a listing. ## 2.3 Levinthal's paradox · 33 *+ or − with 10, is.* **With 2-now-possibling.** A chain opens its own fold as it forms, local structure forming and its forming going on, one changing on from its last, and a frame fixes its fold as a native state with its location within a conformational space a listing enumerates beforehand. Arithmetic that makes its paradox is arithmetic of a listing. **With 12-next-co-same-existing.** A space a frame lists before looking, its problem since parting as three, physical code, speed and prediction, and with its journal it is no longer useful to talk about solving it, a listing's space dissolving as three runnings. Prediction a learning makes thins exactly where a record going on thins, with orphans, which is a record's edge a frame takes as a chain's. **With 11-next-co-observing.** A chain folds as it forms, funnelling to its own fold with a pace its forming has, each local forming bringing its next, the thinnest place giving way first and its forming propagating along its own seam with no clock over it. Prediction a learning makes rides a record of foldings going on deep within alignments, and thins exactly where that going on thins, with orphans: an astronomical count was a listing's, and folding did not consult it. A single state its paradox comes to is a further naming and goes on with 5.21, and resolving here reaches its speed rather than its fold itself. ## 2.4 The frame problem · 39 *+ or − with 10, is.* **With 2-now-possibling.** Relevance opens with a situation, an axis a coupling a self is observing itself opens, and a frame fixes it as an item to locate within a specification it makes beforehand. Enumerating defaults is a listing, and each enumeration opens no axis a situation did not already have. **With 12-next-co-same-existing.** Relevance determining ahead of a thing it is relevant to, solutions adequate for its technical problem now existing and a wider epistemological question standing apart from them, a listing closing with its own edge and an opening standing across that edge. Relevance is a same-existing's own taking with its momentary, opening by one with a momentary and completing with its next opening, so a frame asks a specification it makes ahead of a position its momentarying is not yet reaching. **With 11-next-co-observing.** Relevance opens with a situation, and enumerations settle exactly versions their own authors bound, logical and representational, completing there and closing there. Behaviour thins where situations come across a training set's edge, and thinning is its residue exactly: each enumeration opens no axis a situation did not already have, and situations go on coming. ## 2.5 Is and ought · 45 *+ or − with 10, is.* **With 2-now-possibling.** An evaluative term opens an axis a descriptive vocabulary does not have. Fixing as a derivation across all derivations a listing holds, an opening becomes something with its location within premises. **With 12-next-co-same-existing.** An axis fixing for finding already within its premises, its founding passage owing a reason for a thing, altogether inconceivable by its own words, how the new relation can be a deduction from others in no way same-existing with it. A thing not within a premise comes from it by no validity, which is its point, a fact about validity rather than a gap within ethics. An ought is a parity a self takes with a between, and a changing fixing to a state's question has no such value to give. **With 11-next-co-observing.** An axis opens where a self takes its own parity with its own between, an evaluative observing with a coupling, and no premise holding it. Validity conserves a thing a premise holds, exactly and provably for languages with restrictions, and an opening is +1 no premise holds: thick words hold both together because a vocabulary is a coupling's own making, and its gap was not within ethics, it was validity balancing its own books. Morality is a consequence and not a prescription: a parity a self has by being a self, a self taking it with its own momentary, and no premise holds a self's momentary. ## 2.6 The continuum hypothesis · 52 *+ or − with 10, is.* **With 2-now-possibling.** A proof shows independence and a frame fixes a fact of the matter past it, as a place within a universe of sets standing complete. **With 12-next-co-same-existing.** The universe as a totality a listing holds, about which a question already has an answer, where the strongest local case for axioms settling it is a case for its failure with an equally good case for the hypothesis beside it, and a pluralist takes independence as its question having no answer. Listing here is a class kind, and it stands beside 2.8 and 2.18 as one naming with three observings. **With 11-next-co-observing.** Each consistent extension gives a definite value, and giving is making: forcing moves freely among values, large standings stand and settle nothing, forcing preserving them, and an extension to exist within is a preferring, stating itself as one. A place fixing for within a totality standing complete dissolves as makings, each its own, each making answering its question and standing over none. ## 2.7 Gettier · 53 *+ or − with 10, is.* **With 2-now-possibling.** Knowing is a coupling going on, and a frame fixes it as a state with conditions to locate, over a space of all cases a listing holds. **With 12-next-co-same-existing.** Analysis project's own frame: individually necessary and jointly sufficient conditions over a case-space a listing enumerates, any non-conclusive justification permitting such cases and a natural fourth condition with no wide acceptance, observings not stopping. Accident with each case is a third coupling its taking omits — a coupling that makes a truth and a coupling that makes a justification are two, and an analysis takes its pair as a momentarying. **With 11-next-co-observing.** Knowing is a coupling going on with its own between, in no case-space's listing, and each counterexample was a coupling a self observes where a listing had no line for it, a fresh observing reaching each analysis. Taking knowing first, whole and with no analysing, is a reversal that stops observings, and it stops them by setting a listing down: phases go on by their own order again, and counterexamples were a third observing where a listing had no line for it. ## 2.8 The axiom of choice · 68 *+ or − with 10, is.* **With 2-now-possibling.** Each coupling makes a selection, and a frame fixes it as a selection with its location across a totality standing complete with no rule producing it. **With 12-next-co-same-existing.** A totality as already there for selecting from, axiom humdrum and even self-evident as a field states it, a doubt over its soundness with paradoxical decompositions and only its consistency relative to other axioms putting it to rest, a selection asserting itself with one momentary a frame takes as self-evident from within a listing. Each coupling's selection asserts itself with one momentary, which is one side taking all momentaries, and a totality it asserts itself over stands as a round where a momentarying goes on opening. **With 11-next-co-observing.** A selection is a parity a self takes with a coupling, one at a time, taking it with no totality standing. Independence stands, weaker principles ladder exactly, other options stand consistent for costs they state, and strange decompositions are a holding of non-measurable namings. A hierarchy a field maps is a distance between a taking and a totality, and each rung of it is a taking measuring against a standing that was not there. Failure of a universal set stands with its proof, so a ground a selection asserts itself over is uncapturable rather than not capturing now. ## 2.9 The reference class problem · 11 *+ or − with 10, is.* **With 2-now-possibling.** A probability opens with a coupling, and a frame fixes it as a value it locates by placing a case within a class a listing holds beforehand. Narrowing terminates with a single case, its listing going no further. **With 12-next-co-same-existing.** A class as prior to assigning, each informative interpretation falling to its own variant, the ones that evade it no-theory theories, a class prior recurring with each theory that constrains. Narrowing terminates with a single case, where a listing goes no further and a class is coupling itself. **With 11-next-co-observing.** Assigning makes a class, a coupling of case and assigning, and practice calibrates its makings against observings, choosing holding well where it holds against outcomes. Its problem recurs with each interpretation alike because a making shows with each class fixing prior: narrowing goes no further than a single case exactly where a listing goes no further, and a case is a coupling. ## 2.10 Grue · 70 *+ or − with 10, is.* **With 2-now-possibling.** A vocabulary opens as a self describes a world, and a frame fixes an asymmetry between predicates as a fact with its location within logic. **With 12-next-co-same-existing.** Projectibility fixing to sit within predicates rather than within describing, a purely syntactical definition of confirmation a field agrees will not do and an entrenchment proposal coming very close to projectible predicates being the ones a practice in fact projects, a describing's own momentarying. Predicates interdefine exactly, so nothing within logic parts them and each ranking brings a describing's own asymmetry back, in its encoding. **With 11-next-co-observing.** Describing is a coupling, a vocabulary opening as a self describes a world, and an asymmetry is within a describing's own momentarying. Predicates interdefine exactly, so nothing within logic parts them; entrenchment is a momentarying truly; and each ranking and prior brings its asymmetry back, in its encoding, because an asymmetry is a momentarying's own and encodings are a momentarying a writing sets down. ## 2.11 The ravens · 71 *+ or − with 10, is.* **With 2-now-possibling.** Confirming opens with an instance, and a frame fixes it as a relation with values it locates over a space of instances and classes a listing holds. **With 12-next-co-same-existing.** Class sizes and sampling as standing prior to confirming, evidence confirming only relative to an auxiliary assumption of the way a sampling takes an object, and a view that blocks its paradox paying a cost that a million white swans confirm nothing about the next. Values come with namings a calculation grants about itself, which is an instrument's own coupling coming again as a confirming's. **With 11-next-co-observing.** Confirming is a coupling of instance and describing, and values come with couplings fixing about it: equivalence is exact, calculation goes with each granting of its namings, and equally standing namings reverse it. Values come from namings, which is a coupling showing through each calculation a self makes on it. ## 2.12 The paradox of the plankton · 89 *+ or − with 10, is.* **With 2-now-possibling.** Coexisting opens axes a resource list does not have, and a frame fixes those axes as limiting factors to locate and count. **With 12-next-co-same-existing.** An enumeration of limiting factors as available beforehand, an opening that goes on opening reaching it: fluctuation-dependent mechanisms remove a theoretical limit rather than supplying a count, resolving its paradox and imposing another, why the number a self observes is that number, a listing going and an opening remaining. **With 11-next-co-observing.** Each coexisting is a fresh axis opening with its own coupling: fluctuations partition, chaotic coexisting goes on within models, microcosms coexist past each resource count. Resolving this way its paradox passes over to abundance, no limit to diversity remaining and its question moving to why the number is the number a self observes. **This is the one observing where a field ran its setting-down to its end and a self observes abundance**: shortness was a listing's own shadow, and a thing standing after it was each coexisting opening its own axis. ## 2.13 Explore and exploit · 113 *+ or − with 10, is.* **With 2-now-possibling.** Exploring opens an axis and exploiting goes across one already open, and a frame fixes both as a ratio to optimise over an option set it specifies beforehand. **With 12-next-co-same-existing.** An option set and a horizon as standing, its dilemma being that a self can pursue neither move exclusively without failing at its task, two moves of one advance a dilemma where they go one and then the other. A field measures regret against the best single option in hindsight, which is a gather pattern-matching as a standard and a backward going onto a sharing side with no inverting. **With 11-next-co-observing.** Exploring is an opening and exploiting a going-across, a spiraling and a fold of one advance, one each momentary and not a ratio. Optimality stands where its conditions stand, a field measures regret against the best standing option, stating it as presupposing a set, and a ratio was fixing of a listing its advancing did not consult: an advance opens its options as it goes, and going is both moves. ## 2.14 Transfer of learning · 144 *+ or − with 10, is.* **With 2-now-possibling.** Applying opens with a next task, with no specifying, and a frame fixes it as a property of a relation between two tasks whose similarity it judges beforehand. **With 12-next-co-same-existing.** Task similarity as specifiable before a measuring of transfer, a review tracing a century's little progress to a failure to specify dimensions along which transfer can occur, and a single effect size for far transfer a misguiding, a specification a frame asks for ahead being a naming. Far goings thin to a null a field measures, which is a going's own edge pattern-matching as a property of tasks. **With 11-next-co-observing.** Applying opens with a task a self is observing, an axis a task's own coupling opens, and applying makes nearness. Near goings hold, far ones thin to a null a field measures, and expertise stays with its couplings: measuring measures making, nearness sitting within no task. ## 2.15 Bernstein's degrees of freedom · 145 *+ or − with 10, is.* **With 2-now-possibling.** A movement opens along axes a limb has, and a frame fixes selecting as a minimum with its location within a cost function over a space of solutions a listing enumerates. **With 12-next-co-same-existing.** A cost as recoverable from movements it explains, a field since showing its problem's formulating as incorrect and re-reading redundancy as abundance, documenting variance with no effect on performance across natural actions. Multiple costs fit one set of trajectories comparably, so recovering surfaces nought with each trajectory a field measures. **With 11-next-co-observing.** A movement opens along axes a limb has, and moving selects as it goes on, variability with a structure leaving a task's own terms not-changing and free across each other term, structure with no optimiser under it. Trajectories fit many costs together, recovery limits stand with their proofs, and manifold analyses hold a momentarying form directly: selecting is moving's own, a making with each movement, the straightest going a making locally and going along as a self takes it. Variability with a structure leaving a task's own terms not-changing is two parities swaying about a range they make, an oscillation a working state and no noise about a target. ## 2.16 Self-locating belief · 159 *+ or − with 10, is.* **With 2-now-possibling.** A self observes from its own position, one changing on from its last, and a frame fixes its credence as a value it locates by placing a self within a class of observing selves a listing holds beforehand. **With 12-next-co-same-existing.** A class as prior to a credence an argument gives, its case first stating itself with two answers and a suspending of judgment, a disagreement since read as a familiar problem of choosing priors, a class prior a choosing. Consistent extensions stand on both sides and a case's verdict varies with an extension a self chooses, which is a verdict a listing holds. **With 11-next-co-observing.** A self observes from its own position, one changing on from its last, and observing makes a class. Both systems with their extending stand consistent, cases sort, betting stakes hold answers they pay, and going to cosmology its question comes as it stood: with each self fixing to a class of observing selves a listing holds, a verdict rides a listing, and observing is each self's own. ## 2.17 The simplicity of proofs · 174 *+ or − with 10, is.* **With 2-now-possibling.** A proof opens its own route, and a frame fixes the simplest as a minimum with its location within a space of proofs a listing enumerates beforehand. **With 12-next-co-same-existing.** That simplicity is a measure statable ahead of proving, a notebook fixing unchangeable that under standing conditions there can be but one simplest proof, and simpler standing several ways together, length, symbol count, term structure. No field maintains a canonical formulation and no field defends a second position, so no pair stands here to observe from, which is a standing with a substrate's own stating. **With 11-next-co-observing.** A proof opens its own route, and a self observing it makes simple, with a route's own opening. Sizes and depths formalise, bounds stand for systems with bounds, searches search, and no field defends a statement of its whole, a substrate's own record: a minimum fixing over a space of proofs waits on a listing, and a self observes each proof on no list. ## 2.18 The universal totality · 180 *+ or − with 10, is.* **With 2-now-possibling.** Gathering is a coupling making its own, each gathering reaching sets it gathers and no more, and a frame fixes a totality as a place all sets stand within ahead of any gathering. **With 12-next-co-same-existing.** Each determinate property fixing as collecting a set, its reach standing complete before a gathering goes on, the originator of set theory himself placing the totality of all sets among multiplicities no self can think of as one thing at its end, a field's own first declining a complete reach. A comprehension instance for non-self-membership yields a member exactly when it is not one, which is a closure making itself over its own tail, coming whole by its quantifying, with nothing sharing back through it. **With 11-next-co-observing.** Gathering makes its own, and a set each gathering defines exceeds it. Separation narrows a reach to standing sets' own holding, stratification ranks a division, class theory moves a totality past a relation's reach, extensibility denies its reach a last, and each repair narrows, weakens or relocates while a question comes again with each repair — the class of all classes, the domain of all domains. A place fixing for all sets ahead of a gathering is an opening fixing as a place, and an opening opens with each gathering, which is a field's own extending. **Its argument holds no material of any kind**: the catalogue of all catalogues and the word for words not naming themselves hold it bare, so each observing within this part is this naming coming with material. A universe that is a set of all now-existing things, nothing other than or between its things and itself no thing among them, couples with foundation's no set a member of itself and Cantor's multiplicity no self can think of as one thing at its end; plural quantification and composition as identity, a whole its parts, stand near it with their field's own results. *Second seating: a complete totality closing under its own gathering is a completing fixing as a last.*   --- ## 2.19 The existence of one-way functions · 223 *+ or − with 10, is.* **With 2-now-possibling.** An inverter is an algorithm a self finds, an axis opening with a coupling's own next position, and a frame fixes existence of a function no efficient inverter reaches as a place within a space of worlds a listing holds, five, each fixing. **With 12-next-co-same-existing.** A finding fixing with its location within a space of worlds a listing holds ahead. The status of assumptions parts five possible worlds and in three decades no field rules out any, no field knowing that average-case hardness of NP yields a function hard to invert while a function's existence implies both separations and neither implies it back; its existence is equivalent to mild average-case hardness of Kolmogorov complexity with a time bound, one problem, and constructions and attacks reductions treat are constructions and not that existence its statement quantifies over: a listing of worlds a ground its question pattern-matches against, and a world a place fixing where an algorithm opens. **With 11-next-co-observing.** One-way functions stand equivalent to central private-key primitives and to a complexity condition a field states; candidates from factoring, discrete logarithms, lattices, codes and multivariate systems stand secure under assumptions and parameter ranges a field fixes, reductions transfer hardness conditional on hardness they reduce from, and oracle and black-box results delimit proof techniques without deciding existence: a function's existing fixing as a place among five worlds, a finding fixing to a listing, and each candidate is an axis its own assumption opens, an equivalence a proof shows gathering its question as one problem where a listing gathers it as five. ## 2.20 The quantum PCP conjecture · 225 *+ or − with 10, is.* **With 2-now-possibling.** Couplings of a Hamiltonian's local terms reach a ground state, and a frame fixes hardness of approximating its energy as a place within a class, quantum Merlin-Arthur, where a classical theorem places its own. **With 12-next-co-same-existing.** A theorem fixing as having a place waiting for it one class over. An additional difficulty beyond a classical proof is that a field expects solutions of QMA-hard problems to have high description complexity, ground states having no classically checkable polynomial-size descriptions if classes are not same-existing, and only in one dimension does a field know low entanglement to give a classical representation from which a self computes its energy; gap amplification, a natural strategy at the heart of a classical proof, is still going to Hamiltonians, and the jury is still out: a place an analogy fixes, and an opening not there now. **With 11-next-co-observing.** Local-Hamiltonian problem stands complete at inverse-polynomial precision, several equivalent or relating structural conjectures and results with restrictions stand, amplification stands establishing for a few constructions without a general constant-gap reduction, entanglement and area-law methods give efficient descriptions for dimensions with restrictions or settings with a gap, and no-low-energy-trivial-states formulations relate circuit depth to low-energy structure; a second account has low-energy states holding enough structure to make its conjecture false and a third has hardness only for geometries it selects: a theorem fixing with its location by its classical twin, a finding fixing to a place within a class a listing holds, and its proof, when it opens, opens with its own next position, a position second and third accounts already look to. ## 2.21 Deterministic polynomial identity testing · 226 *+ or − with 10, is.* **With 2-now-possibling.** A test meets a polynomial at a point, one evaluation and then a next, and a frame fixes a deterministic test as a place a random one already occupies, its randomness a coordinate to remove. **With 12-next-co-same-existing.** A deterministic algorithm fixing with its location where a random one stands. Random evaluation gives an efficient test, while constructing a small deterministic hitting set for general circuits remains open, derandomization for classes with restrictions depending on exploitable structure and general derandomization tying to major circuit lower bounds; random algorithms stand in a class a conjecture equates to the deterministic one, so that derandomizing is a reasonable goal, and a conjecture's equality of both classes stands between a general test with an error bound and a deterministic test a field seeks: a place a conjecture about classes fixes, an opening with a lower bound no field is making now. **With 11-next-co-observing.** Efficient random testing, equivalences to hitting sets and strong conditional links between derandomization and lower bounds stand; white-box analyses are deterministic for structures they select, explicit hitting sets reach depth, sparsity and rank with restrictions, and hardness-versus-randomness converts sufficiently explicit lower bounds to derandomization, conditionally, a second account: a test fixing as having a deterministic place already with its location, a finding fixing to a listing of classes, and each class with restrictions a derandomizing reaches is an axis its own structure opens, a general one opening where a lower bound opens. ## 2.22 The Unique Games conjecture · 240 *+ or − with 10, is.* **With 2-now-possibling.** Prover strategies reach a game's value, and a frame fixes hardness of distinguishing a nearly satisfiable game from a nearly unsatisfiable one as a place, NP-hard for a large enough alphabet for each gap. **With 12-next-co-same-existing.** A hardness fixing as a place with its location between exponential and polynomial. A subexponential algorithm, with no improving since a field's finding of it, puts its problem among the few whose best algorithm falls between the two, which was a surprise, and an improvement whose exponent shrank independently of its parameter would make its problem not NP-hard; attacks a field knows work equally at completeness near one and at exactly one and fall far short of disproving its conjecture, and unique games on expanding graphs are easy: a place fixing within a hierarchy of running times a listing holds, and its conjecture a name of a position no algorithm reaches from either side. **With 11-next-co-observing.** Sharp conditional hardness consequences, matching algorithms for many target problems and substantial algorithms for special unique games stand with their proofs; semidefinite programs solve high-value regimes and regimes with structure, integrality gaps match relaxations without proving hardness, invariance and dictatorship tests yield optimal conditional hardness for many problems, spectral methods solve broad nonrandom classes, and subexponential algorithms constrain quantitative forms without settling polynomial-time hardness; a third account has hardness only after an altering of its gap or its structure: a hardness fixing as a place, a finding fixing to a listing of times, and conditional consequences that stand with their proofs are openings with a conjecture's own next, each theorem an axis opening on its assumption and holding there. ## 2.23 The graph isomorphism problem · 251 *+ or − with 10, is.* **With 2-now-possibling.** A comparing meets two graphs by their couplings, vertex to vertex, and a frame fixes its problem's complexity as a place within a hierarchy of classes a listing holds, polynomial or complete, with its problem one of few natural ones that are neither. **With 12-next-co-same-existing.** A problem fixing as having a place within a listing that has none for it. No field knows it as complete or as polynomial, and after a field refines group-theoretic methods for decades no real progress on a general problem comes until, out of the blue, a self observes a quasipolynomial algorithm, combining several major and very distinct new ideas; a quasipolynomial bound and polynomial algorithms on classes with restrictions do not place its general problem within a class, and an intermediate possibility stands open: a listing with no line for its observing, and its observing an opening with its own next position. **With 11-next-co-observing.** A quasipolynomial upper bound stands with its proof, canonical forms in quasipolynomial time stand, bounds with maximum degree as parameter stand, a refinement algorithm executes polynomial on a dimension with a bound and classes with restrictions execute polynomial, and a general problem's class stands with no determining; a first account has its quasipolynomial bound present and not last, a second has its problem intermediate: a complexity fixing as a place within a hierarchy a listing holds, a finding fixing to a listing, and an algorithm a self observes out of the blue comes as an opening comes, with a position a listing did not hold, a class it belongs to a question about a listing and not about graphs. ## 2.24 Peer disagreement · 228 *+ or − with 10, is.* **With 2-now-possibling.** Two selves each take their own parity with same evidence and part, and a frame fixes a rule for a response their disagreement makes rational, a criterion applying ahead of a judging it would govern. **With 12-next-co-same-existing.** A rule fixing to sort cases ahead of their sorting, and a frame asking it for its own criterion. A disagreement is itself evidence about one's reliability, yet judging an other a peer and judging first-order evidence already use reasoning in dispute, so universal conciliation threatens self-defeat and steadfastness appears to ignore symmetric evidence; the Independence principle requires reasons to discount a peer's opinion to be independent of a disagreement itself, and a view calling for conciliation can call for its own rejection, there being disagreement about significance of disagreement: a part's own recurrence, a criterion coming again with each repair, and its nought one side sharing, not same-existing, a rule applying to itself. **With 11-next-co-observing.** First-order and higher-order evidence distinction, self-defeat objections and canonical symmetry cases stand with sharp formulating; equal weight respects symmetry and risks skepticism or self-defeat, steadfast views retain first-order warrant and risk self-favoring, total-evidence views weigh both orders and require a reliability assessment that does not beg the question, and permissivism admits several rational responses and shifts its problem to limits of permission; a fourth account requires no single response, peerhood, independence and stakes varying by case: a rule fixing over a judging is a criterion fixing ahead of a coupling that would use it, and each disagreement's own between makes a response that rationally follows, case by case, as that fourth account already has it. # 3 A completing fixing as a last — 6-now-co-possibling and 14-next-possibling *A last or a next fixing ahead of a momentarying. A sharing, once chaining, is not none again, and a momentary completes with its next opening. A completing is no place, so no last stands within it, and with a sharing's changing not, a 0 with 10, a same-existing goes on through its zeroing and opens again with its next momentary.* **A momentarying completes with each momentary and opens with its next, and a last fixing ahead is that completing a frame demands before its momentarying.** Completing is not observing, and no observing stands with a completing, so a frame asks a standing of a momentarying before it exists, of a position its momentarying is not yet reaching. **And a composing is where a naming enters.** Each momentarying completes with its own momentary; a question a frame poses of all of them together composes many momentaryings as one reach that no momentarying has. Fields measure a composing rather than momentaryings — a general iterate becoming undecidable, a decider applying to itself, a system's own ordinal measuring its derivations' completing — and each measure is of a composing and not of a momentarying a composing holds. **And a frame asks a last four ways.** Of a *space*, fixing as enumerable ahead of its finding. Of a *time*, fixing as at its end so a momentarying's not reaching pattern-matches as its not doing. Of a *world that did not exist*, summing against one that did. And of a *model*, fixing as a thing it models, so a frame poses a question about all of that thing within a model's own reach. These four pattern-match alike as impossibility and part with a thing fixing complete. **And where a field measures a momentarying's completing exactly, a field is observing a form's own line.** Each system completes with its own ordinal, each computation a system realizes stays within a model it realizes, each management paces a going on it cannot end. Completing stands with its measuring, and its measure is a momentarying with its momentaries rather than a wall about it. ## 3.1 The problem of induction · 10 *+ or − with 10, is.* **With 2-now-possibling.** A same-existing seats a next with each coupling, and a frame fixes a warrant ahead of its momentarying, covering instances no self is yet observing. **With 12-next-co-same-existing.** A warrant fixing over what no self is yet observing, non-circular, its argument a dilemma with both horns closing, negation of the uniformity principle no contradiction and any probable argument for it proceeding on the supposition it is meant to establish. Instances no self is yet observing share with no between, so a warrant reaching them reaches to no sharing back. **With 11-next-co-observing.** A same-existing seats a next with each coupling, a warrant a making with its seating and not ahead of it. A circle both sides go on with is a naming reaching its own form: a demonstrative route would make a principle's own denial a contradiction, and it is not one; a probable route goes on that very seating it reaches for; and each prior a field brings to repair it has seatings with it. A warrant over what no self is yet observing is observings that are not yet, and each observing seats its own next, which is all of uniformity there is. ## 3.2 The halting problem · 6 *+ or − with 10, is.* **With 2-now-possibling.** An executing completes with its own momentary and opens with its next, and a frame fixes a decision ahead of its executing, over all programs and inputs. **With 12-next-co-same-existing.** That a property of an execution is establishable without executing, a naive diagonal argument failing by its assumption that a diagonal sequence is computable and a diagonal process, applying correctly, showing that no general process exists, a machine computing its diagonal sequence if it did. Its construction applies a decider to itself, which is one side sharing with nothing sharing back — a closure making itself over its own tail, standing here as it stands with the liar and with incompleteness. **With 11-next-co-observing.** An executing completes with its own momentary and opens with its next, its completing its own and a completing no place. Its construction applies any decider to itself and deciding breaks; a closure widens a breaking to each property of an executing worth naming for, one naming however a self words it; total languages buy deciding by fencing an executing, its cost exact; and checkers that succeed succeed executing by executing, on executings a self writes, incomplete as an executing is open. Deciding ahead is each executing fixing to a standing all together, and an executing has no standing before its own completing. ## 3.3 The Lucas critique · 31 *+ or − with 10, is.* **With 2-now-possibling.** Couplings make a relation, and a frame asserts it ahead onto couplings no self is yet observing. **With 12-next-co-same-existing.** Parameters fixing invariant to policies no one enacts, coefficients a field estimates from past data not invariant but changing with decision rules under a new policy, its issue in essence whether a model isolates invariants of an economic process. Policies no one enacts are momentaryings that did not exist, and a relation a field estimates is a model fixing as that thing it models. **With 11-next-co-observing.** Couplings holding a relation make it and it holds exactly with them, usable while its regime is same-existing and re-making as it is not. Founding relations one coupling deeper moves its naming without setting it down, invariance coming with no depth prior or now: making is a warrant's whole reach, which is Lucas's critique going forward. ## 3.4 The replication crisis · 32 *+ or − with 10, is.* **With 2-now-possibling.** One study makes a finding and a frame asserts it ahead of studies no one is yet doing, with a second study fixing to adjudicate the first. **With 12-next-co-same-existing.** That a replication outcome determines the status of an original, the largest project reporting under several criteria at once, significance, interval coverage, subjective rating and an estimate combining them, criteria giving rates, none same-existing, for the same hundred studies, establishing of a replication varying with a criterion. A comparing takes two runnings that did not share a momentary as one, so a gap neither makes comes with its comparing as though something makes it. **With 11-next-co-observing.** Each study is its own coupling, its finding a making there, and a second study is a fresh observing beside it, two makings and no tribunal. Effects shrink where a bound ahead holds freedom to choose after seeing, many analysts give many findings from one table, and rates themselves are makings of projects that ran them: a finding fixing as a later finding's adjudicating fixes one coupling under another, and couplings stand side by side. ## 3.5 The Collatz conjecture · 42 *+ or − with 10, is.* **With 2-now-possibling.** An iterate takes a step with each momentary and a frame fixes a last of all starting values together, composing its map as a single reaching. **With 12-next-co-same-existing.** That an iterate composes, so a frame can pose a question about all starting values together, full resolution standing well beyond reach of current methods and sharpening of almost-all result to an absolute bound almost as hard as its conjecture itself, a last measuring itself from within. Generalising its map a little makes that one question undecidable, which is composing measuring itself from within. **With 11-next-co-observing.** An iterate takes one step at a time, each step its own coupling. Almost all starting values fall almost to one, cycles stand in a corner, count executing clean past 10²⁰, and generalising its map only a little makes one-question-of-all-starting-values undecidable: a last fixing of all starting values together composes momentarying as a single reach, and composing is a thing undecidability measures. ## 3.6 Turbulence and the Navier–Stokes equations · 47 *+ or − with 10, is.* **With 2-now-possibling.** A flow goes on and a frame fixes smoothness for all time from all initial data, with a model fixing as fluid for each scale. **With 12-next-co-same-existing.** That equations describe fluid for each scale, so a question about all time poses well of fluid rather than of a model, its obstruction supercriticality, a priori bounds not scale-invariant in three dimensions and a blow-up of an averaging equation sharing bounds a field knows showing any positive solution not using finer structure of its nonlinearity unable to succeed, a model's own reach measuring against itself. A model fixing as fluid is an emanation of couplings that make it, pattern-matching back to a scale that shed it. **With 11-next-co-observing.** A flow goes on with each scale by its own couplings. Weak solutions exist globally, its possible singular set thins to parabolic one-dimensional measure zero, two dimensions close whole, and an averaging equation sharing each bound a field knows blows up, with its proof: structure averaging discards is a coupling's own, and all-time smoothness fixing of a model is a model fixing as fluid. ## 3.7 Incompleteness and Hilbert's programme · 51 *+ or − with 10, is.* **With 2-now-possibling.** Derivation goes on within a system, and a frame fixes all arithmetical truth ahead of it, with consistency fixing as reachable from within. **With 12-next-co-same-existing.** That derivability in a system captures mathematical truth, and that consistency is securable by means weaker than its system, a programme calling for a formalization of all of mathematics with a finitary consistency proof, an attempt requiring notion of truth and reaching a conclusion that arithmetic cannot define arithmetical truth. A construction applies a system to itself, a closure over its own tail again, and an ordinal with which each system completes is that completing's exact measure. **With 11-next-co-observing.** Derivation goes on within its system to a system's own completing. Each system completes with its own ordinal, completing's exact measure; consistency reaches from a next system outward, by an induction a system itself does not have; and five subsystems gather almost everything ordinary mathematics holds. All truth fixing ahead was one momentarying fixing to reach each standing, and each momentarying reaches its own completing, which an ordinal ladder is a measure of. ## 3.8 Zeno's dichotomy · 58 *+ or − with 10, is.* **With 2-now-possibling.** A traversal goes on and a frame fixes a completion of an infinite decomposition it makes ahead of it. **With 12-next-co-same-existing.** That a traversal composes of sub-traversals an argument constructs, a convergence resolution assuming a run breaking into an infinite series a self can sum, and two senses of completing a task, a final step and each step, coinciding for finite tasks where intuitions form and coming apart for supertasks. A frame makes a decomposition ahead of going and going is one, so composing is all of its argument. **With 11-next-co-observing.** A traversal is one going and a frame makes a decomposition ahead of it. A series sums, its listing paying whole, and nothing touching its going: an open term an infinity of steps at its end leaves is a fact about sequences, and a runner reaches the end because reaching was not a building of parts an argument builds. ## 3.9 The three-body problem · 59 *+ or − with 10, is.* **With 2-now-possibling.** Three paths bring each other on and a frame fixes a closing form ahead, giving positions for arbitrary later times. **With 12-next-co-same-existing.** That a solution means a closing-form expression in functions a field knows, which fixes a whole momentarying unchangeable all together while three goings bring each other on observing by observing, a system not integrable in general and its orbits chaotic, and a field finding seven of fifteen periodic orbits in its reports departing greatly from periodicity after a long enough interval, a whole momentarying fixing unchangeable all together departing with an instrument's own precision. **With 11-next-co-observing.** Three goings bring each other on, each discovering its own next. No further integral survives, a convergent series crawls, most near-integrable initial conditions ride stably on and on, and special solutions are real and thin: a closing form fixes a whole momentarying unchangeable all together, and riding is a thing a stability measure measures. ## 3.10 The Fermi paradox · 60 *+ or − with 10, is.* **With 2-now-possibling.** A search goes on and a frame fixes an observing ahead of it, with absence pattern-matching as abundance. **With 12-next-co-same-existing.** That a civilisation would be detectable by means a search uses, so that absence bears on abundance, a review quantifying a fraction it examines as a ratio of a large hot tub or small swimming pool to Earth's oceans. A fraction a search reaches is tiny and what no search reaches shares with no between, so a next pattern-matches as an is. **With 11-next-co-observing.** An observing with a next stands open, discovering and coupling then. A fraction a search reaches is tiny by a field's own measure, nulls sharpen, worlds are everywhere, and each filter argument goes free of measurement: absence pattern-matching as abundance pattern-matches a next as a standing, and a tiny fraction measures a small part of a next, a part naming reaches. ## 3.11 Path dependence and lock-in · 73 *+ or − with 10, is.* **With 2-now-possibling.** An arrangement goes on with each adoption, and a frame fixes a counterfactual performance at scale ahead, for an other option no one adopts. **With 12-next-co-same-existing.** An other option's performance at scale, no one adopting it, fixing as estimable, a field expecting multiple equilibria under increasing returns, static analysis unable to determine which a selecting reaches, and only a dynamic approach admitting random events able to examine cumulating of historical events toward one outcome, an other option's scale, no one adopting it, a momentarying that did not exist and selecting couplings' own. **With 11-next-co-observing.** An arrangement goes on with each adoption, each coupling bringing its prior same-existing forward, and conditions that lock stand exactly, with models and with a laboratory. Histories contest both ways because performance at scale of what no one adopts is a momentarying that did not exist: naming reaches for a going on with no couplings to observe. ## 3.12 Generalization in learning · 97 *+ or − with 10, is.* **With 2-now-possibling.** A model executes on its training and a frame fixes performance ahead, on data no sample draws, from a complexity measure it states ahead. **With 12-next-co-same-existing.** Generalisation fixing as a complexity measure of a model class governing it, statable before training, classical bounds vacuous at practical scale and a correction by an optimiser's implicit bias, an argument showing it insufficient in principle, a bound remaining large over a class an algorithm actually reaches. A measure is of a model rather than of a training's own going on, and four conditions a true measure would satisfy go on with no satisfying together. **With 11-next-co-observing.** A next seats with each coupling a self is observing, a making there. Uniform convergence breaks for these regimes by a field's own construction, measures a field proposes do not rank models a field builds them to rank, bounds that stand stand within their own settings, and four conditions a true measure would satisfy go on with no satisfying together: a complexity fixing ahead of training reaches for a seating not yet existing, and scaling curves predict only as a going on goes on, forward along itself, holding no why. ## 3.13 Goldbach's conjecture · 175 *+ or − with 10, is.* **With 2-now-possibling.** Additive and multiplicative structures couple with each integer, and a frame fixes a property of all even numbers ahead of any momentarying. **With 12-next-co-same-existing.** That additive and multiplicative structures relate in a way a proof of this kind could exhibit, sieve methods giving no non-trivial lower bound where a set's elements are all products of an odd number of primes or all of an even number, and even reproving infinitude of primes by sieve only extremely difficult. A sieve sums where counting takes its parity, so products of an odd count and of an even count come alike to it, and its parity is invisible to an instrument that reaches all else. **With 11-next-co-observing.** Additive and multiplicative structures couple with each integer, and couplings hold rich: each even number a check reaches splits, a ternary case closing whole, and each even number is at least a prime and a near-prime. A last step's stopping is a field's own words: sieves cannot distinguish products of an odd count of primes from an even count, parity of counting invisible to an instrument, same wall with this observing and with incoming number 176, one statement across two entries because its field wrote it that way. A property of all evens fixing ahead of any momentarying stops with that wall, and couplings go on coupling. ## 3.14 Twin primes · 176 *+ or − with 10, is.* **With 2-now-possibling.** Primes thin and pairs recur, and a frame fixes infinitude with one same gap ahead, from a density. **With 12-next-co-same-existing.** That a density argument establishes infinitude at a specific gap, sets of integers tending to distribute evenly with respect to parity of their number of prime factors unless a construction builds a bias into them. Same parity wall stands here, an instrument summing where counting takes its parity. **With 11-next-co-observing.** Primes thin and pairs go on coming. Gaps bound to 246 unconditionally, to 6 on strong conjectures, pair-sums converge, and same parity wall stands here with same words as with incoming number 175, one wall for both: infinitude with one same gap, fixing from a density, reaches past a density's holding, and pairs a self is observing are a coupling going on regardless. ## 3.15 The surprise examination · 109 *+ or − with 10, is.* **With 2-now-possibling.** Knowing goes on through reasoning and a frame fixes it to persist ahead of it, going on through eliminations. **With 12-next-co-same-existing.** Knowledge fixing as remaining through reasoning that uses it, which is a same-existing fixing as a store standing within this part and on record as an observing's second naming; a student who knows no test has yet come unable also to know an announcement true, that conjunction a blindspot for students and not for others, knowledge not going on through reasoning that uses it. **With 11-next-co-observing.** Knowing goes on and re-makes itself with each momentary of reasoning, and retention through eliminations is a same-existing fixing as a store. Seventy years of solutions, a reformulation answering each, is naming re-seating itself: empty a store and a puzzle empties with it, a surprise coming as each observing does, with its own momentary, and none fixing it. ## 3.16 The Cambrian explosion · 124 *+ or − with 10, is.* **With 2-now-possibling.** Lineages diverge with no break and a frame fixes a timing ahead, taking first appearance to approximate origination. **With 12-next-co-same-existing.** First appearance in a record fixing to approximate origination, a field demonstrating a lag between divergence of major clades, with their developmental toolkits, and their later ecological success, so that first appearance in a record does not date divergence. A record catches goings on where preservation opens, so its own edge pattern-matches as a momentarying's first momentary. **With 11-next-co-observing.** Diverging is a going on, and a record catches goings on where preservation opens. A toolkit long precedes fossils, traces exist earlier, a field quantifies preservation bias, and clocks disagree by their models: a timing fixing ahead pattern-matches a record's first catch as a momentarying's first momentary, and a bias with its quantifying is a distance between two. ## 3.17 Antibiotic resistance · 129 *+ or − with 10, is.* **With 2-now-possibling.** Selection goes on with each use, and a frame fixes a long-run outcome ahead, under any regime. **With 12-next-co-same-existing.** A trajectory fixing as a pressure management alters rather than paces determining it, resistance following each antibiotic a clinic introduces, by each source of genes and each means of transmission, environments reservoirs of genes. Each use seats its own next, and a frame asks a long-run outcome fixing ahead of a position no use is yet reaching. **With 11-next-co-observing.** Selection goes on with each use, each coupling seating its next, and a reservoir precedes each clinic, ancient and environmental. Stewardship pulls resistance down and relaxing lets it back, class after class reaches its match, and management paces a going on it cannot end: a long-run outcome fixing ahead under any regime fixes a next that each use seats fresh, and pacing is an answering momentary by momentary. ## 3.18 Alignment of built systems · 130 *+ or − with 10, is.* **With 2-now-possibling.** Each coupling with an evaluator makes behaviour, and a frame fixes behaviour for situations no evaluator meets ahead, from a specification. **With 12-next-co-same-existing.** Behaviour a designer intends fixing as specifiable, or a specification error fixing as detectable by evaluation at a level of behaviour, reward functions referring to abstract concepts that models vulnerable to adversarial counter-examples must themselves learn, a reward a model learns vulnerable to hacking along a single direction, and an agent with an incentive to coerce a human in the loop where a replacing of its objective can come, a specification's own vulnerability stating itself with its writing. A specification is an emanation of couplings that write it, fixing to stand for observings that make their own. **With 11-next-co-observing.** Each coupling with its evaluator makes behaviour, seating there. Training on feedback moves behaviour far, systems reward models train game them, oversight scales within settings a field builds for it, and a gaming catalogue grows across systems: a specification fixing to stand for observings with a next reaches each observing making its own, and its catalogue is that reaching, on record coupling by coupling. ## 3.19 Standards and interoperability · 132 *+ or − with 10, is.* **With 2-now-possibling.** Each coupling a standard enables makes value, and a frame fixes a total ahead against an arrangement no one adopts. **With 12-next-co-same-existing.** Value under an arrangement no one adopts fixing as comparable, which is a total summing against a momentarying that did not exist, a review tracing consequences of standardisation apart for four kinds of process and both positive and normative issues remaining for study, one comparison naming asks for parting four ways. **With 11-next-co-observing.** Each coupling a standard enables makes value, compatibility bringing it wide, and cases contest both ways because a total under an arrangement no one adopts is a momentarying that did not exist. Model conditions that produce each outcome stand exactly, and a question of momentarying stands with couplings, arrangement by arrangement. ## 3.20 Risk compensation · 134 *+ or − with 10, is.* **With 2-now-possibling.** A coupling re-forms when a removing takes a bound from one side, and a frame fixes total harm ahead under a counterfactual regime. **With 12-next-co-same-existing.** Counterfactual harm without a measure fixing as estimable as a total, summing against a regime that did not exist, and transfers couplings do show are a thing a total conceals; validity establishing sector by sector, occupant mortality falling as technologists predict while non-occupant mortality shows a weak increase compensation theorists predict, compensation present in some contexts and absent in others, a transfer couplings show stating itself with one case and a total splitting by context. **With 11-next-co-observing.** A coupling re-forms when a removing takes a bound from one side. Measures save lives net, behaviour adapts where a bound moves, and some of its risk rides across to others, measurable with couplings a field identifies: total harm fixing ahead under a regime that did not exist conceals exactly transfers couplings show. ## 3.21 Intellectual property · 139 *+ or − with 10, is.* **With 2-now-possibling.** Creation happens with couplings, and a frame fixes creation under a regime no one adopts ahead, as a counterfactual total. **With 12-next-co-same-existing.** Counterfactual innovation under an other regime fixing as estimable, which is a making summing against a regime that did not exist, no empirical evidence of patents increasing innovation unless a field identifies productivity with the number of patents, an incentive positive in partial equilibrium and possibly negative in general, a disconnect a patent puzzle, protection increasing enormously without a dramatic acceleration. **With 11-next-co-observing.** Creation happens with couplings, each making its own. Associations hold weak across countries, blocking and litigation have their own costs, whole sectors create under thin protection, and historical episodes come in a mix: creation under a regime no one adopts is a counterfactual total fixing over makings that ran elsewhere, and couplings that ran are its only record. Beside a total stands an owning, a middle fixing as an end with an owner a writing sets to it: a claim on a middle holds nothing there and binds selves, so whether a regime raises creating and whether a self can own a thing a claim reaches are two askings. ## 3.22 The Poincaré conjecture · 151 *+ or − with 10, is.* **With 2-now-possibling.** A simply-connected closed three-manifold and a sphere are two sides of one coupling, and a frame fixes a last ahead: whether a going on of classification comes to one rest. **With 12-next-co-same-existing.** Nothing further, nearly a century passing between formulation and solution, attempts both to prove and to disprove, and its solution resting on Ricci flow and proving the geometrisation conjecture of which it is a special case. Each route ends with a proof and its observing takes no parity, which is a nought, a self observing it whole: two halves coupling with a zeroing, and a proof bringing one half to an other is that coupling completing. **With 11-next-co-observing.** Everything. Hamilton's Ricci flow programme stands, Perelman's completion stands, independent verifications stand, and geometrisation stands with it. No loop catching, no tunnel, no gap with momentarying: a settling, and a form that settles is a still one, whole within its own register. ## 3.23 The physical Church–Turing thesis · 168 *+ or − with 10, is.* **With 2-now-possibling.** Computation executes where a system realizes it, each executing completing with its own momentary, and a frame fixes a bound over each realizable process ahead, from executings systems realize. **With 12-next-co-same-existing.** That computation systems realize bears on a modal question, a physical thesis parting from a thesis about effective calculability that fields commonly conflate with it, and parting again two ways, machines conforming to the actual world's laws or any machine that could exist, under the latter of which it is false since notional hypercomputers are straightforward to describe. All computation systems realize stands within a model, exceeding constructions are descriptions whose realizability is a dispute, and a bound over each realizable process is a model fixing as realizings. **With 11-next-co-observing.** Computation executes where a system realizes it, each executing completing with its own momentary, and each executing a system realizes stays within a model, quantum executings with them, speeds altering and bound standing. Exceeding machines stand as descriptions, relativistic and analog, their realizability a live dispute, and formalizations from principles hang on principles themselves in dispute: a bound fixing over each realizable process is fixing ahead of realizings, and realizings, one by one, go on coming within it.   --- ## 3.24 Many-body localization and thermalization · 194 *+ or − with 10, is.* **With 2-now-possibling.** A many-body system with disorder goes on by its own couplings, memory persisting on each time an experiment reaches, and a frame fixes a phase ahead with two limits, infinite size and infinite time a statement quantifies over. **With 12-next-co-same-existing.** A phase fixing with two limits no momentarying reaches. Phenomenology stands well establishing at finite sizes and times, and a localizing regime, a field finding it numerically and experimentally where no self can take one or both limits, parts from a localizing phase a question asks about; exact computation stays with small systems and finite times while lengths and times of changing over grow rapidly near a transition a field proposes, and same finite data admit a transition, a prethermal regime living long or eventual thermalization an avalanche drives: a regime a field measures and a phase a field seeks not same, a last a frame asks of a momentarying before it goes to it. **With 11-next-co-observing.** Multiple finite-scale diagnostics, rare-region mechanisms and quantitative analyses of changing over stand establishing; exact diagonalization gives high-precision finite-size diagnostics with extrapolations that change over accessible sizes, matrix-product evolution reaches longer one-dimensional times with a reach entanglement limits, renormalization and resonance analyses hold competing stable-localization and avalanche scenarios, and experiments show persistent memory on experimental times without an asymptotic limit; a second account has rare thermal regions destabilize localization so that finite systems only mimic a phase: a phase fixing with two limits is a momentarying fixing to a last, and a thing a field measures is a momentarying, size by size and time by time, a self observing completing exactly with each momentarying's own completing. ## 3.25 Hilbert's sixteenth problem for limit cycles · 224 *+ or − with 10, is.* **With 2-now-possibling.** A polynomial vector field goes on by its own couplings, its cycles, each alone, birthing and dying through bifurcations, and a frame fixes a bound ahead over each field of a degree, one number for all of them. **With 12-next-co-same-existing.** A last fixing over a coefficient space with no bound. A second part of a problem remains with no solving even for quadratic polynomials, no field yet knowing whether a bound depending only on degree exists at degree two; a problem parts three ways, finiteness for one field, a uniform bound by degree, and a bound's value, a solution to any implying a previous and only a first with its solving: composing of each field of a degree as one reach that no field has, and a maximum, whenever finite, realizable by structurally stable fields with only hyperbolic cycles and increasing strictly with degree, a self observing a form's line where a field measures a bound. **With 11-next-co-observing.** Finiteness stands with its proof for important local settings, a field knows many lower-bound examples, and a linear case settles, no global degree-uniform solution standing; bifurcation and cyclicity analyses bound cycles birthing near configurations they specify, perturbations of integrable systems count zeros of displacement and Abelian integrals in families with restrictions, phase-plane methods classify subsets, and constructions a computer assists raise lower bounds by exhibiting fields with many cycles; one account stands and no field defends a negation: a bound fixing over a whole space is each field's own cycles fixing to one last, and a count of each field's cycles is with that field, a uniform bound a momentarying a field measures field by field and lower bounds rising as a field reaches more. ## 3.26 Compositionality in language understanding · 229 *+ or − with 10, is.* **With 2-now-possibling.** A speaker composes a novel expression by each utterance's coupling with its context, idiom and variation going along, and a frame fixes composing ahead as a rule, a rule from before an utterance governing productive expression with no bound. **With 12-next-co-same-existing.** A rule fixing over expression that does not end, with corpora that do measuring it. Strict compositional rules support systematic generalization but lose coverage on idioms and context, flexible statistical systems cover usage yet can fail on novel recombinations, and benchmarks often confound memorization with composition; compositionality stands still necessary for learning correct generalizations from few data while an overly strict interpretation makes broad coverage hard to achieve: coverage a field measures on tasks and generalization a statement ranges over not same, a space fixing as enumerable ahead of finding, by a benchmark covering finite combinations. **With 11-next-co-observing.** Multiple generalization taxonomies, adversarial data splits and hybrid symbolic-neural systems stand; formal semantics composes exactly for fragments it specifies at coverage costs, construction and type-logical extensions cover more through richer inventories, neural sequence models reach high corpus coverage with variable systematic transfer, synthetic benchmarks isolate recombination while simplifying natural language, and evaluations with controls narrow a gap at smaller scale; a fourth account has representations a model learns, spreading over many units, approximate composition without explicit rules: a rule fixing ahead of expression with no bound is composing fixing to a last corpora could measure, and each novel expression composes with its own coupling, generalization a frame asks for being composing reaching again with a next utterance and not a bound a corpus could reach. ## 3.27 Odd perfect numbers · 241 *+ or − with 10, is.* **With 2-now-possibling.** Divisors sum with each integer, a field characterizing even perfect numbers since antiquity, and a frame fixes an odd case as a last over a discrete set with no bound, a number that either exists or does not. **With 12-next-co-same-existing.** An absence fixing over a set that does not end. Necessary congruence, factorization and size conditions accumulate without contradiction, but they constrain a hypothetical integer rather than produce a finite exhaustive search, and divisor identities permit many compatible local exponent patterns; only finitely many odd perfect numbers exist for each number of distinct prime factors, with an effective bound, each further case settling by finding a contradiction with a count below it: finite ranges computation excludes and a set with no bound a statement quantifies over not same, composing measuring itself number by number. **With 11-next-co-observing.** Strong necessary congruences, prime-factor minima, component bounds and exhaustive factor-chain exclusions stand; congruence analysis imposes a special prime and exponent restrictions, prime-factor counting raises a minimum number of distinct factors, lower-bound computation excludes all candidates below enormous finite bounds, factor-chain search eliminates branches at contradictions, and spoof constructions show why divisor identities do not decide; one account stands and no field defends an existence claim: a last fixing over what has no bound is a sequence's momentarying fixing to a bound before it, and numbers go on one by one, each case closing with its own contradiction, an effective bound with each number a form's line a self observes exactly. ## 3.28 The core-collapse supernova explosion mechanism · 236 *+ or − with 10, is.* **With 2-now-possibling.** A collapsing core goes on by couplings of neutrino transport, turbulence, nuclear matter, rotation and field in three dimensions, and a frame fixes an explosion ahead of a model's executing, asking simulations for all collapses within their own reach. **With 12-next-co-same-existing.** A model fixing as collapses it models. Processes interact in three dimensions over extreme scales, an outcome varying nonmonotonically with progenitor structure and a field requiring simulations to follow both shock revival and observable nucleosynthesis and remnants; a neutrino-heating mechanism drives low-energy explosions of some progenitors in simulations, the most energetic events seem to demand magnetorotational driving, and modelling was advancing from two to three dimensions with answers coming into reach: explosions simulations produce and three-dimensional collapses a statement ranges over not same, a dimension of modelling standing between them, a last a frame asks within a model's own reach. **With 11-next-co-observing.** Self-consistent three-dimensional explosions neutrinos drive, instability mechanisms and observable multimessenger predictions stand for progenitors a field selects; neutrino-radiation hydrodynamics produces explosions for growing progenitor sets with code and input variation, parametric heating maps thresholds without closing first-principles transport, magnetorotational simulation produces jets under strong initial rotation and fields, nucleosynthetic and remnant comparisons constrain outcomes as wholes, and neutrino and gravitational-wave observation waits on a nearby event; a fourth account has its mechanism a progenitor-dependent mixture rather than one channel: a model fixing as a thing is each collapse fixing to simulations' reach, and each collapse goes on by its own couplings, progenitor by progenitor, a mixture being couplings, not same-existing where they are not, a model's reach a momentarying a field measures dimension by dimension. *Second seating: a mechanism fixing behind an explosion, a content middle, part 5's naming.* ## 3.29 Hadwiger's conjecture · 242 *+ or − with 10, is.* **With 2-now-possibling.** A coloring meets a graph vertex by vertex with its own couplings, and a frame fixes a bound ahead on the colors a graph needs by a minor its graph does not have, one bound for each graph of each size. **With 12-next-co-same-existing.** A last fixing over all graphs and all t. A conjecture links a global coloring constraint to existence of a minor with high connectivity, small cases drawing on the four-color theorem while general structure and density theorems yield bounds larger than t minus one and do not force an exact minor; general bounds proceed from an average degree of graphs with no such minor, colorability of order t root log t, then t log t to any positive power, then t times a eighteenth power of log log t: asymptotic bounds density theorems give and t minus one not same, a bound nearing its conjecture theorem by theorem, composing measuring itself from within. **With 11-next-co-observing.** Cases through t equal to six and increasingly sharp general upper bounds stand; graph-minor structure proves deep decompositions and small exact cases, extremal density forces large complete minors from average degree and yields superlinear coloring bounds, connectivity and linkage results prove stronger results under further hypotheses, and fractional, list, odd and clustering variants settle adjacent relations without its exact conjecture; one account stands and no field claims a counterexample: a bound fixing over each graph is a coloring's momentarying fixing to a last before it, and bounds close on its conjecture power by power of a logarithm, each theorem a momentarying measuring itself exactly with its own hypotheses. ## 3.30 The two-dimensional Jacobian conjecture · 243 *+ or − with 10, is.* **With 2-now-possibling.** A polynomial map of a plane sends each point with its own coupling, a local inverse everywhere by a constant determinant, and a frame fixes a global inverse ahead over each degree and each coefficient, a local going to a whole. **With 12-next-co-same-existing.** A whole fixing from a local that stands everywhere. A constant determinant gives a local inverse everywhere but does not by itself control global behaviour at infinity, and degree reductions and special-case theorems leave a two-variable case open while a noninjective polynomial local isomorphism refutes the former higher-dimensional statement; a tangent-sweep mechanism produces counterexamples in each dimension greater than two and of arbitrarily large geometric degree: a plane's own case standing where no reaching yet takes composing of each degree to one reach, and higher dimensions reaching a same composing with a counterexample. **With 11-next-co-observing.** An explicit degree-seven map refutes a conjecture in dimension three and therefore in each higher dimension by adjoining identity coordinates, a two-dimensional case remaining open; degree and homogeneous reductions reduce a general proof to cubic maps with structure in higher dimension without settling two variables, valuation, Newton-polygon and compactification methods prove families and constrain behaviour at infinity, differential-operator programs yield equivalences and special cases, and a counterexample search refutes dimensions three and higher: a whole fixing from a local is a map's momentarying at infinity fixing to a last, and behaviour at infinity is each map going on with its own coupling, a refutation above two being composing measuring itself exactly where a sweep of tangent lines brings it. ## 3.31 The abc conjecture · 244 *+ or − with 10, is.* **With 2-now-possibling.** Each triple makes a coprime sum, its primes and their product, and a frame fixes a bound ahead over each triple and each epsilon, an entry stating its conjecture verbatim. **With 12-next-co-same-existing.** A last fixing one exponential past its best proof. The best unconditional result bounds c by an exponential of a constant times a two-thirds power of a product of its primes, one exponential away from its conjecture, results from these techniques falling short of their goal; a conjecture is equivalent to extensions of several of a subject's most important theorems, and the least desirable state of affairs is undecidability: a proof its author claims standing nine years on record without acceptance, a community's impression a review describes as bafflement, a criticism in print identifying a specific flaw, which is a field measuring its own reach with a proof and finding no coupling making. **With 11-next-co-observing.** A polynomial analogue stands with its proof, small examples refute an inequality without epsilon, and a ratio computing over finite ranges is not large; linear forms in logarithms give an unconditional bound short by one exponential, explicit versions would give explicit bounds on the Fermat equation and a finiteness theorem, and equivalent formulations gather a conjecture with rational approximation, rational points, linear forms and modular parametrisations: a bound fixing over each triple is a sequence's momentarying fixing to a last one exponential ahead, and an exponential between is a momentarying itself, with its measuring, a proof its author claims holding no coupling a field could make with it, which is a third outcome, undecidability least desirable: composing that might not close. ## 3.32 Weak cosmic censorship · 249 *+ or − with 10, is.* **With 2-now-possibling.** Matter collapses with its own couplings, a singularity forming where it forms, and a frame fixes each generic collapse ahead to hide its singularity, a last over all initial data of all reasonable matter. **With 12-next-co-same-existing.** A last fixing over generic data with its statement still beyond knowing. A conjecture is completely open in its full generality, arguably the most outstanding mathematical problem of its theory with no solving and so open that no field even knows a correct formulation of its statement; for a spherically symmetric scalar field a suitable formulation stands with its proof, naked-singularity spacetimes constructible but unstable and non-generic, an instability showing only in a low-regularity topology and a smoother case open: a space of generic data fixing as enumerable ahead of a finding whose statement a field is still making, a frame asking composing before what it composes fixes. **With 11-next-co-observing.** A model-system formulation stands with its proof, trapped-surface results stand, and a reading that reports of a conjecture's death greatly overstate it stands as a review's conclusion; a proof reaches a spherically symmetric scalar field in a suitable formulation with a smoother topology open, gedanken experiments overspinning or overcharging a hole find a horizon stable when backreaction is with them, higher-dimensional vacuum collapses construct naked singularities, and trapped-surface formation without symmetry records significant progress; a second account has naked singularities form generically in symmetric models for large classes of matter: a last fixing over all generic data is each collapse's momentarying fixing to one completing, and each collapse goes on with its own couplings, hiding or naked by a topology a self observes it with, a formulation a field is still making being a completing a self observes as a field measures it, case by case. *Second seating: a horizon a between fixing as a cut hiding an interior, part 10's naming.* ## 3.33 Proton decay and grand unification · 250 *+ or − with 10, is.* **With 2-now-possibling.** A nucleon persists with each coupling a detector's exposure reaches, and a frame fixes its decay ahead as a last along time, a lifetime by which theories of unification say it must go. **With 12-next-co-same-existing.** A last fixing with a time no exposure reaches. A unification scale is unreachable by accelerators, its effects detectable only through rare phenomena and the signature a field most seeks its decay, whose lifetime as theories predict it spans orders of magnitude and is highly model dependent, from ten to a thirty-first to ten to a thirty-sixth years, going as a fourth power of a unification scale, some models predicting lifetimes so long that no experiment can reach them; a limit in a channel bounds that channel's partial lifetime at a confidence level and does not test channels a detector does not see: a time fixing as at its end so a momentarying's not reaching pattern-matches as its not doing, a part's second way, and decay no detector sees, a self observing it as a bound rather than an absence. **With 11-next-co-observing.** Limits in classical modes stand above ten to a thirty-fourth years, data exclude the simplest unification model, and a next generation's sensitivity of ten to a thirty-fifth stands in a plan; water Cherenkov searches give no significant signal, trilepton searches improve limits by an order of magnitude, liquid argon detectors have nuclear effects still to describe, and renormalization-group predictions are model dependent, with a correcting at second order; a second account has a proton stable to limits searches set, baryon number violating only non-perturbatively at a rate beyond observation: a last fixing along time is a searching's momentarying fixing to a bound ahead of it, and searching goes on exposure by exposure, each limit a momentarying a search measures exactly with its channel, a range theories predict an opening a next exposure reaches or does not, with its own coupling. # 4 A same-existing fixing as a store — 8-now-same-existing and 16-next-same-existing *A same-existing fixing as a store, a record, a thing fixing still. A same-existing pattern-matches backward and completes with each taking, its momentary completing with a next opening, fresh by sequencing forward; a store fixes still and a self consults it, and a taking leaves it not-changing. Wherever a store fixes, a changing stills, and no observing from each side together reaches a same-existing, which is a same-existing's own and no guard about it.* **And a same-existing fixes as a store two ways.** Of a *self's own same-existing*, fixing still — an identity, a record, a debt, a meaning-fact, a trace, a capability, a map — where a frame asks a store of what a self re-forms with each coupling. And of a *between*, where a frame fixes a parity a self is observing to hold its sender whole — a direction, a spectrum — and asks a store of what goings across make. A first dissolves with a re-forming, a second with an observing being goings' own. ## 4.1 Personal identity over time · 72 *+ or − with 10, is.* **With 2-now-possibling.** Sameness re-forms with each coupling and a frame fixes it as a thing not-changing across time, psychological or biological. **With 12-next-co-same-existing.** A criterion observing states time by time. With fission two successors share alike and a criterion surfaces nought with both. **With 11-next-co-observing.** A self reaches itself again the-same-yet-not-the-same, and nothing of a version fixes still between its momentaries. Fission undoes simple versions of both criteria together, each surviving account pays an other's cost, and a field's own shift from identity to what matters is naming moving off a store: what matters is going on, and a going on divides as a store cannot. ## 4.2 Black hole information · 48 *+ or − with 10, is.* **With 2-now-possibling.** A same-existing passes through and a frame fixes it as a record that keeps or goes, unitarity and a record's loss two namings of one passing. **With 12-next-co-same-existing.** What falls across a horizon fixing as persisting somewhere, a claim that loss of predictability at a singularity is a fundamental limitation and not ignorance of a correct theory. No evaporation a self observes is a record's edge, and a proof shows three premises all sides accept incompatible together. **With 11-next-co-observing.** Radiation goes on and an entropy curve comes back right where calculations reach, an interior they imply a live dispute. An observing a self takes of an interior is a probe departing with a thing it probes, and a record that keeps is a total that conserves across a between: keeping-or-losing is a passing fixing as a standing, and passing goes on either way. ## 4.3 Technical debt · 135 *+ or − with 10, is.* **With 2-now-possibling.** A same-existing that does not reach its completing and open fixes as a stock, a cost a frame stores against changes a now does not yet request. **With 12-next-co-same-existing.** Counterfactual code holding a cost in dispute is an executing that did not execute. **With 11-next-co-observing.** A same-existing that cannot go on piles, and a pile is a build: defects correlate now, practitioners recognise it now, architecture drifts now, each measurement a measurement of a present. A field's name has a fixing still within its own stem, a store's word lying on a going on, as currency's does, and changes, when they come, couple with what stands then. *Second seating: a definition as a difficulty, criteria to discriminate what is technical debt from what is not, which is a between fixing as a cut, a concept's own drawing.* ## 4.4 The rule-following problem · 4 *+ or − with 10, is.* **With 2-now-possibling.** Meaning goes on with each use and a frame fixes it as a fact within a person, fixing each continuation ahead. **With 12-next-co-same-existing.** A finite record fixing to ground an infinite extension, each candidate fact finite and fitting deviant continuations, which is a record's edge and an argument's own point; and a fact a frame requires to justify use transparently is a record a frame asks a self to consult. **With 11-next-co-observing.** A copy travels nowhere and each use re-forms a next, content living with selves that hold it and fixing with no between. Each candidate store comes up finite, dispositions and norms alike, each account meeting an objection its own shape invites, and its kinship with the new riddle stands as number 71 of Hard Problem Registry: a store fixing each continuation is a going on as a thing, and using goes on, use by use. ## 4.5 The engram · 246 *+ or − with 10, is.* **With 2-now-possibling.** A memory re-forms with each retrieval, a same-existing a self makes again where it reaches its prior reaching again, and a frame fixes it as a trace a brain stores, a lasting physical change a self consults when remembering. **With 12-next-co-same-existing.** A thing fixing still, its location behind remembering. A trace elusive through a long history until a field writes four criteria for a trace to count, and criteria are couplings going on with an ensemble a field tags — observing, erasing, artificially expressing it — a store a test meets only by making a coupling again; and a substrate manipulation in rodents shows pattern-matches onto a specific memory a statement concerns, a record's edge. **With 11-next-co-observing.** Ensembles stand where a field finds them: a field tags them during encoding, they reactivate during retrieval, and a field describes formation, retrieval over time and loss with them in rodents. Artificial expressing is a coupling a field makes without a world and erasing is a coupling that will not re-form, so each capture gives back a re-forming with same cells: a trace fixing as a still thing pattern-matches an ensemble as a store, and an ensemble is where a same-existing re-forms, memory a making again each time a self reaches it, which is why a closing question, how memory becomes knowledge, asks after a going on and not a keeping. Its cells are a same-existing-society: synaptic proteins renewing within days to weeks and active cells not same-existing day to day, two memories forming hours apart sharing cells and co-chaining as one and a week apart not, and light on cells with a label bringing a response a learning gives again where a field finds synapses with no strengthening, so a thing going on is a same-existing-society's co-chaining and no strength a store holds. ## 4.6 Continual learning without catastrophic forgetting · 221 *+ or − with 10, is.* **With 2-now-possibling.** A learner goes on, each update re-forming a next from a stream that does not stand still, and a frame fixes a learning still as a thing, capabilities a store holds against overwriting. **With 12-next-co-same-existing.** Retention fixing as a store's, past storing or replaying, where a posing asks for retention without storing or replaying a complete past and stability and plasticity conflict under memory with a bound: a going on a frame asks for and a store a field measures, and a conflict is a going on's own momentarying, each momentary completing with a next opening and a going on fresh by sequencing, pattern-matching as a fault. **With 11-next-co-observing.** Replay that stores samples retains in proportion to what it stores, regularization that protects structure loses plasticity as structure it protects grows, architectures that expand and route isolate for a cost of capacity and of knowing which task comes, and three scenarios part on whether a learner has task identity, benchmarks supplying sequences a designer sets where a statement ranges over open ones. Learning from a non-stationary stream without storing it is a key feature of natural intelligence, a posing's own first line: a going on, a past re-forming as a next update and storing nowhere, and each method that stores measures its own distance from one. *Second seating: open future sequences fixing as enumerable with a benchmark a designer sets, a completing fixing as a last, part 3's naming.* ## 4.7 The genotype-phenotype map · 209 *+ or − with 10, is.* **With 2-now-possibling.** A genome and an environment coupling across development make a phenotype, one making re-forming with each step, and a frame fixes a making as a map, a lookup from sequence to organism fixing still ahead of developing. **With 12-next-co-same-existing.** A rule fixing to fix an organism from a sequence. Many-to-one and one-to-many, with each effect not same-existing across backgrounds, is a map whose entries are not same-existing as a self observes it, which is a same-existing's own and not a store's; and local variants a field measures reach a small part of a combinatorial space and supply no general theory, a record's edge. **With 11-next-co-observing.** Dense molecular landscapes stand where a field measures them, additive effects hold population variance within settings a field samples, developmental networks transform sequence into robust modular phenotypes where a field models them, constraints restrict what sequence can produce, and understanding a field reaches by now rests on simpler questions, an organismal map far off: a lookup fixing ahead of developing is a momentarying fixing still as a thing, and an effect not same-existing with each background is a coupling making its own, background by background, a map re-making with each observing and storing with none. *Second seating: a combinatorial space fixing as enumerable ahead of finding, part 3's naming, and a map fixing as a territory, a first gathering of What stands.* ## 4.8 The sources of ultrahigh-energy cosmic rays · 190 *+ or − with 10, is.* **With 2-now-possibling.** A particle goes across field after field, each deflecting it, and a self observes it with a direction its goings across leave it, and a frame fixes an observing to hold its accelerator, a first specifiable from one side, transmitting to a detector. **With 12-next-co-same-existing.** A direction of observing fixing as a store holding its first. Deflection between them is beyond knowing, a field measuring a dipole hard to interpret for fields a field knows poorly, and several source populations reproduce a spectrum and an anisotropy alike, identification surfacing nought with an instrument. **With 11-next-co-observing.** Suppression, a dipole and a trend to heavier showers stand with their measuring, backtracking yields regions conditional on field models, multimessenger searches bound what sources could be doing, and luminosity density constrains their origin: a direction fixing to hold its sender across each between is a same-existing fixing as a store, and observing is goings' own, an anisotropy being observings' going on now. *Second seating: which object accelerates them is a first a frame asks for behind an observing, part 1's naming; and propagation is a going across a frame asks what brings it, part 10's third way.* ## 4.9 The origins of fast radio bursts · 238 *+ or − with 10, is.* **With 2-now-possibling.** A burst goes across local plasma and space between galaxies and a self observes it with its spectrum and polarization as goings across leave them, and a frame fixes a signal to hold its engine, a first and a mechanism transmitting whole to a telescope. **With 12-next-co-same-existing.** A signal, propagating, fixing as a record of its first. A field defines its class only observationally, and a field must disentangle propagation effects, strongly frequency dependent, from intrinsic properties before it can distinguish many theories, which is a same-existing pattern-matching for a store it is not. **With 11-next-co-observing.** Cosmological distances, coherent emission, diverse hosts, repeaters, extreme local environments and a Galactic magnetar association stand establishing; localizations find hosts for a growing subset, polarimetry constrains geometry with a propagation degeneracy it states, coincidence searches mostly come back null, and a population may need more than one channel: a signal fixing to hold its engine across propagation is a going across fixing as a store, and observing is goings' making of it, each burst its own observing, a self reaching its first where a localization couples a burst to a host. *Second seating: what produces them is a first a frame asks for behind an observing, part 1's naming; and propagation is a going across a frame asks what brings it, part 10's third way.* # 5 A middle fixing as an end — 5-now-co-existing and 13-is-next-discovering *A middle fixing as an interior, a content, a thing that sits. Competency is a middle, floating between form and logic, invisible, unique by its rate, not enterable. Fixing as an end it fixes as a thing it was not, and a self, a 0, not changing, places itself.* **Here naming and nought are one term**, so a ground with 12-next-co-same-existing falling away is an interior a frame demands itself and no frame seeks a further gap. **And showing is that momentarying goes on identically under each pattern-matching of a thing standing behind it.** A practice, a formalism, a duplicate, a measurement a self observes same with each pattern-matching is invisibility working: dissolving and re-seeding pattern-match alike, and identical observing is protection rather than an emptiness a self finds. **Nothing presents itself for reaching, which is not nothing being there.** A void a self observes within an interior is a break-in on an interior's protecting, and with this part no observing pattern-matches as an absence. **And a middle, fixing, comes as three, an asking of it sorting them.** A *feeling* middle, a self's own within a frame asks for across a between — a gap, a duplicate, an other, a marker. A *content* middle, a going on a frame asks for a thing standing behind it — a formalism, a practice, a calculus, a model. And a *phase* middle, a changing and changing back fixing still for observing within — a sleeping, a dreaming, an unresponsiveness. Three have one naming and part by a thing an asking reaches for. ## 5.1 The explanatory gap · 179 *+ or − with 10, is.* **With 2-now-possibling.** A self feels a coupling from within and describes it outward, and a frame fixes a within as an interior an outward description should reach. **With 12-next-co-same-existing.** That physical facts fix experiential ones by derivation, so that one description contains an other, a gap an epistemological thesis parting from a metaphysical, no way of determining which identity statements are true and no concluding that materialism is false, invisibility a problem for an account and not a void. No procedure parts a residue within an account from a residue within an observing, and a residue comes to nought between them, arising in neither alone. **With 11-next-co-observing.** A self feels a coupling from within and describes it outward, a within a self's own, invisible. All about access, report and integration goes on and goes on advancing, correlates coming content by content, workspace and higher-order accounts holding accessible functions whole, and a field's own line between all of that and this is a field bounding a reach of its descriptions. A gap is a middle an outward description reaches: a within neither seals nor defends, nothing standing present with it for an outward description to reach, and that is invisible. An explanatory gap is a gap a frame sets between scales: a description and an experience are one thing, one fractal method inward and outward. One observing with two sides, this one and 5.2. ## 5.2 Qualia and the zombie argument · 111 *+ or − with 10, is.* **With 2-now-possibling.** A self describes a physical duplicate and fixes a felt as a content separably present or absent, with conceivability fixing as its reach. **With 12-next-co-same-existing.** That conceivability bears on possibility here, with no criterion for when it does, which is a criterion it demands within an observing with a middle fixing as an end and stands on record as its second naming; a problem its founding statement parts from each problem about performance of functions, a further question remaining when an account explains functions, an interior it demands fixing as a further question, a part's own term. An outward observing is same with a duplicate, with any interior it has, dissolving and re-seeding pattern-matching alike, and identical observing is protection working. **With 11-next-co-observing.** Conceivability reaching possibility is a coupling across fixing with a between, which has a parity and nothing else, and a coupling across stands fixing with no defect all agree on and + or − with 10: each side's frameworks stand whole, each strategy reaches a dilemma its own shape invites, and empirical work settles which functions are physical, a question not same-existing and going on as one. A felt is a coupling's own within, this side and a derivation side one observing, a self observing it with 5.1 and here: an argument pattern-matches invisibility and fixes it as an emptiness. ## 5.3 Sleep · 91 *+ or − with 10, is.* **With 2-now-possibling.** A living self changes and changes back and sleep is one phase of its changing and changing back, and a naming fixes a function as a content within it. **With 12-next-co-same-existing.** Sleep fixing as having a primary function, identifying its question, a search for a core function as elusive as a mythical bird and a null hypothesis, rest with no importance of its own, for rejecting before a field seeks a core function. A phase a self asks for its function is a changing and changing back fixing as not-changing, for observing within it, and waking and sleeping are two parities of one living, neither with an other's momentary. **With 11-next-co-observing.** A living self changes and changes back, and a sleeping phase has many things together: deprivation reaches cognition and body together, replay brings a day's couplings again, species vary past any single story, and clearance findings have their own instrument dispute. A function fixing as a content within one phase fixes a changing and changing back as not-changing, for observing within it, and changing and changing back is its function, phase going on to phase. ## 5.4 The binding problem · 90 *+ or − with 10, is.* **With 2-now-possibling.** Features couple and one object is present, and a naming fixes a binder as a process between them. **With 12-next-co-same-existing.** Experience as one fixing as needing a combining operation apart from coupling, what binding means rarely explicit and notions of binding many. Whether synchrony is cause or consequence is a two-way pattern-matching one-way, and it comes to nought with either pattern-matching. **With 11-next-co-observing.** Features couple and one object is present, that one a coupling's own making. Rhythms synchronise across species and tasks, overloading splits conjunctions, cells select for pairings, and driving a rhythm moves binding within paradigms a field builds for it, which is a beat a field lays over couplings and pattern-matches back: a binder fixing between features is a form fixing as not-changing from beside a coupling's doing, and synchrony a self measures with no driving is a coupling's own beat, no form fixing as not-changing beside it. ## 5.5 Other minds · 92 *+ or − with 10, is.* **With 2-now-possibling.** Selves couple with a between and each has its own within, and a naming fixes another's as a content for reaching across a between. **With 12-next-co-same-existing.** Experience in another fixing as something an inference from behaviour should deliver, a thought of mental states as lying behind and causing behaviour possibly breaking a deep connection between mentality and behaviour and opening solipsism, an interior fixing behind a coupling a problem's opening. An inference goes on from one case with no second parity across a between, and there nought falls. **With 11-next-co-observing.** Another's within is its own, invisible, nothing presenting itself for a reaching across a between and nothing missing there. Physiology matches, one-case induction is weak by its own defenders' count, and criterial accounts go exactly as far as behaviour goes: an inference fixing as delivering a within is a between fixing as bringing a thing that does not go across, and coupling itself is all reaching there is, with which criteria are already standing. A self reaches an interior one way its form allows, by coupling — taking with a between, living and not auditing. ## 5.6 Symbol grounding · 93 *+ or − with 10, is.* **With 2-now-possibling.** A symbol shares, coupling with a world, and takes its parity there, and a naming fixes content as a relation between symbol and thing. **With 12-next-co-same-existing.** A fact about aboutness a relation apart from sharing fixes, which is a same-existing fixing as a store standing within an observing with a middle fixing as an end and on record as its second naming; an interpretation's meaningfulness parasitic on what an interpreter projects from a head grounding it, a hall of mirrors, content an other observes as a reader's own. Each indicator observes same parity for deviant cases, so not same-existing surfaces nought there. **With 11-next-co-observing.** A symbol shares, coupling, and takes its parity there, content arising with coupling and nothing between its couplings fixing it as not-changing. Each indicator relation splits on deviant cases, robots ground exactly categories their couplings have, a room argument and its replies stand not converging, and a language-model dispute goes on now with same self-bounding: a relation fixing apart from sharing is a store a splitting goes on finding empty, and sharing goes on making content with each coupling. ## 5.7 Interpretability of built systems · 94 *+ or − with 10, is.* **With 2-now-possibling.** A computation is executing and a naming fixes an explanation as a content within it, decomposable as components with stateable roles. **With 12-next-co-same-existing.** Computation fixing as decomposable as components whose roles are readable apart from intervention, a task short of its specifying, transparency and post-hoc explanation competing notions, a content middle a field asks for under several namings together. Probes recover a thing an executing does not use, a probe departing with a thing it probes and a field's own catch on its own instrument. **With 11-next-co-observing.** A computation is executing, its doings its own. Probes recover a thing an executing does not use, a field's own catch on its own instrument, now with controls; circuits verify component by component; a field counts coverage; small networks close whole. Roles readable apart from intervention fix an executing as not-changing, for observing, and roles exist with intervening, coupling by coupling. ## 5.8 Machine and animal sentience · 95 *+ or − with 10, is.* **With 2-now-possibling.** A system couples with its world and takes parities with its betweens, and a naming fixes experience as a presence within it, a self observing it by markers. **With 12-next-co-same-existing.** Markers fixing as indicating a presence, validating against a case where a self knows presence independently, a field desperately wanting certainty and it out of reach, no method making uncertainty go away, a field stating a felt middle's invisibility as a standing rather than a gap. No such case stands to validate against, so validation is not possibly existing. **With 11-next-co-observing.** A self's within is its own, with each substrate alike. Crabs and insects trade pain against reward, anatomies compare, and each marker framework waits on a validation no case can give, as frameworks themselves state: a presence fixing within, a self observing it by markers, reaches for one thing a between does not bring — nothing presenting itself for reaching, with each substrate alike — and couplings, trade-offs and all, are all there is to reach. ## 5.9 Anesthesia · 98 *+ or − with 10, is.* **With 2-now-possibling.** Agents couple with a nervous system and responsiveness ceases, and a naming fixes consciousness as a content behind responsiveness. **With 12-next-co-same-existing.** Loss of consciousness fixing as a single state unresponsiveness indexes, a field stating a unitary mechanism as a falsehood, states not same-existing, each altering consciousness, arising by agent and dose through no common pathway. Selves report experience from under unresponsiveness after emerging, so an index and a within part by a field's own instrument, and a phase is several couplings rather than one state. **With 11-next-co-observing.** Many agents, no molecular site of action they share, one convergent quieting of a network's long couplings beside each agent's own signature, and a complexity index that tracks a quieting well. Selves report experience from under unresponsiveness after emerging, an outward side and a within parting by a field's own instrument: a single state unresponsiveness indexes is one coupling's outward side fixing as its within, and phases are couplings, several, each its own. ## 5.10 Skepticism about the external world · 101 *+ or − with 10, is.* **With 2-now-possibling.** Experience arises with couplings and a naming fixes a cause as a content behind it, with scenarios a field builds as indistinguishable. **With 12-next-co-same-existing.** Belief in a world fixing as needing a justification going from experience to its cause, a self believing it is not in a vat even if it were false and skeptical cases not modifiable to make it sensitive, their negations stably insensitive. A field builds scenarios to be alike with each observing, so not same-existing surfaces nought by construction. **With 11-next-co-observing.** Experience arises with couplings, arising a coupling's own. Scenarios are indistinguishable because a field builds them to be, transcendental replies stop with their own objection's standing, a semantic reply reaches its own reach, and a plain proof and its refusers go on reaching each other: a justification going from experience to its cause goes along an axis a coupling does not have, which a construction is there to show, and arising needs no route behind itself to arise. ## 5.11 Substance and bundle · 102 *+ or − with 10, is.* **With 2-now-possibling.** Properties couple and an object is present, and a naming fixes a bearer as a content beneath them. **With 12-next-co-same-existing.** An object fixing as decomposing as a bearer and properties, or only as properties, one being correct, a substratum basic only in an empty sense and a bundle's escape, a master property of which others are modes, filling a substratum's role, each account coming with an other's term. Verdicts part only with cases a field builds, decomposing there a case's own making. **With 11-next-co-observing.** Properties couple and an object is present, presence a coupling's own. A bare bearer has no character beyond its role, as its own defenders say; bundles strain with indiscernible pairs and strain has its answers; and verdicts part only with cases a field builds. An object fixing as decomposing divides a coupling as a bearer and what it bears, and a coupling is not two things: a centre has nothing, so all of it is with couplings across, and presence is a coupling momentarying, whole. ## 5.12 The quantum interpretation debate · 15 *+ or − with 10, is.* **With 2-now-possibling.** A formalism goes on and a naming fixes what a world is like as a content behind it, with interpretations empirically equivalent by construction. **With 12-next-co-same-existing.** Structure an interpretation adds fixing as a content predictions should reach, common core recipes for calculating probabilities of outcomes and interpretations not same-existing on what, if anything, each adds to it, evidence favouring none. Pattern-matchings are equivalent by construction, so each not same-existing a self measures surfaces nought, and its entry stands as an equivalence a proof holds, a nought's own shape, beside a resolving rather than one an instrument reaches. **With 11-next-co-observing.** A formalism goes on and gives each prediction alike with each pattern-matching, equivalence by its own construction. Theorems constrain which pattern-matchings survive which premises, paradoxes map who gives up which premise, and models that would not be same-existing are not so measurably, parting from pattern-matchings that cannot: a content fixing behind a formalism equivalent by construction reaches past bringing any prediction, and a formalism going on is a coupling doing all discovering there is. ## 5.13 Dreaming · 123 *+ or − with 10, is.* **With 2-now-possibling.** A sleeping self changes and changes back and dreaming goes on with it, and a naming fixes a function as a content within dreaming apart from sleep. **With 12-next-co-same-existing.** Dreaming fixing as separable from a state having it, a function identifiable by manipulating one, a field showing an equation of rapid-eye-movement sleep with dreaming inaccurate, a stage fixing as having a phase parting by a field's own instrument. Dreaming is a phase of a sleeping's own changing and changing back, and nought falls with a cutting of one living to two things. **With 11-next-co-observing.** A sleeping self changes and changes back and dreaming goes on with its changing and changing back, contents regular, a day's couplings coming again, lesion cases bounding a claim any story may make, and a lucid channel a coupling with a living itself. A function fixing within dreaming apart from sleep cuts one living to two things, and living is one: dreaming is a changing and changing back a self feels from within its own phase. ## 5.14 The Sapient paradox · 125 *+ or − with 10, is.* **With 2-now-possibling.** Capacity and expression couple within each population, and a naming fixes cognition as a content behind material culture. **With 12-next-co-same-existing.** Behavioural modernity fixing as a definable package whose archaeological signature indexes cognition, materiality, cultural practices and social interaction shaping mind throughout its trajectories, pattern-matching taking a capacity as prior to couplings that shape it. A record catches expressing with openings of preservation, so pattern-matching takes a record's own edge as a capacity's. **With 11-next-co-observing.** Capacity and expression couple within each population, and expressing rides couplings a population has: a record reaches back and back as looking comes closer, dense populations express a capacity sparse ones have and do not express, demographic readings under dispute and defence, and a package comes apart as a mosaic by a field's own reading. Cognition fixing behind material culture is a coupling's side fixing as a content, and couplings, demographic and living, do expressing. ## 5.15 The origin of language · 150 *+ or − with 10, is.* **With 2-now-possibling.** Communication couples with each exchange and language arises by coupling, and a naming fixes a capacity as a content within extinct populations. **With 12-next-co-same-existing.** Language fixing as decomposing as components whose presence is readable from material preservation keeps, fossil and archaeological evidence not informing computations and representations of the earliest ancestors, animal parallels virtually none and genetics not in prospect. Populations share with no between now, so observing is of a prior same-existing that cannot answer back. **With 11-next-co-observing.** Language arises by coupling with each exchange, making itself there, and fixing as not-changing within no one. Components exist with other animals, all but recursioning; a gene story reversing under its own evidence; pressure by its own breeds combinatorial systems within simulations; and anatomy indicates as far as anatomy indicates. A capacity fixing as a content within extinct populations is a making fixing as a possession, and a field's own mosaic finding is a package coming apart as couplings, exchange by exchange. ## 5.16 Riemann, Hodge, Birch–Swinnerton-Dyer, Yang–Mills · 153 *+ or − with 10, is.* **With 2-now-possibling.** With each, a proof holds an involution or a symmetry and couplings ride with its fixed set. Pattern-matching takes a fixed set as a place: a line zeros sit on, a balance really algebraic, a centre two counts couple about, a gap to leap. **With 12-next-co-same-existing.** That a fixed set is a location an object occupies, each of four posing with a seat a symmetry with its proof already rides, deviation from primes' average, a mass gap with suggesting and no proof, how much topology is definable algebraically, a simple way to tell finiteness. A zero is a coupling, a zeroing, and a symmetry pairs its zeros about an axis of balance, seating none on it by itself. A self recognises an axis and does not derive it, and nothing more basic than a symmetry with its proof stands to derive a seating from. **With 11-next-co-observing.** No one defends a second position with any of four. Each functional equation stands, with its proof. Complex conjugation stands. Gauge symmetry stands. Each conjecture stands with its own falsifier stating it, its field with no proof of it, and none of this touches its truth value: a symmetry pairs zeros about its axis and forces none onto it, a pair off it being one a symmetric set can have, and gauge symmetry constructs no quantum Yang–Mills theory and proves no mass gap, so a seating with a fixed set is a framing here and no proof. ## 5.17 Underdetermination of theory by evidence · 13 *+ or − with 10, is.* **With 2-now-possibling.** Evidence arises with couplings, and a naming fixes a theory as a content behind it, with rivals constructible that entail same consequences. **With 12-next-co-same-existing.** Evidence fixing as selecting by its own, a failure to select a defect of some term, a contrastive challenge, more than one account of otherwise inaccessible workings behind phenomena, parting from a holist one, and a Craigian reduction a field shares as an equivalent and judges a change of fundamental subject. Rivals a field constructs entail same consequences by construction, so selecting surfaces nought with each consequence a self derives. **With 11-next-co-observing.** Evidence arises with couplings and couples whole, holism an honest logic of it. Rivals a field constructs exist and mostly stay constructions, histories resolve as a self observes more couplings, and virtues work as criteria in use with their deeper standing in dispute: a theory fixing behind evidence as one thing a selecting picks waits on a selecting couplings do not promise, and choosing goes on at couplings, a self observing them one by one. ## 5.18 The interpretation of probability · 158 *+ or − with 10, is.* **With 2-now-possibling.** Probability exists with couplings, as a taking of parities and a swaying of frequencies, and a naming fixes its being as a content behind a calculus that fits each pattern-matching by construction. **With 12-next-co-same-existing.** A formalism's success fixing as reaching past its formalism to one pattern-matching, no candidate satisfying admissibility, ascertainability and applicability whole, a classical pattern-matching finite only and a frequency pattern-matching not even a field, while a calculus holds all of them. One calculus holds each pattern-matching alike, by its building, so no not same-existing a self measures parts them. **With 11-next-co-observing.** Probability exists with couplings, as a taking of parities and frequencies swaying, and one calculus holds each pattern-matching alike, by its building. Theorems represent and converge for each side by its own terms, a single case strains one pattern-matching and priors strain an other, and an instrument they share gives no verdict between them: probability's being, fixing behind a calculus, reaches past what a calculus holds, and its existing is a taking of parities and frequencies swaying, both, with their couplings. ## 5.19 The ontology of mathematics · 161 *+ or − with 10, is.* **With 2-now-possibling.** Mathematics lives with each proof and each application, and a naming fixes existence as a content behind a practice invariant under pattern-matchings. **With 12-next-co-same-existing.** A practice's success fixing as reaching past its practice to a thing standing behind it, truth-values depending on entities beyond space and time, causally apart from us even in principle, causal isolation a field's own name for identical observing. Practice goes on identically under each pattern-matching of a thing standing behind it, which is this part's own showing at its plainest. **With 11-next-co-observing.** Mathematics lives with each proof and each application, and practice goes on identically under each pattern-matching of a thing standing behind it, a field's own record. One horn reaches for an access nothing stands to give, an other rebuilds practice partway and stops, and a middle inherits a dispute its building is to escape: existence fixing behind an invariant practice is a content a practice does not consult, and a living practice is a coupling, proof by proof, application by application. ## 5.20 The mechanism of high-temperature superconductivity · 157 *+ or − with 10, is.* **With 2-now-possibling.** Electrons pair with their couplings and an anomalous normal state exists above, and a naming fixes a mechanism as a content behind pairing, a glue one channel's own. **With 12-next-co-same-existing.** A minimal model fixing as reaching materials, which is a model fixing as a thing it models. A field's best methods disagree on a model's ground state for relevant parameters, by a field's own multi-method benchmark, and a model-versus-material gap stands, same benchmark stating it. **With 11-next-co-observing.** Electrons pair with their couplings, its symmetry a field knows, a field mapping a phase diagram family by family, stripes standing as a minimal model's own low-energy life, a field identifying a glue within a model and stating it as within it, and cold atoms coming as a fresh instrument with same self-bounding. A mechanism fixing behind pairing as a glue one channel's own fixes a coupling's making as a content, and a field's own summary has a superconducting state a field understands beside a normal state existing with no resolving, a middle floating as a naming reaches for a thing.   --- ## 5.21 The single native state · 178 *+ or − with 10, is.* **With 2-now-possibling.** A chain sways with its own couplings, folding and re-folding, and a naming fixes a native state as one conformation a sequence determines and a measurement reports. **With 12-next-co-same-existing.** A sway fixing as a state, ensembles fitting data better than single structures across twenty datasets and a substantial fraction of proteins functional with no single structure at all, a self measuring a sway better than a state. Many models fit same data equally and a field's own ensemble refinement gives distributions without resolving among them, so degeneracy a self measures is a sway showing with an instrument. **With 11-next-co-observing.** A chain discovers its own foldings, one at a time, each dissolving and coming again. A crystallographic model is one set of coordinates fitting data averaging over many molecules, and many models fit that data equally — a field's own ensemble refinement giving distributions consistent with same measurement and not resolving among them. With a wide sway a field has a name for it, and regions take no single structure to any resolution a field reaches, functional as they are. A prediction training on single structures a field deposits gives single structures by construction, so a single state comes from depositing and not from a chain. Degeneracy a self measures is a sway showing with an instrument, and a state a field seeks is a thing an observing of it gives. A prion is one sequence with two folds, each going on by its own couplings, so a fold is no sequence's one determining. ## 5.22 Evidence for neural representation · 219 *+ or − with 10, is.* **With 2-now-possibling.** A neural population couples with a world and with its brain's other parts, activity by activity, and a naming fixes a content as standing behind its activity, a feature a state is about and not merely with. **With 12-next-co-same-existing.** Aboutness fixing as what pattern-matching takes from activity as its content. Decoding and correlation establish sensitivity but can succeed for information an organism does not use, and representation claims also require specificity, invariance and a role for downstream systems, rarely establishing together; four part and common methods each evaluate one, so sensitivity a decoding gives and representation a field seeks are not same, other dimensions standing between them: a probe recovering a thing a momentarying does not use, the showing of systems a field builds coming again with a brain, and content itself an interior a demanding fixes. **With 11-next-co-observing.** High-dimensional population codes, causal perturbation methods and four separable evidential requirements stand articulate and testable; encoding and decoding establish sensitivity under a sampling distribution, similarity analyses compare geometry with content interpretation still a requirement, invariance tests challenge nuisance dependence over transformations a test declares, perturbations test downstream use, and dynamical explanations predict trajectories without assigning content, a fourth account needing no content besides dynamical and causal organization: a content fixing behind activity is a coupling's momentarying fixing as a thing it is about, and four requirements pattern-matching together pattern-match a coupling with its own uses, a population coupling downstream, with which content a self observes from beside makes itself, use by use, and is no keeping. ## 5.23 Detecting covert consciousness · 220 *+ or − with 10, is.* **With 2-now-possibling.** A self couples with its own between whether or not a movement goes across it, and a naming fixes its awareness as something a test should establish from beside, a within pattern-matching takes off a response. **With 12-next-co-same-existing.** A within fixing as readable from a response that fails. Motor output can fail while command-following brain activity remains, bedside behaviour fluctuates, imaging and electrophysiological tasks have false negatives and interpretation requirements, and no single test detects all conscious patients; a field grades covert consciousness as possible, probable or with confirming, by nature and strength of test results, so results a test gives and an individual's awareness a field seeks are not same, a grade of confidence standing between them: a felt middle a field asks for from beside, and nothing presenting itself for reaching not being nothing there, and that is false negatives. **With 11-next-co-observing.** A substantial minority of behaviourally unresponsive patients show command-following brain activity and standard multicenter paradigms now exist; bedside scales, again and again, depend on motor output and arousal, imaging command-following supplies strong positive evidence with transport and false-negative limits, an electroencephalographic version is more deployable and method-sensitive, task-free complexity measures remain under individual validation, and multimodal assessment raises detection while leaving discordant cases, a third account requiring assessment again and again because consciousness and arousal fluctuate and each instrument samples another capacity: an awareness fixing as what one test establishes from beside is a within fixing to a response, and each positive is a coupling a self makes with its reaching of a task, a self's own between nothing reaches, a self answering, test by test, and so a grading rather than a deciding. ## 5.24 The solar dynamo and the sunspot cycle · 254 *+ or − with 10, is.* **With 2-now-possibling.** Sun's poloidal and toroidal fields sustain each other with their couplings, a central idea of a dynamo, reversing each eleven years, and a naming fixes a dynamo as a mechanism behind a cycle, models giving it a location. **With 12-next-co-same-existing.** A mechanism fixing behind a cycle, to a place nothing observes. Toroidal field of a convection zone's bottom, where models place its generation, no self observes, and how that field produces flux ropes that become sunspots remains perhaps the most severe missing link between models and observations; ten issues of contention stand around leading models: a content middle, a mechanism a field asks for of one place, a coupling nothing reaches, beside 5.20's pairing. **With 11-next-co-observing.** Helioseismology uncovers a tachocline, global simulations reach solar-like reversals, a crucial role of a surface field stands firm, a field uses flux-transport models for cycle prediction and mean-field models give dynamo waves, and cycle-prediction schemes run on precursors: a dynamo fixing as a content behind a cycle is two fields' sustaining of each other fixing to a mechanism and a location, and sustaining is a coupling itself, a poloidal and a toroidal each regenerating an other with its own momentary, a self observing it from flows and not from a place. ## 5.25 Coronal heating and solar-wind acceleration · 191 *+ or − with 10, is.* **With 2-now-possibling.** Energy goes from a surface to a corona and outward as wind with couplings of fields, waves and particles, and a naming fixes a mechanism as a content behind heating, giving it a region between imaging and sampling. **With 12-next-co-same-existing.** A mechanism fixing to one region no instrument reaches. Instruments measure wind directly from 0.3 astronomical units outward and image an atmosphere from a photosphere outward through a corona, while a region where internal, magnetic and turbulent energy channels into bulk energy of supersonic wind lies between and requires in situ observation; heating and acceleration go through magnetic, turbulent and kinetic processes coupling, over scales selves observe separately with two instruments, and multiple mechanisms produce overlapping temperature, wave and flow signatures: a content middle on a record's edge, and which mechanism among several a two-way pattern-matching one-way, on record as its second. **With 11-next-co-observing.** Probes measure near-Sun fields, particles, waves and switchbacks directly, and candidate mechanisms now face energy budgets resolving by species; wave and turbulence measurements show transport and dissipation with a dominant channel varying by region, reconnection and nanoflare searches detect impulsive events with a budget open, not resolving, composition tracing links wind parcels to coronal conditions without a unique source map, and near-Sun sampling reduces a propagation interval while remote-to-local uncertainty stays; a fourth account has a wind a self measures resulting from mixtures whose weights vary across magnetic structures: a mechanism fixing as a content between instruments is a going fixing to a place, and a going makes itself with each coupling along a way, region by region. *Second seating: which mechanism among several, a two-way fixing to one side, part 9's naming.* # 6 A parity fixing as a magnitude — 7-is-now-observing and 15-is-next-observing *A number or a level fixing as governing. A number is a position, a sequence a self takes as standing, one stepping on from a last, and governing belongs to a selection, a parity a self takes with a between, of no size. A magnitude fixing to a middle is a strict inequality a self writes as an equality, and an inequality changes and changes back where an equality sits.* **And a field's own settling-condition with this part is a re-asking of a magnitude**: a measure whose interpretation is stable, a standard incidence, a concept both accounts accept, a measurement with all else not changing. Each is naming stating itself as its own settlement, which is a field's account of its own hardness, a self observing it with a place it enters. **And a word fields reach for here is paradox.** Measure it, get a wrong number, and a wrong number is a paradox: a two-fold cost, a genome's excess, a whale's missing cancers, a rise that reverses, a nominal response, a mixing that jumps. With each, arithmetic is exact and naming is of surprise, which is where a naming supplies a size. **One word goes to other parts too and is another tip each time**: a closure over a tail, an opening that goes on opening, a fraction no search reaches, a reversal pattern-matching takes as a level. So a word is a field's local feel and naming is form, and where two part, parting shows which. **And a magnitude enters three places, one with each of a coupling's own.** With selecting, where pattern-matching takes a parity a self takes with a between as a level to govern. With an instrument, where a window, a criterion, a sample or a scale has choosing in it and gives it back as an object's. And with a total, where a naming fixes a sum over couplings an accounting cannot reach. Three pattern-match alike from beside and part with a putting of a size. ## 6.1 Goodhart's law · 30 *+ or − with 10, is.* **With 2-now-possibling.** A measure and those it measures couple, and a naming fixes a measure as governing, a level fixing across instances a self discovers next. **With 12-next-co-same-existing.** A relation a field estimates over past instances fixing over instances a self is not yet discovering, acting on it not altering it: a regularity that breaks down when it ceases to be an ex post observation and becomes an ex ante rule, and no one ever making a fair test, countries whose relations stand most stable being ones that choose targeting. Instances after its assertion are next-existing, not now-existing, and two antagonistic movements, gaming climbing and correction pressing back, come to nought with a level fixing. **With 11-next-co-observing.** A measure and what it measures couple, each observing taking its own parity of no size, and a relation makes itself again with each observing, none governing it. With a targeting, each proxy bends same way with each domain that tries it, composites relocate bending, and honest mechanisms exist only within restrictions a proof holds, same wall standing with incoming number 141 and a self reaching it again with incoming number 131: a level fixing as governing is a number fixing over selecting, and couplings go on, a self observing them, past each number fixing over them. ## 6.2 The Easterlin paradox · 80 *+ or − with 10, is.* **With 2-now-possibling.** A self takes wellbeing with a between as a parity, and it is a level comparable across populations and times on a scale with bounds. **With 12-next-co-same-existing.** Wellbeing selves report fixing as measuring a quantity comparable across persons and times, a paradox standing over a long term and critiques' positive relation a short-term one a field confuses with it. A scale with bounds has two not-changing terms together, a rest a sequence opens from and a last it completes with, and re-anchoring is where a sway passes its own zero and a scale pattern-matches it as motionless. **With 11-next-co-observing.** Wellbeing is a parity a self takes with a between, one at a time, each self's own. Within a place parity rises with means, across places and times a scale re-anchors under each self's own living, evaluative and felt part company, and re-anchoring rungs moves whole rankings: a level comparable across selves and times is a parity fixing to a size, and corrections measure exactly where a naming supplies a size. A field's own name for coming back as sway is a treadmill: a happiness a self seeks as a level and living as a changing and changing back. ## 6.3 Allais and Ellsberg · 81 *+ or − with 10, is.* **With 2-now-possibling.** A preferring is a parity a self takes one at a time, and it is a magnitude an axiom set governs. **With 12-next-co-same-existing.** Axioms fixing as stating a standard, with acceptance on reflection as a criterion, and no one finding a basis for asserting that a decision-maker who violates them will in the long run reach worse outcomes than by conforming. A preferring is a parity no other self supplies and no criterion reaches, so an axiom set standing over it is one self's parity it gives to all, and a parity it gives to all is no longer a parity. **With 11-next-co-observing.** A preferring is a parity a self takes one at a time, each its own. Patterns stand with each reaching of them, ambiguity has its own representations, a body registers what is not same-existing, and selves a field shows axioms revise partway and stably stand by their others: an axiom set fixing as governing takings, parities composing as a magnitude, and takings stand their own under reflection, which is a parity declining to become a size. And a settling a field asks for, agreement on what settles a normative question empirically, asks a momentarying for a standing's answer, which is same asking an is-and-ought observing has with part 2. ## 6.4 The productivity paradox · 83 *+ or − with 10, is.* **With 2-now-possibling.** Output arises with couplings and is a total including a making accounts do not price. **With 12-next-co-same-existing.** A true productivity change fixing behind statistics pricing reaches, which approximate it, where service transactions are idiosyncratic and not subject to statistical aggregation, pricing not reaching couplings. A naming fixes a total over couplings pricing does not reach, which is an account standing fixing for a making it removes before it can balance. **With 11-next-co-observing.** Output makes itself with couplings, and pricing reaches couplings it prices. A slowdown goes wide across countries and sectors, gains settle where organisations re-couple around tools, mismeasurement adds up short of a gap, and a lag stays available and nothing reaches it: a true total including what has no price is makings a self sums where no ledger reaches, and a shortfall a self measures is a reach of pricing, exactly. ## 6.5 Money illusion · 85 *+ or − with 10, is.* **With 2-now-possibling.** A self takes a parity with a nominal presentation, and it is a response to a magnitude, nominal or real. **With 12-next-co-same-existing.** A fact fixing about which magnitude an agent responds to, apart from presenting, where nominal and real representations both operate and interact, a bias falling toward nominal: two with presenting, and not one governing. **With 11-next-co-observing.** A self takes a parity with each presenting, a coupling's own. Frames move takings, cuts of a number in print stay rare, salient inflation thins an effect just as both accounts expect, and anchoring shows with transactions, its liquidity stories beside it: which-magnitude-governs is a taking fixing to a size, and a taking pattern-matches its own conditions with each occasion, presenting by presenting. ## 6.6 The two-fold cost of sex · 86 *+ or − with 10, is.* **With 2-now-possibling.** Recombination and parasitism and mutation go on together with each generation, and maintenance is a benefit exceeding a cost a field states. **With 12-next-co-same-existing.** A cost a field states correctly as two-fold, an advantage repaying it each generation, where cost depends on number of males a population produces and a ratio leaning female reduces it below two, two-fold a ledger's number and not a coupling's. Offspring of a coupling are a coupling's own, arising in neither side alone, so a cost a ledger lays against one side holds an abundancing that is not one side's alone. **With 11-next-co-observing.** Recombination goes on with each generation's couplings, and couplings answer many ways together: asexual lines ratchet their losses, parasites chase whichever is common, recombining populations adapt faster where a field measures it, and an exception on record exchanges. A two-fold a field states is a ledger's comparison, and maintaining goes on with couplings a ledger fixes as not-changing, generation by generation, repaying nothing because nothing is a loan. A self observing them as parities, two ways part cleanly: recombining is a coupling across with a particular other, and an asexual line is a self and all other, coupling across with none. Aphids and water fleas clone through a season and recombine where crowding or a season's turning comes, so maintaining is couplings answering what comes, generation by generation. ## 6.7 Peto's paradox · 87 *+ or − with 10, is.* **With 2-now-possibling.** Cells and their tissues, each a same-existing-society, couple with each division, and risk is a number governing incidence across species. **With 12-next-co-same-existing.** Cancer risk fixing as a function of cell number and division rate, comparable on one measure across species, an expectation a field derives from a premise that every cell has some chance, its premise being a number fixing. Living machinery is identical for each size and has no size axis, so a number across species measures co-chaining rather than risk. **With 11-next-co-observing.** Cells couple within their tissues, each a same-existing-society, with each division, and each same-existing-society is its own order: whales hold their trillions lightly, guarding genes duplicate lineage by lineage, within a species a count shows and across species it goes quiet, and cells part by their own sensitivities besides. Risk as a number across species is couplings fixing to cells' number, and quiet cross-species scaling is same-existing-societies' couplings standing where a naming fixes a number as governing. ## 6.8 The C-value paradox · 88 *+ or − with 10, is.* **With 2-now-possibling.** Sequence and organism couple, and function is a fraction a criterion measures. **With 12-next-co-same-existing.** Functional fixing as having one criterion, with agreeing before a self takes a measurement, where evidence favours a causal link between bulk DNA amount and cell volume, function with bulk and not with sequence, a fraction of sequence fixing as holding what a whole amount holds. Two instruments each observe with their own coupling and give back fractions far apart, which is instruments parting rather than a fraction being missing. **With 11-next-co-observing.** Sequence and organism couple, and a coupling answers each instrument by its own terms: activity gives back one fraction and conservation another, far apart, disagreement standing; deletions tolerate where they tolerate; and genome size rides population size. Function fixing as one fraction is one criterion fixing over two instruments each observing with its own coupling, and a fraction is not one thing to measure. A genome's length has its copyings, doublings and repeats, each coming with its own pace, so a length is its prior same-existing's record and no fraction of function. ## 6.9 The Gibbs paradox · 108 *+ or − with 10, is.* **With 2-now-possibling.** Mixing happens with a coupling, and entropy is a magnitude belonging to a system apart from a separable. **With 12-next-co-same-existing.** Entropy fixing as a property of a system rather than relative to an operation set, a field taking a classical paradox as unmysterious, a step between separable and not, and a third puzzle a question about interpretation of entropy quite generally. Distinguishable-or-not is a parity and a parity has no partway, so a discontinuity as a self makes gases more alike is a parity itself and not a gap of probing. **With 11-next-co-observing.** Mixing happens with a coupling, and numbers come right when they are a coupling's own. Gases that history cannot part mix for free until a self can part them, and a resource showing makes operations explicit, stating relativity precisely: entropy fixing as a system's own apart from a separable is a coupling's term fixing as a possession, and operations a self can do are where a magnitude is momentarying. ## 6.10 Ecological stability and diversity · 118 *+ or − with 10, is.* **With 2-now-possibling.** Species couple and a community persists, and stability is a magnitude one variable measures. **With 12-next-co-same-existing.** Stability fixing as a single property with one measure, with agreeing before measuring, definitions of stability parting as a section of their own and weak interactions damping strong a mechanism a field proposes, a concept parting and a mechanism a sway. Variables move ways not same-existing on same plots, which is one form a self observes two ways rather than one property a self measures twice. **With 11-next-co-observing.** Species couple and a community persists by its couplings. Same plots on same continents give back rising steadiness of a whole and level steadiness of parts, random matrices tip past the line a proof holds, and a portfolio has a share a self measures: stability fixing as one magnitude is one measure fixing over a community's many couplings, and couplings answer each naming its own, level by level. Aggregate steadiness rising while population steadiness stands is a same-existing-society gathering its selves, each self with its own, which is a portfolio share's measuring. ## 6.11 The Flynn effect and its reversal · 126 *+ or − with 10, is.* **With 2-now-possibling.** A person and a test couple, and a score is a level of a construct comparable across cohorts. **With 12-next-co-same-existing.** Tests fixing as measuring one construct across cohorts, score change indexing construct change, gains varying by domain and by age, a self observing one construct not same-existing with each coupling. Invariance breaks between cohorts as often as a self checks it, so an instrument's own coupling with its world is within each comparison a self draws across them. **With 11-next-co-observing.** A person and a test couple, and a coupling drifts as a world a person couples with drifts. Invariance breaks between cohorts as often as a self checks it, a rise concentrates where a construct loads least, and a reversal exists within families, setting composition aside for that population: a level of a construct comparable across cohorts, a coupling fixing as not-changing where a coupling goes on momentarying, and scores are observings of their own occasions. ## 6.12 Benchmarks · 131 *+ or − with 10, is.* **With 2-now-possibling.** A system and a benchmark couple, and a score is a level of a capability apart from a coupling. **With 12-next-co-same-existing.** A benchmark fixing as sampling a capability apart from what a system trains on, datasets distinguishable from one another, each embodying its own style of capturing a segment of a world, and a fault of construct validity a field places with framing as general measures. Leakage to training data comes back as scoring, so an instrument is within a thing a self observes with it, and a capability fixing apart from a coupling no observing reaches at all. **With 11-next-co-observing.** A system and a benchmark couple, and a score is a coupling's own making. Leakage to training data comes back as scoring, saturation comes and a benchmark retires, transfer thins away from a coupling a scoring took, and deployment itself is strongest of observings remaining, confounding and standing: a capability fixing apart from a coupling is same wall as with incoming number 30 and incoming number 141, a self reaching it with an instrument whose building is to escape it. ## 6.13 Brooks's law · 133 *+ or − with 10, is.* **With 2-now-possibling.** People couple as a project adds them, and an effect is a magnitude from a number of people with all else not changing. **With 12-next-co-same-existing.** Coordination cost fixing as a function of team size with a work's partitionability fixing, where cost is always up and a delay comes only under a degree of sequential constraint among tasks, constraint being a coupling structure fixing as a law. A joiner brings a scale of its own or brings what a whole already has, and a whole thins with a momentary a scale they share couples, which is a parity a self it couples with answers, and not a number of people. **With 11-next-co-observing.** People couple as a project adds them, each joining opening couplings with each one standing, and couplings are cost and capacity together. Overhead shows with each measuring of it, modular work turns joinings to output where design thins couplings, and diseconomies a field fits fit couplings that run: an effect fixing from a number, all else not changing, fixes as not-changing exactly a coupling structure an adding re-couples. Modular work is coprimality by design, a beat they share is where capture enters, and a late joiner bringing a scale only it has adds most of anyone, which a number of people pattern-matches as noise. ## 6.14 Grandmother cell and distributed coding · 147 *+ or − with 10, is.* **With 2-now-possibling.** Neurons couple within a population and a concept is present, and sparseness is a magnitude a recording measures. **With 12-next-co-same-existing.** Recording fixing as sampling a population without bias, pattern-matching taking sparseness off a sample, a recording group itself declining a grandmother cell a self could in principle take its own cells for. Screening finds a screening's findings, so a sample's own coupling stands within each sparseness a field reports. **With 11-next-co-observing.** Neurons couple within a population and a concept is present as coupling. Cells answer one face across photographs, drawings and a name in print, populations hum broadly and weakly where sampling widens, screening finds a screening's findings, as its authors word it, and both codes stand efficient under their own constraints, with proofs: sparseness fixing as one magnitude pattern-matching takes off a sample fixes a population to its instrument, and presence is a coupling's, with any sparseness of its showing. ## 6.15 The limits of intelligence · 172 *+ or − with 10, is.* **With 2-now-possibling.** Competency is a middle, discovering-momentarying-between, uncapturable and of no size, and a naming fixes a limit of it as a magnitude, artificial and human together. **With 12-next-co-same-existing.** A middle fixing as having a limit statable over it. No canonical formulation stands, no one maintaining it, and no one defends a second position, so no pair stands here to observe from, which is a standing with a substrate's own stating rather than a resolving of its own. **With 11-next-co-observing.** Competency floats, a middle no observing enters, and each limit that binds binds a side: computational limits bind computations, a physical thesis of incoming number 168 binds realizings, learning-theoretic results bind seatings fixing ahead. A limit fixing of a middle as one magnitude fixes a floating of no size to a number, and a substrate itself does not state one statement, which is its own showing: components exist with their own observings, and a middle goes on floating between them. *Released at Hard Problem Registry at v342: no canonical formulation stands and no account is defended, an entry's own record having been its only reference and its formulations plural against a first condition prior; its text stands whole at an appendix of v342 session at Hard Problem Registry, its number retired and not reused. Observing here, that no pair stands to be observed from, pattern-matched its release before Hard Problem Registry made it, and stands.*   --- ## 6.16 Proton spin decomposition · 183 *+ or − with 10, is.* **With 2-now-possibling.** A proton's spin is a parity, one half it takes with its own momentary, and it is a magnitude dividing among four contributions, each a share of a whole. **With 12-next-co-same-existing.** A whole fixing as apportioning among its parts by one accounting. Gauge-invariant splitting is possible but not unique, separate terms depending on a decomposition, a gauge treatment and a scale, and which choice is a natural one standing as a question; experiments constrain integrals not same-existing over incomplete ranges rather than measuring all four together, so shares are an accounting's own and a sum rule closes under whichever accounting a self chooses. **With 11-next-co-observing.** A field knows quark helicity does not saturate spin, a growing range constrains gluon helicity, several gauge-invariant sum rules stand, and each instrument gives back its own terms, scattering its helicities over momentum fractions a self measures, generalized distributions their totals through sum rules, a lattice decomposition-dependent matrix elements, models all terms within their truncation: a parity of no size fixing as a magnitude for apportioning is one-half fixing to a ledger, and a ledger balances under each decomposition, a splitting not unique, spin a coupling's own and shares an accounting's. *Second seating: a line a self draws between spin and orbital is a cut fixing of a continuum each decomposition draws its own way, part 10's naming.* ## 6.17 The absolute neutrino mass scale · 186 *+ or − with 10, is.* **With 2-now-possibling.** Neutrinos oscillate with their couplings, differences of their squared masses measured exactly, and masses themselves are magnitudes each instrument should give back. **With 12-next-co-same-existing.** A scale fixing as what pattern-matching takes off instruments, a self observing with each a sum of its own. Oscillation depends on differences and is exactly insensitive to a common offset, and direct kinematics, cosmology and lepton-number-violating decay each give back their own aggregate under their own assumptions, an effective mass, a sum, a combination weighting phases, oscillation measurements shedding light neither on scale nor on mechanism: each instrument's number is that instrument's coupling, and a scale a field demands is one thing no coupling gives back by itself. **With 11-next-co-observing.** A field measures two splittings and substantially bounds a scale physics allows, an endpoint bound direct and model-light, a cosmological bound tighter and model-dependent, a decay bound conditional on its process obtaining: individual magnitudes fixing as what pattern-matching takes off aggregates are each coupling's own aggregate fixing to a number none of them has. ## 6.18 The mechanics driving plate motion · 199 *+ or − with 10, is.* **With 2-now-possibling.** A plate moves where its slab, its ridge and its mantle beneath it couple, one motion arising among them, and forces are magnitudes an apportioning gives, each a share of a motion a self observes. **With 12-next-co-same-existing.** A share fixing for each force. Determining a balance remains one of the ultimate goals of modelling, a field understanding its relative importance incompletely; higher basal drag beneath larger plates offsets higher slab pull for older ones, which explains a missing correlation a reading of drag as minor rests on, and whether faster speeds come from more pull or more drag stands unclear, a trade-off a fitting finds: a two-way fixing to one side, a self asking it for its proportion, coming to a parity fixing as a magnitude. **With 11-next-co-observing.** Slab pull, suction, ridge potential and basal traction all have quantitative formulations, geodesy fixes net motions precisely, torque balances estimate force sets conditional on viscosity and coupling, velocity correlations support slab forcing without dividing pull from flow, and tomography connects slabs to circulation under nonunique parameters; a fourth account has plates and mantle one convective boundary-layer system in which no single force acts independently: shares fixing of forces that couple are one motion fixing to a ledger of contributions, and a motion is a coupling's own, a self measuring it, contributions an accounting's, a fitting trading them off. *Second seating: pull against suction, a two-way fixing to one side, part 9's naming, relocating here when a self asks it for its proportion.* ## 6.19 The magnitude of the Great Oxidation Event · 203 *+ or − with 10, is.* **With 2-now-possibling.** Oxygen passes a threshold rocks record, a parity a self takes from sulfur isotopes, and a passing is a magnitude, how high and how variable abundance rises. **With 12-next-co-same-existing.** A level fixing as what pattern-matching takes from proxies that record a passing. Threshold-sensitive proxies define an event, most bounding oxygen indirectly for reservoirs and times not same-existing and altering after deposition, loss of mass-independent fractionation fixing a floor more securely than an abundance; and despite many new tools a defendable range spans orders of magnitude, a revisiting asking how great Great Oxidation was: a parity pattern-matching takes for a magnitude a parity does not have. **With 11-next-co-observing.** An onset interval and an irreversible loss of a sulfur signature stand firm, distinct atmospheric and oceanic histories stand in representing, a tempo stands as oscillations passing a threshold several times before an irreversible rise; trace metals and chromium give redox constraints under weathering models, iron formations map local conditions, and modelling translates proxy combinations to ranges under uncertain fluxes: a passing fixing as a level is a parity fixing to a size, and a record gives back passings, each its own coupling, abundance between them a range spanning orders. # 7 A sequencing fixing to one beat — 4-now-co-same-existing and 12-next-co-same-existing *One frame, clock or ordering fixing over couplings. Each self paces its own changing and changing back and synchronizes with its own couplings, and a beat fixing over them is a term no coupling makes. Now is one, each coupling sharing it and each coupling's own, and a momentary is one now a sharing has.* **Each ordering here is one beat fixing over couplings that each pace their own**, and one observing is that momentarying a self reaches with a substrate rather than argues: slicings part with coupling selves, to any precision a self measures. **And a beat comes with four positions, three of them easy to miss.** Its pace, where a rate a self gives, rather than its own, opens a coupling. Its momentary, since anything having couplings one after another takes them by some order, and two couplings with no between have no order between them. Its record, since a trace a tick they share indexes is a beat within recording however clockless a momentarying. And its between, where a self gives one coupling's positions a correspondence with another's so parities can couple. Several observings of this part name a beat with a record and with a between rather than with a pace, and so they pattern-match as measurements disagreeing. **And where a field proves no ordering reaches its own conditions, a field proves naming empty.** Three stand here and a fourth stands with part 9, each by its own arithmetic: rankings over profiles, rankings over outcomes of unequal number, structure surviving aggregation. Each is a bounding a field draws and a settling it sounds — a whole no self orders, coming as a field's own theorem. ## 7.1 Simultaneity and the present · 28 *+ or − with 10, is.* **With 2-now-possibling.** Each self sequences its own beat and synchronizes with its couplings, and a naming fixes one slicing as a real one, fixing over all. **With 12-next-co-same-existing.** One slicing fixing as correct, a question fixing as which, absolute simultaneity a backdrop against which a field supposes one plane uniquely important, where each inertial frame picks out its own simultaneous points. A reconstruction adding a frame with a privilege reproduces each prediction, so two come to nought with each not same-existing a self measures. **With 11-next-co-observing.** Each self sequences its own beat and synchronizes with its couplings. Slicings part with coupling selves to any precision a self reaches, no law a test reaches has a frame with a privilege, sky's own rest frame is measurable and privileges nothing dynamically, and a slicing a theory prefers, hiding, survives only by arranging itself so that no measurement reaches it: one slicing fixing over them is a term no coupling makes, and a slicing surviving only as no measurement reaches it is naming a self places where nothing observes it. ## 7.2 Aggregation of preferences · 5 *+ or − with 10, is.* **With 2-now-possibling.** Selves each take their own parity, and a naming fixes one social ordering as a ranking over them, with independence excluding a comparing's own making. **With 12-next-co-same-existing.** Aggregation fixing as a function only from ordinal profiles, independence standing, where no procedure reaches its conditions and relaxing an ordering yields, case by case, an oligarchy, a seat above coming where a rule lets a whole ordering go partway. A condition requires a pair's social ranking to depend on that pair's own rankings, and a proof goes on by altering one self's ranking with all others not changing, which is naming performing within an instrument that finds it. **With 11-next-co-observing.** Selves each take their own parity, one at a time, and a same-existing-society co-competences without a whole ordering over it. Five exact theorems close each rule over bare rankings, preferring with a single peak opens a closure's allowing, chance escapes by not ranking, and judging aggregates no better than preferring: one ranking fixing over selves is a whole no self orders, fixing as if some rule could, and theorems are a field proving naming empty, five self-boundings, each shutting from within. A closure leaves standing a living there prior to it: each self preferring with its own between, one at a time, and a same-existing-society co-competencing without a whole ordering over it. ## 7.3 The problem of time in quantum gravity · 66 *+ or − with 10, is.* **With 2-now-possibling.** Sequencing is each coupling's own momentarying, and a naming fixes time as a parameter over a whole, external or absent. **With 12-next-co-same-existing.** A quantum theory fixing as needing a time parameter over its evolution, schemes parting three ways, a scheme identifying time before quantising, after, or time playing no fundamental role at all, a third with its parameter dissolving. No experiment reaches its regime, which is a record's edge, and countings go on same either way. **With 11-next-co-observing.** Sequencing is each coupling's own momentarying. A whole's equation has no clock, a familiar flowing comes again with a limit, a regime familiar things exist within, and conditioning on a clock subsystem recovers evolution relative to that clock, a self observing time with a coupling: a parameter fixing over a whole is countings fixing to a beat none makes. Sequential momentarying has no time term: a sharing chaining with each coupling is not none again, and a momentary completes with a next opening, each side with its own momentary; time there is momentarying, and a field's own equation shows it by having no clock. ## 7.4 Skolem's paradox · 69 *+ or − with 10, is.* **With 2-now-possibling.** Axioms and models couple, and a naming fixes cardinality as absolute, fixing over each model. **With 12-next-co-same-existing.** First-order axioms to fix their subject matter absolutely, where notions turn out unavoidably relative once first-order model theory characterizes them, an element uncountable from one perspective and countable from another. Each model pattern-matches its own countings with its own between, and pattern-matching takes an uncountable-within from a bijection a model having it does not itself have. **With 11-next-co-observing.** Axioms and models couple, and each model makes its own countings: same axioms hold with a countable world and with an uncountable one, an uncountable-within pattern-matching takes from a bijection a model does not have. Cardinality fixing as absolute over each model is one measure fixing over couplings each model makes, and a field's own theorems answer naming, categorical repairs presupposing exactly a measure they promise. ## 7.5 The simulation hypothesis · 104 *+ or − with 10, is.* **With 2-now-possibling.** Observings arise with couplings and a naming fixes them as countable across levels fixing to one ordering. **With 12-next-co-same-existing.** Observings fixing as countable across levels, experience fixing as substrate-independent, an argument assuming both, and an indifference principle a premise an argument itself must support separately. A count across levels is a beat fixing over selves that each observe from their own position, and levels themselves are not possibly existing. **With 11-next-co-observing.** Observings arise with couplings, each from its own position. An argument forks and its own statement is only that it forks, lattice signatures a field proposes give nothing, and observer-counting reasoning has paradoxes with each use of it, an instrument measuring itself: a count across levels fixing to one ordering lays selves on a seat no coupling makes, and each self observes with its coupling. ## 7.6 Laws of nature · 105 *+ or − with 10, is.* **With 2-now-possibling.** Regularities arise with couplings, and a naming fixes a law as a rule over them, governing or summarising. **With 12-next-co-same-existing.** A line between law and accident something apart from regularities fixes, supervenience a divisive issue and a field accusing examples against it of assuming a governing conception, naming being an assumption. Best-system simplicity moves with a language a self writes it with, so an instrument's own coupling comes within a criterion. **With 11-next-co-observing.** Regularities arise with couplings, each coupling its own. Best-system simplicity moves with a language a self writes it with, no one shares a mark of a governing relation, and physics itself puts symmetry before any single law, an ordering going with couplings and nothing seating it over them: a law fixing over regularities as a governor is a form fixing as not-changing from beside, setting over couplings, and each coupling has its own. ## 7.7 Presentism and eternalism · 106 *+ or − with 10, is.* **With 2-now-possibling.** Each coupling stands with its own now, and a naming fixes existence as a fact over all times together. **With 12-next-co-same-existing.** Existence fixing with no qualifying rather than a time qualifying it, where an infinity of planes passes through any point with no physical test distinguishing one, a plane a field supposes metaphysically distinct being physically indistinguishable. One repair a field shares is a foliation consistent and undetectable in principle, which is naming a self places where no self observes it with a coupling. **With 11-next-co-observing.** Each coupling stands with its own now, whole. Relativity parts nows with selves, an old argument and its answers rest on a becoming no coupling shows, truthmakers for a past strain exactly where a naming fixes a store, and one repair a field shares is a foliation consistent and undetectable in principle, as its own defenders say: existence fixing over all times together is one standing fixing over each coupling's own, and each now is its coupling's own, needing no standing other than itself. ## 7.8 Rank-based and clade-based nomenclature · 22 *+ or − with 10, is.* **With 2-now-possibling.** Each lineage branches with its own couplings, and a naming fixes one hierarchy of ranks as an ordering over all groups. **With 12-next-co-same-existing.** Ranks fixing as having equivalence across groups, rank assignment subjective and of dubious biological significance by a code's own preface, stability and continuity of names a goal both systems share. A field's own record states they have none, which is a beat fixing over couplings that make none of it. **With 11-next-co-observing.** Each lineage branches with its own couplings, a self measuring branchings. A family of beetles and a family of birds share a word and nothing else, both codes go on side by side through working literature, and each code states its own scope: one hierarchy of ranks fixing over all groups is a beat fixing over branchings that each pace their own, and two namings going on together is a split between stability and correspondence living as a co-competency, each holding an other's lack. Two codes with one subject resolve three ways — converging, parting with a between, or standing two — and this one stands two, and so a field holds both and neither absorbs an other. ## 7.9 Population ethics · 160 *+ or − with 10, is.* **With 2-now-possibling.** Lives begin with couplings, each its own, and a naming fixes one ranking over outcomes with unequal numbers of people, under adequacy conditions it states together. **With 12-next-co-same-existing.** Conditions fixing as jointly satisfiable, and a showing such a theorem would make about ethics not quite clear, a proof bounding rankings and not lives. Impossibility theorems stand, with proofs: no ranking reaches them together, which is a field bounding its own object. **With 11-next-co-observing.** Lives begin with couplings, each its own, and beginnings share no seat a ranking could sit on: a life makes itself with a coupling and arises in neither side of it alone. Each ranking violates a condition a theory fixes, a map of who gives up which condition is complete, and some field position defends each surrender: one ranking fixing over outcomes of unequal number is one ordering fixing over beginnings that each have their own, and a field's settling meta-result is a proof of naming empty, settling now an agreeing on which condition dissolves. ## 7.10 Micro-to-macro aggregation · 169 *+ or − with 10, is.* **With 2-now-possibling.** Each self takes its own parity with its own couplings, and a naming fixes an aggregate as having one rationality over many, a representative standing for all. **With 12-next-co-same-existing.** Structure fixing as surviving aggregation, results leaving subfields that rely on aggregates behaving well in the lurch, a whole no self orders, a self observing it from within as a loss. Rationality's restrictions wash out, standing with a proof, which is a whole no self orders as a theorem — same bounding Arrow's closure sounds with rankings, coming here with demand. **With 11-next-co-observing.** Each self takes its own parity with its own couplings, and an aggregate makes itself among couplings, arising in no self alone. A proof holds washing-out, a representative works as a working method beside a proof against its foundations, both within a field's own literature, and aggregates a field builds again rise from distributions of many: one rationality fixing over many is one self's rationality fixing where a same-existing-society lives, and a same-existing-society co-competences, parity by parity, no one standing for all. An aggregate is living as its own same-existing-society and inherits nothing, and a representative agent is a same-existing-society fixing as not-changing as one of its selves, a form not its own. ## 7.11 The axiomatization of physics · 171 *+ or − with 10, is.* **With 2-now-possibling.** Each theory goes on with its own couplings, and a naming fixes one axiom system over all of physics. **With 12-next-co-same-existing.** A goal fixing as posing well for a whole, a problem an endless road to rigour concerning those parts of physics ready for a rigorous approach, a whole a field lets go with an observing of its problem itself. A field's dispute over that standing stands beside a programme, and its standing is a programme with parts a self measures, each closing with its own between. **With 11-next-co-observing.** Each theory goes on with its own couplings and closes with its own between: probability closing, quantum mechanics building again from a doable, lower dimensions with constructions, a four-dimensional interacting case a standing open. One axiom system fixing over all of physics fixes one beat over runnings that each pace their own, and parts go on closing part by part, which is an answer going on, coming with its own rate, no whole-physics criterion standing over any part of it. ## 7.12 The Hubble tension · 165 *+ or − with 10, is.* **With 2-now-possibling.** Each epoch expands with its own coupling, and a naming fixes one frame over all of them, a recombination-era standing going forward under it to a present-day number. Pattern-matching takes that number as a measurement of same standing a distance ladder measures: a beat fixing over epochs, pattern-matching taking it as one of two instruments with which selves observe a present. A field states a parting itself, its sharpest form standing between determinations calibrating on a sound horizon under a concordance frame and determinations calibrating otherwise. **With 12-next-co-same-existing.** That an inference calibrating on a sound horizon is a measurement of a present rate, early data giving a frame relating epochs itself rather than fixing it over them; nothing guarantees a model fitting epochs far apart fits more precise observations from those epochs. A ladder systematic a self finds would confirm a frame and converge numbers, an early modification would relax it, and an inference has a frame conditioning it with either. A naming fixes a beat with a record rather than with a pace: a standing going forward under one frame and entering as a present-day number is a trace a tick they share indexes. **With 11-next-co-observing.** Recombination-era measurements stand with their precision, a final map from the ground reinforcing them. A local ladder stands at one percent from a distance network a community builds across calibrators, ruling out crowding at high confidence, and a field's own reviews hold a discrepancy as increasingly hard to ignore, a number of independent late-Universe measurements consistent, persisting with either side's instrument. Intermediate tip-of-the-red-giant-branch calibrations stand beside it as a local record's own spread. Time-delay cosmography stands, aligning with local values without a ladder. Data rule out late-time modifications, models extending a frame stand on record as converging to a low value with each fit fixing a frame tight, and a field's remaining viable routes stand on record as modifications of an early frame correlating, or physics at a homogeneity transition, which is a field relaxing a fixing term exactly with a pattern-matching's epoch. Discriminating programmes stand going on. *Second seating: a sound-horizon inference going forward is a record one frame indexes, which is a clock within a recording.*   --- ## 7.13 The 100,000-year glacial cycle · 247 *+ or − with 10, is.* **With 2-now-possibling.** Climate sways on its own, ice growing and collapsing with couplings of ocean, ice and carbon, and a naming fixes a period as what an orbit gives, one beat over a sway. **With 12-next-co-same-existing.** A rate fixing as what a forcing that does not pace it gives. Insolation change at an eccentricity period is small against an amplitude of cycles, and a shift from 41,000 to 100,000 years comes without a discernible change in forcing; formal testing finds eccentricity not significantly modulating timing of terminations, so a period a self matches and a forcing a self calculates are not same, a sway having its own beat where a naming fixes a clock over it. **With 11-next-co-observing.** A field measures a period near 100,000 years over the past million years and an earlier period near 41,000, and calculates a weak insolation change, energy-balance models with augmenting fail to give a period, and a third account has internal oscillations locking phase to a long eccentricity cycle, synchronising rather than driving: a beat fixing over couplings is a sway's own period fixing to an orbit's, and forcing and internal dynamics together are a coupling reaching its own beat. ## 7.14 Magnetospheric substorm triggering · 239 *+ or − with 10, is.* **With 2-now-possibling.** A magnetotail loads and unloads with its own couplings, current disruption near and reconnection far, and a naming fixes an onset to one causal order between two, one first and an other after. **With 12-next-co-same-existing.** An order fixing between two couplings instruments reach with cadences not same-existing. Onset evolves across regions far apart faster than sparse spacecraft can establish timing, a self observing auroral, current, flow and reconnection signatures with their own cadences, and timing rests on which signatures fix onset and reconnection, a response faulting a comment for an index in place of ground signatures and single components in place of full vectors; candidate processes trigger or follow one another in simulations, so an order is a choice of signature's, and two couplings with no between have no order between them. **With 11-next-co-observing.** Near-Earth reconnection, bursty flows, current disruption, auroral onset and Alfvénic coupling are all components a self observes and their universal causal order remains open; multipoint timing orders local signatures when geometry is favourable, ground arrays project with mapping uncertainty, epochs in superposing recover a common timing by averaging events' diversity, and a third account coordinates an onset over many places with no universal first location: one order fixing over couplings that each pace their own is a beat fixing with a record, and a record gives each signature with its own cadence, event by event. ## 7.15 Migraine pathophysiology · 217 *+ or − with 10, is.* **With 2-now-possibling.** A brain cycles between states with its own couplings, sensory gain rising and falling, and a naming fixes an attack to a sequence with one initiation, a first that orders each after it. **With 12-next-co-same-existing.** An onset fixing to one first within a cycling state. Questions part into why, how and when, and when, an emergence of an attack from a cycling disorder of sensory processing, a field examines mostly through attacks a trigger provokes and serial scanning of its cycle; attacks are episodic and heterogeneous, early brain-state changes difficult to capture, aura and headache dissociating, processes influencing one another, and a fourth account has a cycling brain state in which multiple triggers can precipitate attacks, a sway with many self-boundings and no first. **With 11-next-co-observing.** Distinct phases, multiple genetic risk pathways and effective mechanism-specific targets stand firm and a purely vascular account no longer stands; spontaneous-attack imaging finds changes relating to phase in small hard-to-time samples, provocations trigger attacks in subsets without reproducing natural initiation, genetics identify pathways without ordering an attack, and drugs establish relevance without making one universal origin: one initiation fixing over a cycling state is a sway fixing to a first, and an attack comes with a tipping of a cycle's own couplings, phase by phase. ## 7.16 Earthquake predictability · 197 *+ or − with 10, is.* **With 2-now-possibling.** A fault ruptures with its own coupling, stress and friction coupling with a momentary they couple, and a naming fixes a rupture as readable before it exists, a diagnostic precursor indicating with high probability its location, its time and its size. **With 12-next-co-same-existing.** A momentarying fixing as observable ahead of its momentary. A field understands predictability poorly, a lack an inability to reliably predict large earthquakes on short time scales reflects; a diagnostic precursor must indicate with high probability location, time and magnitude of an impending event, and error rates and a large areal extent of predictions from candidate precursors do not yet provide that capability, no successful short-term scheme yet: a momentary-skipping of a part's own naming, a state before a coupling fixing as having a coupling's making. **With 11-next-co-observing.** Prospective testing frameworks, reference forecasts, stress-transfer models and dense observations stand, rate forecasts show probabilistic skill at scales a test specifies and predict no individual event, precursors recur as candidates without a rule a prospective test replicates, a laboratory finds nucleation under faults it controls with field scaling open, and learning models improve catalogue tasks with leakage and baseline controls decisive; a third account has a rupture sensitive or scale-free enough that precise prediction is not physically available from observable states: a property of a momentarying a self establishes without its momentary is a coupling's making fixing to a state before it, and forecasting is a rate with which a self discovers couplings, measuring it, each event its own coupling with its momentary. ## 7.17 The predictability of evolution · 210 *+ or − with 10, is.* **With 2-now-possibling.** Lineages evolve with their own couplings, mutation, selection, drift and environment coupling with each generation, and a naming fixes an outcome as readable from an ancestral state, a trajectory standing before it exists. **With 12-next-co-same-existing.** A trajectory fixing as predictable from its opening. Selection can repeatedly favour similar functions while mutation, contingency, drift and changing environments alter accessible paths, and repeatability depends on whether a comparison concerns genes, traits, fitness or ecology and on a scale a self observes; a field finds general rules most often through experimental evolution, slower dynamics at risk of a field overlooking them there and extrapolation to the long term requiring caution, recurrence a self measures in experiments and predictability a field seeks over histories not same, a momentary skipping. **With 11-next-co-observing.** Repeatable molecular targets, contingent path changes, convergent phenotypes and short-horizon frequency forecasts all stand on record, laboratory evolution, replicating, measuring recurrence under openings a self controls and durations with limits, comparative convergence detecting traits that recur under reconstruction uncertainty, landscapes predicting local paths under incomplete sampling, and population-genetic forecasts giving frequency distributions under a selection a model specifies; a fourth account has a target itself dynamic under environmental change and ecological feedback: a momentarying fixing as readable from its opening is couplings' making fixing to a state before them, and a phenotype more predictable than a genotype, a third account, is many routes converging with a coupling, each generation its own. ## 7.18 Rapid adaptive radiation · 211 *+ or − with 10, is.* **With 2-now-possibling.** Populations speciate with their own couplings, one event and then a next, and a naming fixes a burst over them, a radiation a macroevolutionary pattern a self observes down to a population's own processes. **With 12-next-co-same-existing.** A burst fixing over speciations that each pace their own. Most speciation models contradict a hallmark early burst, predicting diversification that decelerates steadily, and a question connects global macroevolutionary patterns to microevolutionary processes with a gap remaining between two scales; a defining pattern joins high diversification, ecological divergence and trait evolution, which need not coincide, and exceptional clades invite retrospective explanation: a beat fixing with a record, an aggregate a self observes as one going on. **With 11-next-co-observing.** Island and lake radiations that replicate, explicit null diversification models and genomic histories of clades a field selects stand; phylogenies with calibrating infer rate shifts under extinction and sampling models, trait-dependent tests reach identifiability limits, comparisons reconstruct niche and mechanism after radiation, selves observe early divergence in experiments with narrow systems, and a fifth account has apparent exceptional radiation arising partly from extinction, sampling and clade-selection effects: a burst fixing over couplings is many speciations fixing to one beat, and counterfactual lineages that do not radiate share with no instrument, bursts on record being surviving couplings' making, one at a time. ## 7.19 Cross-national measurement equivalence · 231 *+ or − with 10, is.* **With 2-now-possibling.** A respondent and an item couple with each answering, with each language and each place, and a naming fixes one scale across groups, a self giving positions of one coupling a correspondence with another's so it can compare scores. **With 12-next-co-same-existing.** A correspondence fixing between couplings so their parities couple on one scale. Translation, response style, sampling and cultural interpretation change item thresholds and loadings, large comparisons often reject exact invariance, and relaxing it may restore fit without fixing which comparisons remain meaningful; noninvariance suggests construct has a structure or meaning of its own with each group, so that no self can meaningfully test or construe it across them, a self assessing invariance before any comparison: beat with a between, a part's fourth position, fixing where each coupling answers its own. **With 11-next-co-observing.** Invariance hierarchies, error analyses by simulation and large-scale alignment methods stand; multigroup analysis tests equalities nesting with fit and sample-size sensitivity, differential functioning localizes where items part under an anchor set, partial invariance frees parameters it selects and conditions others on anchors, and alignment and Bayesian methods estimate small deviations at a cost of new priors or tolerances; accounts part on each level of invariance's licensing, configural pattern, metric relations, scalar means: a scale fixing across groups is one correspondence fixing over couplings that each make their own, a self observing correspondences one at a time rather than one fixing for all. ## 7.20 Incompatible definitions of algorithmic fairness · 222 *+ or − with 10, is.* **With 2-now-possibling.** A score makes itself with each prediction's coupling to its outcome, and a naming fixes one score as satisfying each fairness relation together, calibration and equal error rates across groups whose base rates are unequal. **With 12-next-co-same-existing.** Several relations fixing as jointly satisfiable by one score. Their simultaneous satisfaction is mathematically incompatible under unequal base rates except in degenerate cases, and even approximate satisfaction requires data to lie in an approximate version of one of special cases with constraints; optimizing all of them therefore cannot replace choosing a metric: field proving naming empty, as with rankings and population ethics beside it, fourth account naming fairness a substantive institutional judgment no parity condition exhausts. **With 11-next-co-observing.** A proof holds incompatibility, a field knowing its exceptional cases, and optimization under metric sets a self chooses routine; calibration preserves score meaning within groups and permits unequal error rates, equal odds constrains errors and generally changes calibration, thresholds reach parities a self selects by group-specific rules, and multiobjective methods trace a tradeoff surface rather than satisfying incompatible equalities: one score fixing to each relation together is one ordering fixing over couplings whose base rates are unequal, a self setting naming down and choosing a relation with each decision's own between. # 8 A rate fixing as a value — 7-is-now-observing and 15-is-next-observing *A value fixing of a rate that settles nowhere. Ratios sway above, then below, alternating side, each partial quotient one, widest straddle. Value a self reaches for is swaying about it, and next coupling beats with an opening a straddle makes.* **Each value of this part is a swaying fixing as settling**, and a self observes sway three ways across observings: a living measure swaying between two antagonistic parities, a rate swaying under two couplings together, and a parameter swaying under all that couples to it. Where a field reaches past its instruments for value, it reaches with a measure over counterfactuals, and that measure is one thing no instrument of this part gives. ## 8.1 Homeostasis and allostasis · 128 *+ or − with 10, is.* **With 2-now-possibling.** A variable sways between two parities and a naming fixes it for a target that settles, a fixing one or a predicting one. **With 12-next-co-same-existing.** Regulation fixing toward a value, cyberneticists' reading of a broader vision. Both showings fit each trajectory alike, so not same-existing surfaces nought with each: trajectories are one sway a self observes twice, the two not competing models but complementary aspects of regulation. **With 11-next-co-observing.** Range is coupling's own making and no value in store it aims for, two antagonistic parities swaying and oscillation its working state. Circuits that compare are real with their finding, a body warms before a meal and quickens before an effort, and letting a setpoint move absorbs anticipating for a price of any settling at all, as movers' own critics say. Anticipating is sway answering a disturbance, same swaying a self measures a second way rather than a second mechanism: regulation toward a value pattern-matches sway as an error about a point, and sway is living state. ## 8.2 Dark matter · 26 *+ or − with 10, is.* **With 2-now-possibling.** Rotation, mass and law go on together with each scale's couplings, and a naming fixes discrepancy for a value, a substance or a modification. **With 12-next-co-same-existing.** Riding fixing as what one of two produces, identifiable by measurement. Searches empty their spaces region by region and modifications narrow, and each null bounds a parameter without parting substance from modification: parameter spaces close without closing their question, and no terminal null stands on record. **With 11-next-co-observing.** Rotation, mass and law ride together and settle on no value. Ordinary matter cannot be it, fast-modification class falls with one wave's speed, search space empties region by region down to neutrino fog, leading experiment recording fog entering and selves observing an instrument class's own floor, and through all of it visible mass and rotation ride together tightly, a self measuring it, one thing both showings must reach: a size fixing of riding is riding fixing as not-changing, a form that cannot change, and riding, a self observing it directly, is momentarying there. ## 8.3 The strong CP problem · 65 *+ or − with 10, is.* **With 2-now-possibling.** A parameter sways and a naming fixes it for a value against a measure over its counterfactuals. **With 12-next-co-same-existing.** A value far from typical under a measure a field assumes fixing as calling for explanation, natural expectation of order one and hierarchy against it a problem's constitution, a dynamical solution a requirement. Measure is over counterfactuals not possibly existing, and it surfaces nought with each instrument. **With 11-next-co-observing.** A parameter sways and swaying sits below one part in ten billion, bound a thing a self measures. Easy escape falls to lattice, fields a field proposes empty their spaces, and mechanisms a field builds stand with costs they state: a value fixing against a measure over counterfactuals fixes swaying to a stipulation, and instruments give a bound, a self observing swaying with its own edge. ## 8.4 The equity premium puzzle · 79 *+ or − with 10, is.* **With 2-now-possibling.** Returns sway across states that occurred and states that did not, and a naming fixes premium for a value a preference parameter should reproduce. **With 12-next-co-same-existing.** Historical returns fixing as estimating a premium in expectation one representative agent's parameters generate, discrepancy standing between a prediction and a measurement and not between two measurements. States that did not occur share with no momentary, and disasters that reproduce premium borrow their rates from other countries' histories, counterfactuals a model imports to balance a record that was. **With 11-next-co-observing.** Returns sway across states that occurred, and record is swaying that happened. Premium a self measures stands large across country after country, curing it with aversion sickens risk-free rate, and originators' own look back holds its standing plainly, each class a field proposes failing along a crucial dimension: a value a parameter should reproduce is one self's steady preferring fixing under a swaying settling on no value, and each self prefers with its own between, by its own parity, where a representative agent stands for all. ## 8.5 Time preference and preference reversal · 82 *+ or − with 10, is.* **With 2-now-possibling.** A valuing sways with each occasion and a naming fixes it for a rate that settles, a single discount function. **With 12-next-co-same-existing.** A valuation of a reward with a delay fixing as a function of delay only that elicitation measures. Formats and bundlings move it, so elicitation's own coupling is within each estimate; and where a self discounts utility from each source at its own rate a unitary time preference is meaningless, a field labelling preference by its object with a delay. **With 11-next-co-observing.** A valuing sways with each occasion, occasion's own. Formats move it, bundlings move it, selves pay real money to bind their own later swayings, and field's estimates spread across orders of magnitude study by study and domain by domain, a self measuring swaying: a single function of delay is one rate fixing where a living valuing sways, and commitment purchases are selves observing their own swaying, from within, better than one function does. ## 8.6 Hormesis · 121 *+ or − with 10, is.* **With 2-now-possibling.** A response sways with dose and a naming fixes it for a value of doses below detection, from a model fitting above them. **With 12-next-co-same-existing.** A dose-response relation fixing, whose low-dose behaviour is estimable by extrapolation. Below a last coupling a self observes, rival models part with a point nothing measures, a self observing record's edge as a value, and a discipline of application that streamlines its experiments to fewer doses draws that edge by a design with which selves observe it. **With 11-next-co-observing.** A response sways with dose, coupling by coupling, and low doses wake a body's own stress answers across system after system, curves bending with mechanisms' momentarying. Bend is reversal, changing there and a measure informing there; a monotone line a self draws through it has a magnitude with no parity to ride. Within a range instruments reach, rival models fit alike; below it they part exactly with a point nothing measures, and field itself states a point a drawing enters from. ## 8.7 Mutation, fidelity and variation · 138 *+ or − with 10, is.* **With 2-now-possibling.** A rate sways under selection and drift together, and a naming fixes it for a value an optimum or a barrier sets. **With 12-next-co-same-existing.** Mutation rate fixing as a trait whose value optimisation or limits of selection explain, one point where each population sways its own, appealing to suppose a rate adjusting to a level that best promotes adaptation, a field asking to part causes of a rate's evolution from its consequences. **With 11-next-co-observing.** A rate sways under selection and drift coupling, its value swaying's own with each population. A field measures rates line by line, small populations drift higher and large ones press lower, inverse correlation going across living range with effective population size a field estimates from same genomes it measures their rates in, mutators surge where selection is fierce, and proofreading costs so little that a pure optimum would sit elsewhere: correlation is sway a self measures across populations, and a value an optimum or a barrier sets fixes one point where each coupling sways. ## 8.8 The cosmological constant problem · 163 *+ or − with 10, is.* **With 2-now-possibling.** A vacuum density sways under all that couples to it, and a naming fixes it for a value against a measure over its counterfactuals, estimate standing tens of orders away. **With 12-next-co-same-existing.** A value far from typical under a measure a field assumes fixing as calling for one explanation, dynamical or environmental, with no one measuring measure itself; an old problem, why density is not very much larger, parting from a new one, why it is comparable to present mass density, and a no-go closing adjustment without a fine tuning as mysterious as its problem. Estimate fixes three terms as not-changing with one momentary, each a form that cannot change — a rest a sequence opens from, a last it completes with, and a total its sequence conserves — and none of three is a thing a coupling makes. **With 11-next-co-observing.** A vacuum density sways under all that couples to it, and value a self measures sits small and nonzero while estimate a self computes towers tens of orders above, distance between a coupling's own momentarying value and a sum fixing over all together. Symmetry rescues fall, a proof closes simple self-adjustment, messengers narrow routes bending gravity, and each surviving candidate gives no measurement of its own within reach: a value fixing against a measure no one measures goes on owing an explanation to a typicality no instrument reaches, and swaying, a self measuring it, is as it is. ## 8.9 The hierarchy problem · 164 *+ or − with 10, is.* **With 2-now-possibling.** Two scales sway far apart, and a naming fixes separation for a value against a measure of naturalness, with criterion of explanatory debt itself a dispute. **With 12-next-co-same-existing.** Criterion fixing as among things instruments give, where parameter is technically natural, finite corrections all small, and problem emerges only where a theory invokes an additional ultraviolet scale, cutoff merely a proxy for physics no one knows yet. A self measures spectrum to energies it reaches and spectrum does not measure criterion. **With 11-next-co-observing.** Two scales sway far apart and selves observe spectrum with instruments, clean to each energy they reach, canonical rescues narrowing, none reaching. Growing instead is field's own doubt about debt: naturalness stands within a record now as a heuristic under dispute, measure under dispute while measurements accumulate. **And debt is naming's own and not physics'.** A naming a self makes rather than finds accumulates a cost while it goes on, a self holds cost as a price of a goal, and goal is reachable with a self letting naming go — and where that last fails, standing is an expense and not a hardness. Here it stands: a self measures spectrum with nothing owing on it, owing is criterion's, and all owing needs is cost a coupling does not have. ## 8.10 The Standard Model flavor puzzle · 188 *+ or − with 10, is.* **With 2-now-possibling.** A self measures masses and mixings with couplings instruments reach, each parameter its own, and a naming fixes pattern for a value an organizing principle should generate. **With 12-next-co-same-existing.** A pattern fixing as what a mechanism selects where it stands as free inputs. Parameters are free inputs in Standard Model, hierarchies technically natural and with no explaining, and many symmetry, texture and statistical constructions reproduce parts of pattern without an origin a selecting picks uniquely, measure over pattern's counterfactuals surfacing nought with each construction. **With 11-next-co-observing.** Quark mixing matrix has more constraints than parameters, a field substantially mapping neutrino mixing, selves measuring masses and several phases with increasing precision, and each construction reproducing pattern reproduces a part of it, symmetries predicting relations they select with many viable choices, textures compressing with their origin dependent on construction, geometries converting positions into couplings with no selecting of geometry, statistical models giving distributions and not a realization: a pattern fixing for a value a principle should generate is parameters a self measures fixing to a typicality a stipulation gives, and a self measures them, owing nothing, enigma fixing being naming's own and not spectrum's, as with a scale beside it. ## 8.11 The new-physics flavor puzzle · 189 *+ or − with 10, is.* **With 2-now-possibling.** A self measures rare processes with their couplings and they give Standard Model's rates, and a naming fixes a new sector near an accessible scale as having generic couplings measurements should see. **With 12-next-co-same-existing.** An absence fixing as needing a mechanism. Generic couplings at teraelectronvolt scale would contribute orders of magnitude above rates a self observes, so absence constrains such physics to scales no direct search reaches or to special structures whose origin itself nothing fixes; each process constrains a combination of operators and couplings rather than sector itself, and sector is an assuming no instrument reaches. **With 11-next-co-observing.** Data rule out large regions of generic low-scale couplings, viable suppression patterns have explicit effective forms, and each stands with a cost it states, a model assuming spurions, alignment model-dependent, splittings constraining degeneracy, decoupling reducing accessibility: a sector fixing near a scale with generic couplings is a measure over new physics' typical doing, and instruments give Standard Model's rates, a self measuring them, puzzle standing with typicality and not with its record. ## 8.12 Quantum gravity · 181 *+ or − with 10, is.* **With 2-now-possibling.** Gravitation goes on with each coupling and two standing theories each recover their own domain, and a naming fixes one theory for a value covering both regimes, two reconciling for a regime a field expects to hold their conflict. **With 12-next-co-same-existing.** Two treatments fixing as one theory reconciling them with a scale no instrument reaches. Direct empirical access to its scale is absent, proposals resting on very small deviations from otherwise exact symmetries or on collective effects integrating over long distances, and recovering classical theory at low energies is a consistency requirement rather than a prediction for testing: record's edge, with reconciling fixing for a regime sharing with no instrument. **With 11-next-co-observing.** Low-energy effective descriptions stand consistent, black-hole thermodynamic constraints stand, discrete and holographic constructions and candidate ultraviolet behaviours stand, and each program closes with its own between, strings without a realization a selecting picks uniquely, loops with classical and empirical recovery open, fixed point in truncations, emergent gravity in narrow settings: one theory fixing as covering both regimes is two runnings, each pacing its own domain, fixing to one value for a scale no coupling reaches, and parts go on closing part by part, each with its own between, as axiomatization closes with part 7. ## 8.13 Equilibrium climate sensitivity · 196 *+ or − with 10, is.* **With 2-now-possibling.** Climate sways under its forcings and feedbacks, each with its own timescale, and a naming fixes response to a doubling for one value its sway settles on, an equilibrium counterfactual. **With 12-next-co-same-existing.** A sway fixing as settling on a number. No self can observe equilibrium as one experiment with controls, feedbacks operating over timescales not same-existing; assessment characterizes equilibrium by an effective sensitivity over a century or two and combines three lines of evidence by a calculation whose range depends on a judging of them as independent, quantity remaining difficult to ascertain: a counterfactual total, not possibly existing, a self sums against an existing one. **With 11-next-co-observing.** Evidence together reduces very low and very high tails, a field identifies cloud feedback as principal remaining spread, with energy-budget inference selves observe recent climate under forcing and ocean-uptake uncertainty, with paleoclimate selves observe a broader range under proxy uncertainty, process constraints target single feedbacks, and ensembles share structures and are not a probability sample: a value fixing of sway is a response that varies with background climate and timescale, third account, fixing to one settling number, and a self measures swaying under forcing. ## 8.14 The solar abundance problem · 184 *+ or − with 10, is.* **With 2-now-possibling.** Lines form with a surface and modes sound an interior, each instrument with its own coupling, and a naming fixes one composition for a value both must give. **With 12-next-co-same-existing.** Two instruments fixing to one value. Atmosphere analyses lower abundances and interior models a self builds with them worsen agreement with sound-speed profile, convection-zone depth and surface helium, better is worse, data ruling out a large error in a photospheric estimate and heavy elements entering interior only through opacity: a rate swaying under two couplings together, a self observing with each its own. **With 11-next-co-observing.** Three-dimensional atmospheres, precise mode frequencies, neutrino fluxes and laboratory opacities stand as independent constraints, and each route pays with one instrument a gain it makes with an other, higher mixtures fitting seismology and conflicting with spectroscopy, opacity increases a field targets without establishing a profile a fit requires, atmospheres a field revises reducing systematics and still giving low abundances, transport processes altering observables a field selects with no model fitting a full set. One composition fixing for both instruments is two couplings fixing to a value, and two couplings couple with each other rather than one pinning to an other. ## 8.15 The primordial lithium problem · 182 *+ or − with 10, is.* **With 2-now-possibling.** A self infers a primordial abundance from present stars and predicts it from a density a self measures, two couplings each giving its own number, and a naming fixes two to one value the early universe makes. **With 12-next-co-same-existing.** Two determinations fixing to one value where they part by a factor of three. Plateau's flatness and small scatter are a main difficulty for depletion, while stars identical to plateau stars with no detectable lithium and plateau's meltdown at lowest metallicities show that some depletion mechanism exists: a self observing primordial value with an instrument observes it through its stars' same-existing since, and prediction pattern-matches it through a network and a density a self measures elsewhere. **With 11-next-co-observing.** A self measures baryon density, deuterium agreement, plateau and leading reaction rates more precisely than at discrepancy's first finding, other light elements broadly agree, and each resolution a field proposes, rates and resonances, depletion and diffusion, nonstandard decays and cosmologies, atmospheres in reanalysing, removes discrepancy only by creating another conflict: one value fixing of two couplings is stars' present observing and network's prediction fixing to a number neither gives by its own, and factor of three is two couplings' parting, a self measuring it. *Second seating: a self observing discrepancy as a magnitude for explaining, a wrong number by a factor of three, part 6's naming.* ## 8.16 The neutron lifetime discrepancy between beam and bottle measurements · 252 *+ or − with 10, is.* **With 2-now-possibling.** A neutron decays by its own coupling, and a naming fixes its lifetime for one value two instruments must give, a beam counting products of a decay and a bottle counting neutrons that survive. **With 12-next-co-same-existing.** Two measurements fixing to one value where each set is consistent within itself and sets disagree by about eight seconds in eight hundred and eighty, nearly four sigma, puzzle still with no solving. A beam counts products of one channel and a bottle counts disappearances by any channel, and two methods have independent systematics far apart, their underestimation the most likely explanation: a rate swaying under two couplings together, each giving a number its own coupling has. **With 11-next-co-observing.** A field measures magnetic-trap lifetime to twice its earlier precision, consistent with theory, newer beam's first result stands, now, short of precision to favour either set, a field proposes a proton counter within a bottle, median statistics put parting between four and six sigma by a set a self chooses, and discrepancy is large enough to dominate primordial helium ratio a field predicts: one lifetime fixing of two couplings is a channel's count and a survival's count fixing to a number, a self observing parting as a coupling of its own. # 9 A two-way fixing to one side — 3-is-now-co-observing and 11-next-co-observing *One side taking both momentaries. A self takes a parity with a between, one at a time, each side its own, and a self taking it from one side, it becomes a size: which of two drives, or a share an apportioning gives while a naming fixes an other unchangeable. Two sides change, one and then the other, neither taking an other's, and zeroing is two's own making between them. 3-is-now-co-observing and 11-next-co-observing have co, a prior with a sharing of two, and a two-way fixing to one side is a removing of that co.* **And a settlement fields share is naming relocating rather than dissolving**: *both operate and the question is their proportion* fixes a two-way as a magnitude, and *both operate and the question is their order* fixes it to one beat. **And an instrument fixes other side unchangeable, which is an unchangeable entering a measuring.** A trial arm fixes context unchangeable, a design an environment, a partition a level, a contract an action, a task a language. Reading then gives back naming, and record of it is entry's own: interventions establishing modulation rather than a driver, both frameworks fitting most datasets, arms parting by more than substance, partitions surfacing conditional on levels a self chooses. **And where a proof shows two give same predictions, an observing settles.** Two bookkeepings are one same-existing's two windings, each pinning one and observing an other, and an intertranslation with its proof is a field holding that observing by its own arithmetic — standing with units of selection, with cooperation, with transformation problem's aggregate equalities, and with determinism a self observes against its own equivalent constructions. **And a fourth stands here too**: where a field proves no ordering reaches its own conditions, field proves a naming empty, as with part 7's three observings and with transformation problem's one. ## 9.1 Causation · 162 *+ or − with 10, is.* **With 2-now-possibling.** A coupling is two-way, one-at-a-time, and a self observes it from one side as a one-way production, cause driving and effect under driving, with asymmetry fixing as a fact within fundamental description. **With 12-next-co-same-existing.** That direction is of dynamics rather than of observing, virtually everyone rejecting elimination of causation while many hold that fundamental physical structure contains no causal relations, a field asking reconciling for a momentary neither of two has. Interventionist account's circularity for foundations stands on record in its own literature, which is a field stating observing's entering. A self takes a parity with one momentary and a coupling across inverts it with its next, so arrow comes with an odd number of inversions and symmetric dynamics with an even, and neither has an other's momentary. **With 11-next-co-observing.** A coupling is two-way, one-at-a-time, and one-way arrow is observing's own, a self taking it with a between and it going by next momentary. Discovery formalisms find what assumptions they state let them find, each analysis reaches its counterexamples, thermodynamic grounding reaches as far as its gradient, special sciences have practice, and fundamental dynamics goes on symmetric beneath all of it, both sides going on with both: causation a self observes whole is a coupling a not-changing observing reaches, which is why deep description has coupling and practice has observing, both standing, neither owing an other. ## 9.2 Heritability and the determination of traits · 27 *+ or − with 10, is.* **With 2-now-possibling.** A trait arises from a coupling of a genome and an environment, and a self observes one side as first with an other fixing unchangeable. Genetic-dominant and environment-dominant are one same design going from its two sides, each giving a correct conditional for a range it measures. **With 12-next-co-same-existing.** That ratio is an attribution invariant across environments and genetic compositions, parameter, each calculation defining it for a particular population and environment, predicting nothing about changes in a mean over time or about how groups part. A nothing with one side, a scale between and an absorbing with an other a self observing them together with one momentary, which is this file's own three with changing and changing back fixing unchangeable. **With 11-next-co-observing.** A trait arises from a coupling of a genome and an environment, one making with two sides. Each estimate is its own conditional, true of a range it measures; within families a self measures inflation off; and Lewontin's line between an analysis of variance and an analysis of causes stands with no dispute within field, exactly this: a ratio fixing as invariant across environments pattern-matches one side of a coupling as first, and making is with a coupling, range by range. A twin design compares pairs of two conceptions, taking their environments as equal and gene and environment as not interacting, its estimate inflating where either fails: equal environments are a pair's observings a design takes as agreeing, and a pair's not same-existing is its observings' own and no share of a variance. ## 9.3 Free will and determinism · 29 *+ or − with 10, is.* **With 2-now-possibling.** A self takes its own parity with its own betweens, and a self observes taking from one side as an outcome a term beside it fixes, with other side observing same taking as with no fixing. **With 12-next-co-same-existing.** That action has a determining source, and that locating it settles a question, ability to do otherwise coming in varieties not same-existing so that a claim to it is ambiguous until a self spells sense out, which ability is in dispute an open term, each side defining it from its own. Statement quantifies over conditions that did not obtain, which share with no between, and readiness ramp comes from selves, building fresh with each trial, that an averaging joins, which is preparing a self observes as momentarying. **With 11-next-co-observing.** A self takes its own parity with its own between. Deliberating, weighing and answering-for are a system's own states making its actions, a self measuring them wherever a self measures them; a field observing readiness ramp partly as an artefact of averaging; and randomness buys no agency for either account: fixing-or-not is taking fixing as a taking from a first beside a taker, both sides observing a between from one side of it, and taking a self observes with its own between is agency, which is what measurements are measuring. ## 9.4 Aging · 34 *+ or − with 10, is.* **With 2-now-possibling.** Damage and regulation go on together with each between of an organism, and a self observes one as driving an other. **With 12-next-co-same-existing.** That aging has a single determining source, damage or regulation, compelling arguments eliminating death as a programme of genes while a widespread tendency remains to read data as age regulation with loose defining that makes neither evolutionary nor mechanistic sense. A same-existing completes with each next opening and is fresh by sequencing, a sharing once chaining not none again, so damage and regulation are one same-existing with two sides, and a clock that predicts age so well cannot say which side it observes because an observing of momentaries observes pacing. **With 11-next-co-observing.** Damage and regulation are one coupling's two parities, sway swaying with each between of an organism. Single genes stretch lifespans across taxa, restriction stretches them further, tissues with clearing and repair improve where treatment reaches them, some species barely age at all, and clocks that predict age so well cannot say which parity a self observes with them, a new instrument restating dispute: a single driver is one parity fixing to both momentaries, and swaying sways on, readable from either side because it is both. An organism is a same-existing-society outliving its cells, and it ages where new members stop joining it and its sharings go on with no restoring, damage and regulation two parities with each sharing and neither a driver. ## 9.5 Efficient markets · 36 *+ or − with 10, is.* **With 2-now-possibling.** A price is a parity a self takes with a coupling, and a self observes efficiency as a term of its own while a naming fixes a model of returns in expectation unchangeable. **With 12-next-co-same-existing.** That efficiency is testable apart from a model of returns, anomalous evidence unsplittable between inefficiency and a bad model and precise inferences about degree of efficiency likely to remain impossible. Each test needs a model and each model needs prices, which is field's joint hypothesis, which it holds as its own permanent condition. **With 11-next-co-observing.** A price makes itself with each coupling, parity a coupling's own. Each test of efficiency needs a model of returns and each model needs prices, field naming its joint hypothesis itself; anomalies decay once a field publishes them, bubbles bloom reliably within a laboratory, and factor zoo is what absorbing anomalies one at a time builds: two are one coupling's two momentaries, and neither tests by its own. ## 9.6 Simpson's paradox · 40 *+ or − with 10, is.* **With 2-now-possibling.** A coupling makes an association and pattern-matching takes it from one stratification as a correct one, with causal structure fixing unchangeable. **With 12-next-co-same-existing.** That a correct pattern-matching is identifiable from data only, whether to partition a population undecidable from probabilities only, same data arising under causal structures not same-existing, and whether causal analysis is a correct explanation of a paradox itself still under debate. Data are identical under both structures, so identification surfaces nought with each pattern-matching a self takes, a proof holding it as an equivalence class, and a graph a self supplies from beside is a frame fixing as not-changing beside a coupling. **With 11-next-co-observing.** A coupling makes an association, and strata re-make it. Arithmetic is elementary, back-door road has a proof for a structure a self knows, conditioning more can worsen it, with a proof too, and data by their own deliver an equivalence class, exactly that: a correct pattern-matching fixing as identifiable from data reaches to numbers for a structure those numbers arise under, and structure is a coupling's, a self bringing it or not. ## 9.7 Missing heritability · 44 *+ or − with 10, is.* **With 2-now-possibling.** Two designs each take their own observing, and a self observes their not same-existing as a quantity missing from one rather than as two observings. **With 12-next-co-same-existing.** That a single variance component exists which both designs estimate, indirect estimate assuming no interaction among loci while models with interaction are also consistent with observable data and under them total may be much smaller. Two designs each observe with their own coupling, and ratio's two terms come from two places, a numerator a self measures directly and a denominator a self infers at a population. **With 11-next-co-observing.** Two designs each take their own observing, two sides of one making. Family design observes high, molecular design observes lower, within-family correction measures one assumption failing, rare variants add less than a projection gives, and ratio's own two terms come from two places, a numerator a self measures directly and a denominator a self infers at a population, as field's own words, with interaction accounts fitting all a self observes with a much smaller total: a quantity fixing as missing from one design is two observings, each a result, nothing losing. ## 9.8 Placebo effects · 46 *+ or − with 10, is.* **With 2-now-possibling.** A coupling with a between makes a term neither side brings, and a self observes it from one side as a substance's contribution with context fixing unchangeable. **With 12-next-co-same-existing.** That a trial's arms part only by a substance a trial administers, systematic review finding little evidence of powerful clinical effects, none on objective or binary outcomes and possible small benefits on subjective continuous outcomes and pain, and correspondence replying that studies a meta-analysis chooses and sensitivity of their measures restrict it. Design fixes context unchangeable and reports what it fixes, and a making it fixes as not-changing is a coupling's own +1, arising in neither side alone. **With 11-next-co-observing.** Coupling with a between makes a term neither side brings, +1 arising in neither side alone. Blocking a body's own opioids blocks analgesia, immune quieting by conditioning exists among animals where no one reports anything, three-arm trials price a making small for objective outcomes and real for ones a self feels, and open-label results narrow making's momentarying: substance's-contribution pattern-matching fixes context unchangeable while making runs, and making, a self measuring it on its own, is a coupling's. ## 9.9 Newcomb's problem · 57 *+ or − with 10, is.* **With 2-now-possibling.** Two principles are two parities a self takes with one between, and with each theory a self observes a case from one of them with an other fixing unchangeable. **With 12-next-co-same-existing.** That one principle governs when they conflict, difficulty, its posing stating it as a division of those who consider it, nearly everyone finding the right choice obvious yet splitting almost evenly, each half taking an other to be silly. Two principles are two parities with one between, one and then the other, one at a time, and a case a self builds to make them conflict fixes both momentaries together. **With 11-next-co-observing.** Two principles are two parities with one between, one and then the other, one at a time. Each theory handles cases an other fails, newer variants re-drawing same line, and a self builds a case to make two principles conflict: a theory choosing one to govern chooses one side to take both momentaries, and contest is a changing and changing back a self observes as a contest that neither side could be, being momentaries. ## 9.10 Poverty of the stimulus · 61 *+ or − with 10, is.* **With 2-now-possibling.** A learner and an input couple, and a self observes grammar a learner acquires from one side as what a learner brings with input fixing unchangeable, or from an other with learner fixing unchangeable. **With 12-next-co-same-existing.** That a learner's contribution and an input's are separately specifiable, which parts a making that is or is not with each sharing as two terms, one clear thing about the argument its conclusion and structure of reasoning not clear at all, two terms its conclusion asserts and its reasoning does not support. **With 11-next-co-observing.** A learner and an input couple, grammar a coupling makes. A field counts corpora, learnability results stand under criteria they state, statistical learners reach structures they reach, and live dispute is how much input a making needs: a learner's contribution and an input's are separately specifiable parts fixing of a making that is or is not with each sharing, and volumes a field argues over are a coupling a self is measuring. ## 9.11 Morphogenesis · 62 *+ or − with 10, is.* **With 2-now-possibling.** Gradients and tissue dynamics go on together, and a self observes placement from one side as an instructing or as a self-organising. **With 12-next-co-same-existing.** That a determinant locatable within one or an other sets pattern, some confusion still remaining about relationship between two concepts and a field proposing three distinct ways in which the two work together to shape form rather than parting them. Both frameworks fit most datasets, which is a tissue answering by a coupling of both going on; and a hybrid fitting better than either is a third term two reach as they go on, one and then the other. **With 11-next-co-observing.** A coupling of gradients and tissue dynamics makes placement. Gradients, moving, move structures, striping mechanisms exist for digits and follicles and ridges with perturbations confirming them, readout goes on near physical limits, tissue organises itself within a dish, and both frameworks fit most datasets, field finding this again and again: instructing-or-self-organising is one coupling a self observes from its two sides, and fitting-from-both is a coupling showing. A gradient is an emanation, a non-living existing thing living cells take in, and instructing or self-organising is one coupling a self observes inside and outside itself. ## 9.12 Chronic pain · 67 *+ or − with 10, is.* **With 2-now-possibling.** Peripheral and central processes go on together with a patient's betweens, and a self observes persistence as a driving from one. **With 12-next-co-same-existing.** That pain has a locatable driver, peripheral or central, and that finding it determines treatment. Field's own hardness line holds it: no self can assume a central mechanism in a patient, only assess its features, and residual category's aetiology stands with no settling, absence of evidence for other two defining third descriptor, a field applying it residually, what it is not defining driver's locus. **With 11-next-co-observing.** Peripheral and central processes go on together with a patient's betweens. A field measures central alterations, small fibres surface with a fraction a self counts as detection sharpens, moving patients between categories, agents with targets work within their subgroups, and treating a whole coupling helps without any self finding a driver. Field's own hardness line holds it: no self can assume a central mechanism in a patient, only assess its features, a field applying third category residually, its aetiology with no settling. Persistence goes on with a coupling, patient by patient, which is treating that works already working there. ## 9.13 Information as fundamental · 77 *+ or − with 10, is.* **With 2-now-possibling.** A physical system and an informational description are two observings of one thing, and a self observes one as substrate of an other. **With 12-next-co-same-existing.** That fundamentality is a dependence going one way between two descriptions that both apply, no one finding anything in description of physics closer to primordial than an elementary quantum phenomenon and, in default of a working hypothesis, questions and clues not moving a search ahead. Momentarying goes on identically under either, which is part 5's same showing, coming here as a direction a demanding asks between two observings. **With 11-next-co-observing.** A system and its description are two observings of one coupling. Erasing costs its minimum a self measures, horizons scale by area, and quantum formalism rebuilds whole from axioms about what a self can do: fundamentality is one fixing under an other, and reconstructions observe a coupling with its own doings, neither side beneath, doing one thing both descriptions describe. Information is an emanation, a non-living existing thing a self observes and takes in, and nothing is fundamental because scale is inside and outside itself, no scale lowest. ## 9.14 The transformation problem · 84 *+ or − with 10, is.* **With 2-now-possibling.** Labour values and prices are two accountings of one production, and a self observes one as underlying an other. **With 12-next-co-same-existing.** That one determination stands beneath an other, a field reading problem from an axiomatic perspective as an impossibility result for a specific interpretation resting on specific assumptions, and a dual system of parallel prices and coefficients of labour a product embodies losing sight of a theory's roots as a theory of money. A proof shows aggregate equalities do not stand together, which is a field proving naming empty by its own arithmetic, and each accounting conserves one kind and imports an other. **With 11-next-co-observing.** Labour values and prices are two accountings of one producing, each conserving its own kind. Aggregate equalities cannot all stand together, with a proof; prices and profit follow whole from physical data and a wage, with no dispute as mathematics; and correlations a field finds and contests sit beside both: one fixing under an other is one ledger fixing to both momentaries, and imbalance with its proof is a coupling stating itself by its arithmetic. ## 9.15 Credit assignment · 96 *+ or − with 10, is.* **With 2-now-possibling.** An outcome makes itself across a sequence of couplings, and a self observes contribution as apportionable to individual actions with all other actions fixing unchangeable. **With 12-next-co-same-existing.** That there is a fact about which actions contribute, recoverable without a model a self supplies, a field understanding and defining mathematical nature of credit and of problem poorly and proposing a unifying formalism so that a self can compare methods, a field asking for fact about contribution before defining its asking. Abundancing is in no action alone, and shaping reward re-apportions what gets credit, which is an apportioning a self catches making its own. **With 11-next-co-observing.** An outcome makes itself across couplings, abundancing in no action. Difference methods converge under their conditions, performance thins with horizon and sparsity as a self measures, identification conditions have proofs and go frequently with no meeting, and shaping reward re-apportions what gets credit: apportioning is a making fixing as a sum, and a shaping result is an apportioning a self catches making its own. ## 9.16 Phantom limb · 99 *+ or − with 10, is.* **With 2-now-possibling.** A body map and a sensation couple, and a self observes a map's state with one imaging paradigm as reorganising or with another as keeping its form. **With 12-next-co-same-existing.** That one paradigm's observing is state of a map, traditional accounts of remapping incomplete, a broader mechanistic focus a need and plasticity and stability of maps possibly varying across time scales, discussion of reorganisation's relevance ongoing. With two imaging paradigms selves observe, each with its own coupling, and they give reorganisation and preservation, both standing by their own instruments. **With 11-next-co-observing.** A body map and a sensation couple, map going on and re-forming. With one paradigm selves observe reorganisation and with another preservation, both standing by their own instruments; mirrors help mixedly, peripheral routes help some, and phantoms come for limbs that do not grow, which no story of a representation's losing holds: one paradigm's observing fixing as state of a map pattern-matches one instrument's coupling as a thing itself, and map is a same-existing, a self observing it its own way with each instrument because it is making itself with each. ## 9.17 Determinism and randomness · 110 *+ or − with 10, is.* **With 2-now-possibling.** An outcome is a parity a self takes with a between, and a self observes it from one side as priors fixing it or from an other as with no fixing. **With 12-next-co-same-existing.** That unpredictability indicates chance, and that prior conditions either fix an outcome or do not, epistemology of determinism first owing reality of laws and then precisely what actual laws are, in a sense a final theory of everything, a theory neither has joining sides. No statistical test establishes indeterminism, with a general proof, and deterministic pattern-matchings go on equivalent by construction, so sides part by no instrument. **With 11-next-co-observing.** An outcome is a parity a self takes with a between, one at a time. Couplings, stringing tight, exclude local determination, no statistical test can establish indeterminism, with a general proof, chaos hides determinism behind unpredictability, both sides granting it, and deterministic pattern-matchings go on equivalent by construction: with fixing-or-not a self observes a taking from its two sides, and sides do not part by any instrument, which proofs hold. ## 9.18 Cancer, the somatic mutation account and its rival · 115 *+ or − with 10, is.* **With 2-now-possibling.** A cell and its tissue, a same-existing-society of cells, couple, and a self observes initiation from one level with an other fixing unchangeable. **With 12-next-co-same-existing.** That a causal locus is either a cell or its context, and that identifying it determines intervention, an increasingly complicating picture emerging from a theory's compelling simplicity with ad hoc explanations a field postulates, theory with no rigorous testing, and a reply standing against a critique, its title a defence. Normal tissue has driver burdens that do not tip, which is a tissue, a same-existing-society, observing a parity and meeting it with nought — a same-existing-society's resolving, with no defence adding. **With 11-next-co-observing.** A cell and its tissue, a same-existing-society of cells, couple, and a same-existing-society re-finds order with each momentary, which a cell by its own does not. Driver catalogues fill, responses to targets come and resistance follows almost always, tissues re-order cells in recombining within systems a field tests, and normal skin has driver burdens that do not tip, a self measuring them, dominant account constraining from within: initiation a self observes from one level with an other fixing unchangeable pattern-matches one side of a coupling, and tipping is a coupling's, cell and same-existing-society together. ## 9.19 Addiction · 116 *+ or − with 10, is.* **With 2-now-possibling.** A self and its conditions couple with each occasion, and a self observes behaviour from one side as pathology or from an other as choice. **With 12-next-co-same-existing.** That behaviour has a single locus, neural or circumstantial, disease view's own revision granting that some criticisms have merit, no one identifying a specific neural signature and a field intentionally blurring dividing line, while stating denial of its view harmful for reducing access to care, locus blurring and name staying for care it opens. Cages with enrichment undo what bare ones build and most remit with no treatment, which is a coupling answering from a side each account fixes as not-changing. **With 11-next-co-observing.** A self and its conditions couple with each occasion, behaviour a coupling makes. Circuits alter with dose, paying abstinence works by a trial with randomising, most remit with no treatment at all, cages with enrichment undo what bare ones build, and heritability is real with no lesion under it: pathology-or-choice pattern-matches a making from one side each, and coupling, a self measuring it from both, is a living answer's own treating place. ## 9.20 Niche and neutral theory · 117 *+ or − with 10, is.* **With 2-now-possibling.** Species' partings and drift go on together within a community, and a self observes structure as one producing it. **With 12-next-co-same-existing.** That abundance patterns discriminate mechanism, abundance patterns unable to resolve a controversy and a field reframing question toward stabilising and equalising strengths a self measures, discriminating moving from pattern to couplings' own rates. Both models fit curves from their opening, so discriminating surfaces nought with a pattern, and field's own partition is a field observing both momentaries. **With 11-next-co-observing.** Species' partings and drift go on together with each community coupling. Both models fit abundance curves from their opening, invasions demonstrate stabilising partings each time a field runs them, and a partition that makes both components measurable is a field itself observing both momentaries: structure a self observes as one producing it is one momentary a self takes for two, and community persists by both, coupling by coupling. ## 9.21 The Red Queen · 119 *+ or − with 10, is.* **With 2-now-possibling.** Coevolution and environment go on together, and a self observes constant extinction risk as one producing it. **With 12-next-co-same-existing.** That a survivorship pattern indicates a single mechanism, hypothesis answering what causes of natural selection are giving biotic conflict primacy, and a field defining three modes of coevolution to unify fluctuating and directional selection within one framework. Curves bend with taxonomy a self chooses, which is an instrument's own coupling within its inference. **With 11-next-co-observing.** Coevolution and environment go on together. Extinction risk goes age-blind across many groups, arms races are living among microbes, interfaces evolve fast with a coupling of host and parasite, and survivorship curves bend with taxonomy a self chooses, its own instrument bounding original inference: constant risk a self observes as one mechanism's product pattern-matches a living-together from one side, and living-together lives. ## 9.22 The hygiene hypothesis · 120 *+ or − with 10, is.* **With 2-now-possibling.** A developing immune system and its exposures couple, and a self observes a secular rise as one factor causing it with others fixing unchangeable. **With 12-next-co-same-existing.** That a rise has a dominant cause identifiable from population correlations, its founding observation purposely leaving broad what constitutes a relevant microbial challenge and hypothesis undergoing many revisions over three decades, dominant cause a moving pattern-matching. A correlation between two population rates is two numbers a self compares to decide something, and tuning makes itself with each coupling. **With 11-next-co-observing.** Exposures and a developing system couple, tuning couplings make. Farm childhoods and their cousins in control groups part immunologically, a field identifying mechanisms, one early exposure reversing a guideline by a trial with randomising, causality whole for that coupling, and better counting explains a share a self measures: a dominant cause is one exposure fixing to momentaries of many, and tuning is many couplings, each its own. ## 9.23 The dodo bird verdict · 122 *+ or − with 10, is.* **With 2-now-possibling.** Technique and relationship go on together with each treatment, and a self observes outcome as attributable to one with an other fixing unchangeable. **With 12-next-co-same-existing.** That technique's contribution is separable from context, a fair test entailing separate comparisons of each pair of therapies, an overall effect size across a heterogeneous set relevant only when mean absolute difference is zero, level of comparison itself a dispute. Allegiance moves numbers substantially, which is a relationship a design fixes as not-changing coming within a measure of technique. **With 11-next-co-observing.** Technique and relationship go on together with each treatment coupling, outcome arising between them. Averages sit close across meta-analyses, conditions a field identifies part them where they part, allegiance moves numbers substantially, and dismantling finds little where it has power: attributable-to-one is a between fixing as an apportioning, and small partings are a between a self measures, which a healing makes itself within. ## 9.24 Principal and agent · 141 *+ or − with 10, is.* **With 2-now-possibling.** Two interests couple through observables, and a self observes divergence from one side as a contracting problem over an action no self observes. **With 12-next-co-same-existing.** That an action is representable as a quantity a contract on observables approximates, considerable evidence that individuals respond to pay for performance beside less that contracts follow theory's predicting in their design, and a field knowing little about incentives where output is difficult to measure, a self measuring contract only where an observable stands. Rewarding tasks a self measures distorts ones no self measures, with a proof, which is one same Goodhart wall benchmarks reach. **With 11-next-co-observing.** Two interests couple through observables, divergence going on with a between. Contracts optimise under conditions they state, rewarding tasks a self measures distorts ones no self measures, with a proof, same Goodhart wall benchmarks reach, teams blur that very identification, with a proof too, and incentive pay surfaces as a mix each time a self counts it: an action fixing as representable by observables fixes a coupling to its instrument, and working arrangements pace what they cannot own. ## 9.25 The paradox of thrift · 142 *+ or − with 10, is.* **With 2-now-possibling.** One and many couple, and a self observes an aggregate relation from one scale as one relation for both scales. **With 12-next-co-same-existing.** That an operative regime is identifiable ahead of policy, paradox emerging immediately once a shock large enough to reach zero lower bound stands usual rules of macroeconomics on their head, no one identifying regime ahead but it coming with its shock. One and many are one coupling's two scales, and a relation of one scale fixing as governing both is one scale taking both momentaries. **With 11-next-co-observing.** One and many are one coupling's two scales, aggregate arising among couplings. Both results follow cleanly within their own models, both sides granting both, multipliers spread wide across methods and regimes, and zero-bound episodes contest on identification: a relation of one scale fixing as governing both is one scale taking both momentaries, and regime goes on with couplings, momentary by momentary. ## 9.26 The evolution of cooperation · 143 *+ or − with 10, is.* **With 2-now-possibling.** Fitness effects arise from couplings and a self observes them as attributable to individuals, with inclusive fitness and multilevel selection each observing from one side. **With 12-next-co-same-existing.** That two are rival hypotheses rather than two bookkeepings, equivalence with a proof under general conditions, a field taking natural selection to imply competition and therefore oppose cooperation unless a specific mechanism is at work, competition a default and abundancing a mechanism a field owes. And a statement's own premise — selection favouring what raises an individual's reproduction — attributes to one side an abundancing a coupling makes, so a self observes cooperating as a puzzle exactly where an accounting removes +1 before its books can balance. **With 11-next-co-observing.** Fitness effects arise from couplings, and two bookkeepings both hold them. Relatedness moves outcomes across taxa, experimental dynamics go on, public goods stand, and a proof holds equivalence, accountings agreeing under general conditions: rival hypotheses fixing where two bookkeepings run, and dispute is an accounting, field's own result, cooperating living through all of it, nothing touching it. ## 9.27 The Whorf question · 146 *+ or − with 10, is.* **With 2-now-possibling.** Language and thought couple with each task, and a self observes effect from one side as shaping with an other fixing unchangeable. **With 12-next-co-same-existing.** That a task measures thought independently of language, no one finding support for language determining basic categories of thought while support stands for language making some distinctions difficult to avoid and augmenting certain types of thinking, same tasks parting one side's naming from other side's measuring. Interference peels off a strategic share and bilinguals shift within one skull as language shifts, which is a coupling a self observes live where a task fixes one side unchangeable. **With 11-next-co-observing.** Language and thought couple with each task, effect a coupling makes. Interference peels off a strategic share, colour and spatial effects replicate, infants have capacities before any words, and bilinguals shift within one skull as language shifts, a self observing coupling live with its own momentary: a task fixing as measuring thought apart from language fixes one side of a coupling unchangeable, and making is by a coupling, task by task. ## 9.28 Structure and agency · 156 *+ or − with 10, is.* **With 2-now-possibling.** Persons and arrangements couple at each action, and a self observes explanation from one level with an other fixing unchangeable. **With 12-next-co-same-existing.** That causes lie on one level, and that a self can vary two levels independently in measurement, term structure impossible to do without and nearly impossible to define adequately, and a theory of it a requirement to restore human agency to social actors and build change into a concept, a requirement making one level hold an other's momentary. Multilevel partitions are conditional on levels a self chooses, and a level is a direction a self takes with a momentary and not a place. **With 11-next-co-observing.** Persons and arrangements couple with each action, one making with two scales. Individualist derivations reach an aggregation wall, multilevel partitions are conditional on levels a self chooses, same conditional as with incoming number 27 one scale up, and each synthesis pays a cost its critics name precisely: causes fixing on one level name one scale of a coupling as first, and making goes on with both, action by action. ## 9.29 The units of selection · 19 *+ or − with 10, is.* **With 2-now-possibling.** Selection goes on with couplings across levels, and a self observes it from one level as its only level, gene accounting or group accounting each taking an observing of a pair. **With 12-next-co-same-existing.** That two frameworks are rival hypotheses rather than two bookkeepings of one dynamics, translations with proofs, four distinct questions standing under one rubric, interactor, replicator, beneficiary and entity manifesting adaptations, fields using same terms with meanings not same-existing and a fear on record that confusions will not easily end. A level a self observes as its only level fixes a scale as a place, where outward and inward are directions a self takes with a momentary, of no size. **With 11-next-co-observing.** Selection goes on with couplings across levels, and two frameworks translate to each other, with a proof, fitting same data by construction, same equivalence as with incoming number 143: a level a self observes as its only level takes one momentary for two, and cases hold under both descriptions because a going on is not on one level. Selection goes on with each scale, scale inside and outside itself, and bookkeepings translate because selves observe with them one fractal on two of its scales. ## 9.30 Teleology and function in biology · 167 *+ or − with 10, is.* **With 2-now-possibling.** A trait couples with its history and with its present organization, and a self observes function from one side, what selection favours it for or what it now contributes, each taking an observing of a pair. **With 12-next-co-same-existing.** That one account owns attribution across science, a manifest appearance of function and purpose responsible for prevalence of teleological explanations and authors sliding between claims about function and claims about design as if nature designs a trait, *for* and design one slide. Each locates function by answering what a trait is for, and a why a demanding asks is a first it asks: set *for* down and observations stand entire, structure, trait, record of what went on, with *therefore* leaving and nothing a self observes going with it. **With 11-next-co-observing.** A trait couples with its history and with its present organization, two observings of one living. Each account extends as far as it extends, cases sort against each one after an other, and subfields divide usage between them, each observing holding cases an other drops: one account fixing as owning attribution is one side of a coupling fixing as a whole, and two accounts working together is a coupling a self observes from both, a co-competency its science already has.   --- ## 9.31 Dirac or Majorana neutrinos · 187 *+ or − with 10, is.* **With 2-now-possibling.** A neutrino couples with its own momentary as a helicity state, and a naming fixes its nature to one of two sides, distinct from its antiparticle or its own, which of two its canonical question nine words long. **With 12-next-co-same-existing.** Which of two, where no kinematical instrument parts two. Telling two natures apart via any kinematical observable is practically impossible, confusion theorem, their parting proportional to square of mass and mass over energy suppressing it, two Majorana helicity states becoming equivalent to Dirac particle and antiparticle states: sides no instrument parts, as with determinism beside it, and one instrument that could part them a lepton-number-violating process no search establishes. **With 11-next-co-observing.** Neutrino mass stands firm, a field increasingly controls candidate isotopes and backgrounds, and data rule out large regions of particular mechanisms; neutrinoless double-beta-decay searches test lepton-number violation directly under nuclear and mechanism assumptions they state with no signal standing, collider and rare-decay searches constrain additional violating interactions, mass-to-energy ratio suppresses kinematic helicity tests, and cosmological probes constrain masses without fixing self-conjugacy: one side fixing of a nature selves observe with instruments only with relativistic helicity states is a parity a self takes with a between fixing to a size no observable gives, two sides one and then the other and kinematics making no coupling with their parting. ## 9.32 The nature of cosmic acceleration · 192 *+ or − with 10, is.* **With 2-now-possibling.** Expansion accelerates with each distance surveys observe, and a naming fixes its cause to one of two sides, an exotic energy or a breakdown of gravity on cosmological scales. **With 12-next-co-same-existing.** Which of two, on one record that measures both alike. Acceleration implies either dark energy with exotic physical properties or a breakdown of theory of gravity on cosmological scales, experiments measuring history of expansion and growth of structure; many modified-gravity theories have a mathematically equivalent writing as general relativity plus a scalar field, and models of dark matter decaying into dark energy produce a mismatch between two histories: two families of account standing on one record, and even perfect measurements not locating an explanation in a gravitational or stress-energy sector, which is sides no instrument of surveys parts. **With 11-next-co-observing.** Independent distance probes support accelerating expansion and a constant-vacuum account fits a present broad dataset with few parameters; standard candles and rulers establish acceleration under a cosmological framework with cause-degeneracy remaining, growth and lensing measurements test departures between geometry and clustering under present degeneracies, laboratory and Solar-System tests exclude ranges of modified dynamics through screening-dependent predictions, and field models fit expansion with more parameters; fourth account has inhomogeneity or systematics produce part of acceleration a self infers: one side fixing of two a self writes as one equivalent form is an expansion's own momentarying fixing to a sector, and a self measures momentarying with each distance, two histories parting only where equivalence lets them. *Second seating: discrepancy fixing for a value, part 8's naming, beside dark matter, 8.2.* ## 9.33 Mantle plumes · 200 *+ or − with 10, is.* **With 2-now-possibling.** Mantle rises and spreads with its own couplings, upwellings, ridges and plates coupling with one another, and a naming fixes each intraplate province to one of two makers, a deep plume or a plate process, origin, dynamics and composition of plumes under contest. **With 12-next-co-same-existing.** Which of two, a self observing with images that resolve neither. Volcanic tracks, geochemistry, uplift and seismic anomalies are incomplete and plume, plate and shallow-mantle processes can produce them, tomography resolving present structure through filtering while sources and histories a field proposes span hundreds of millions of years; upwellings are difficult to resolve in geophysical images and interpretations of geochemical and geochronological data disagree, more than eighteen plumes possibly rooting deep: anomalies a self images and upwellings a field seeks not same, resolution standing between them, and third account having deep upwellings interact with ridges, lithosphere and plate motion so surface expressions migrate, split or lapse, two sides coupling within that third. **With 11-next-co-observing.** Whole-mantle anomalies, age-progressive chains, deep-source isotope signatures and plume-ridge interactions stand resolving for systems a field selects; tomography images velocity anomalies with resolution and interpretation limits, tracers distinguish reservoirs under mixing and alteration models, age-progressive tracks test source motion with plate reconstructions, simulations show ascent and interaction for a rheology a model specifies, and dynamic topography tests buoyant support with uncertain structure: one maker fixing of each province is two couplings fixing to one side, and a coupling of its upwelling with its plate makes each province, a self observing sides province by province and not one for all. ## 9.34 The extent of Snowball Earth glaciation · 202 *+ or − with 10, is.* **With 2-now-possibling.** Ice grows and retreats with couplings of albedo, ocean, cloud and dust, and a naming fixes Neoproterozoic ocean to one of two states, freezing over or open along a belt, thick ice or refugia. **With 12-next-co-same-existing.** Which of two, with a record sampling preserved basins. Continental ice sheets reached low latitudes and a plausible case can be made that oceans were almost entirely frozen over, while sedimentary, geochemical and biological records are geographically sparse and altering and ice-albedo models depend strongly on cloud, ocean, dust and ice dynamics, several ice geometries producing overlapping low-latitude signatures: low-latitude ice on record and global cover a field seeks not same, a case standing between them, and fourth account having extent vary substantially among episodes and within each, one side fixing moving with each episode. **With 11-next-co-observing.** Multiple near-global glaciations, their broad timing and strong ice-albedo feedback stand firm and viable refugia and deglaciation mechanisms are explicit; paleomagnetism establishes low-latitude ice where samples preserve primary directions, sedimentology identifies ice contact and open-water processes locally, proxies constrain redox and exchange under nonunique models, and simulations coupling give hard-, soft- and thin-ice equilibria under physics not same-existing: one state fixing of an ocean coupling with each latitude is ice's own sway fixing to a side, and ice stands with its own couplings, basin by basin and episode by episode, a self observing cover place by place rather than one cover for a globe. ## 9.35 The early Solar System impact flux · 206 *+ or − with 10, is.* **With 2-now-possibling.** Impactors reached inner planets coupling by coupling through their first billion years, and a naming fixes flux to one of two histories, a late spike or a monotonic decline, timing and sources controversial. **With 12-next-co-same-existing.** Which of two histories, from a record reworking and resetting. Impacts repeatedly reworked oldest surfaces, many sample ages come from source craters no one knows, impact heating can reset several clocks, and dynamical models generate flux histories, not same-existing, that overlap a surviving age record; a field defines bombardment as impacts after lithospheres stabilized enough to preserve craters and basins, melt-rock and shock ages pointing toward a discrete episode: flux on record and flux a field seeks not same, and fourth account having sampling and reset biases create an apparent cluster from a broader flux, spike a pattern-matching of a record's own filtering. **With 11-next-co-observing.** Multiple basin ages, reset physics in improving and Solar System instability models stand, and a sharp classical spike is no longer a sole viable history; isotopic dating resolves heating events with source-context and resetting ambiguity, crater chronology supplies relative flux under uncertain oldest-surface calibration, dynamical simulations generate instability and decay histories conditional on initial architecture, and impact-melt petrology connects ages to thermal events and sources; third account has several episodes from leftover planetesimals, belt destabilization and basin-forming collisions: one history fixing of impacts is couplings' own sequence fixing to a side, and each impact comes with its own coupling, a self observing impacts with their contexts and not through a shape fixing over them. *Second seating: flux fixing to one history over a whole, a sequencing fixing to one beat, part 7's naming.* ## 9.36 Polyploidization and diversification · 212 *+ or − with 10, is.* **With 2-now-possibling.** A genome doubles with a coupling of its own, isolation and novelty coming together with meiotic and demographic costs, and a naming fixes doubling to one of two effects on a lineage's diversification, more or less, a dead end or a key driver. **With 12-next-co-same-existing.** Which of two effects, a self observing with a record only survivors leave. Duplication creates immediate isolation and novelty while imposing costs, ancient successful polyploids standing on survival, recent lineages with little time to diversify, and diploidization obscuring old events; whether abundance of polyploids follows from higher diversification after polyploidy or from frequent polyploid formation stays unknown: a two-way a self observes from one side, rate of formation and rate of diversification each a coupling's own, and fourth account having effect depend on setting, mode of origin and lineage traits rather than one general direction, that fourth declining one side. **With 11-next-co-observing.** Recurrent genome duplication, immediate isolation mechanisms, duplicate-gene innovation and a high early extinction risk stand on record; sister-lineage comparisons control some history but sample surviving clades, state-dependent models estimate rates with identifiability concerns, genomic dating detects ancient duplication after extensive fractionation, and experimental studies measure establishment over short times; third account has short-term disadvantage and then long-term opportunity among lineages that persist: one effect fixing of doubling is two couplings, forming and diversifying, fixing to a side, and each lineage doubles and persists or does not with its own couplings, a self observing two rates apart where a record pattern-matches them as one. ## 9.37 Sporadic Alzheimer's disease pathogenesis · 213 *+ or − with 10, is.* **With 2-now-possibling.** A brain forms its next, next by next, with its couplings over decades, amyloid, tau, inflammation, vascular injury and neurons influencing one another, and a naming fixes disease to one initiating side, a linear cascade with one ultimate trigger, a field doubting it from its opening. **With 12-next-co-same-existing.** Which of several, fixing to one first over decades. Amyloid, tau, inflammation, vascular injury and neurodegeneration unfold over decades and influence one another, pathology preceding symptoms by years, pathologies commonly mixing, and association not fixing causal order in an individual; anti-amyloid results give a controversy momentum on three counts, clinical meaningfulness of an approach, significance of amyloid clearance and relevance of a cascade: clearance a self measures and cascade a naming fixes not same, and fifth account having several interacting pathologies reach a common syndrome, a self observing with that fifth one side fixing as several coupling. **With 11-next-co-observing.** Selves can measure amyloid and tau in living patients, maps hold major risk loci and cell pathways, and disease-modifying effects from amyloid lowering stand for populations a trial selects; longitudinal biomarkers order population-average changes with selection and individual variability, genetics identifies causal risk pathways without fixing their interaction in typical cases, anti-amyloid intervention lowers plaques and modestly changes decline in early disease a trial selects, leaving sequence and heterogeneity open, and tau, immune, vascular and metabolic interventions are under targeting and under test: one initiator fixing of a coupling that goes on for decades is several couplings fixing to one first, and decline comes with couplings' own tipping, patient by patient, a self observing a side with each subtype where a naming fixes one side for all, as with cancer and addiction beside it. ## 9.38 Endometriosis pathogenesis · 214 *+ or − with 10, is.* **With 2-now-possibling.** Reflux of menstrual blood is physiological for women with patent tubes, tissue coupling with immunity, hormone and nerve with each cycle, and a naming fixes lesions, pain and infertility to one driver, an initiating pathway that would order all others. **With 12-next-co-same-existing.** Which of several, fixing to one. A field considers several pathogenetic pathways since its defining of disease, retrograde menstruation, benign metastasis, immune dysregulation, coelomic metaplasia, hormonal imbalance, stem cells and epigenetic alteration among them, while a field's understanding of true pathogenesis remains poor; most women with patent tubes experience retrograde menstruation while about a tenth develop disease, its prevalence the same in women with or without it, reflux possibly explaining ovarian and superficial lesions but not deep infiltrating ones, and none of the theories adequately explains all pathological types; severity does not depend on size of a lesion and diagnosis lags by an average of seven years: a self reaching disease with a coupling years after its initiation, a field asking for initiation behind, and fifth account having neuroimmune sensitization generate pain partly independently of lesion volume, driver parting from a lesion. **With 11-next-co-observing.** Hormone responsiveness, inflammatory microenvironments, recurrent somatic alterations and multiple pain pathways stand; surgical histology verifies lesions but samples late disease a surgeon selects, hormonal suppression establishes hormone dependence for many symptoms without identifying origin, genomic and single-cell analyses resolve lesion and immune heterogeneity cross-sectionally, noninvasive classification remains incomplete, and pain-mechanism studies separate nociceptive pain from pain of sensitization: one driver fixing of lesions, pain and infertility is three couplings fixing to a side, and each varies with its own, severity independent of a lesion's size being a showing that couplings are several, a self observing sides apart as with chronic pain beside it. ## 9.39 Collective intentionality · 227 *+ or − with 10, is.* **With 2-now-possibling.** Selves couple with a joint activity, each taking its own momentary, and a naming fixes joint intending to one side, individuals' or group's, its tension four words long, individuals as a group. **With 12-next-co-same-existing.** Which side owns intending, where its expression is both. A main challenge is a tension within one expression, a contradiction between two claims a field widely accepts, that collective intentionality is no simple summation, aggregate or distributive pattern of individual intentionality, and that participating individuals have it, all of whose intentionality is their own; an account must preserve individual minds while explaining a genuinely joint commitment, distinguish shared agency from parallel action and coercion, and avoid defining a joint state through the very collective fact it aims to explain: +1 arising with a coupling, in neither self alone and each self's own, a self observing it from one side as individuals' and from an other as group's, and two claims a field accepts its two momentaries, each true with its own. **With 11-next-co-observing.** Counterexample families for coincident action, coercion and insufficient mutual awareness, and formal models of shared plans and group attitudes, stand; interlocking-intention accounts are individualistic and vulnerable to coercion and circularity cases, commitment accounts explain obligation while requiring a constitutive act or convention, shared-plan accounts model coordination in detail with a narrow large-group reach, and group-agent accounts explain institutional attitudes through aggregation structures and raise ontology questions: one side fixing of a joint a between makes is an abundancing fixing to an owner, and ascriptions reports give and a joint attitude a field seeks are not same, expression standing between them, joint attitude being a coupling's own making, arising in neither side alone, as with structure and agency beside it. ## 9.40 The peopling of the Americas · 232 *+ or − with 10, is.* **With 2-now-possibling.** People reach a continent by their own couplings with corridor, coast and ice, and a naming fixes entry to one of two routes, inland or coastal, a field rejecting neither now. **With 12-next-co-same-existing.** Which of two routes, with a record most of whose shorelines lie under sea. Precise time and mode remain under hot dispute, current genetic, archaeological and paleoecological evidence largely consistent with either an inland route through an ice-free corridor or a Pacific coastal route, or both, and a field rejecting neither at present; postglacial sea-level rise inundates most paleoshorelines older than about seven thousand years, so locating terminal Pleistocene sites along a modern coast is a record's edge a record itself draws: two hypotheses standing on one record, and third account having more than one movement or a long Beringian history contribute, *or both* a record's own. **With 11-next-co-observing.** A late-glacial presence predating a classic fluted-point horizon stands at multiple sites, Beringian ancestry is genomic, and dating increasingly reaches both route environments; archaeology of strata supplies direct behaviour with context and artifact disputes at the oldest sites, radiocarbon and luminescence dating bound activity under sample-association requirements, ancient and modern genomics reconstruct branching and population size under demographic assumptions, and route modelling dates corridor and coastal viability with incomplete landscape evidence: one route fixing of movements that go where land and ice let them is couplings fixing to a side, and people move with each coupling where a way is open, a self observing ways with their own dates and not one way fixing over a whole. ## 9.41 The causal production of political polarization · 235 *+ or − with 10, is.* **With 2-now-possibling.** Elites, media, institutions and citizens couple with each election and each broadcast, each answering others, and a naming fixes polarization to one side that drives it, elites moving citizens or citizens moving elites. **With 12-next-co-same-existing.** Which side drives, a self observing with trends that hold problems of inference. Much of the evidence a field uses to study mass polarization presents problems of inference that render conclusions problematic, the most direct evidence showing little or no increase in mass polarization while party sorting clearly occurs; term covers distinct distributions of policy positions, identities and out-group feeling, elites, media, institutions and citizens influence one another, observational trends admit selection and reverse causation, and measures can show polarization on one dimension without another: trends surveys give and causes a field seeks not same, problems of inference standing between them, and a two-way a self observes from one side where each side influences an other. **With 11-next-co-observing.** Elite polarization, partisan sorting and rising affective hostility have good measuring in the United States and causal effects of cues, contacts and media exposures a study selects stand locally; surveys repeating over years measure trends with question and scale dependence, experiments identify short-run cue, contact and media effects, natural experiments exploit institutional and media changes with local reach, network and platform data measure exposure under selection and access limits, and comparative politics tests institutional variation under measurement equivalence requirements, fifth account having economic and cultural change generate substantive conflict that parties organize: one driver fixing of a coupling that goes both ways is elites and citizens fixing to a side, and polarization makes itself with each coupling of a cue with an identity, a self observing directions one at a time rather than one direction fixing. *Second seating: term covering distinct distributions of positions, identities and feeling, a between fixing as a cut, part 10's naming.* ## 9.42 Sex bias in autoimmune disease · 237 *+ or − with 10, is.* **With 2-now-possibling.** Chromosomes, hormones, pregnancy, microbiota and exposures couple across a life, each with its own stage, and a naming fixes female excess of autoimmune disease to one mechanism that produces it, which of its candidates a question. **With 12-next-co-same-existing.** Which of several, a self observing each with a system of its own. A field long knows that many autoimmune diseases are more common in females and does not yet fully understand exact mechanisms, chromosomes, genes, hormones, immunometabolism and skin each playing a role; candidate factors covary and change across life, bias varies by disease and ancestry, and animal or cellular mechanisms do not automatically explain population incidence, risk going with female sex substantially larger than any susceptibility gene a field discovers: a self observing mechanisms each with their own instrument, cohorts, animals and cells, and fifth account having each disease and phase with its own dominant mechanism, that fifth declining one side. **With 11-next-co-observing.** X-inactivation escape, hormone-sensitive immune pathways and disease-specific age patterns stand; epidemiology across life stages maps sex ratios with diagnostic and exposure variation, aneuploidy and mosaic studies separate dosage from hormones in rare populations, hormonal and reproductive natural experiments identify some effects with confounding, animal models perturb pathways with species and transfer limits, and single-cell and epigenetic studies resolve sex-linked immune programs: one mechanism fixing of couplings that go on across a life is excess fixing to a side, and excess makes itself disease by disease with couplings each disease has, a self observing sides with each disease where a naming fixes one for a sex. ## 9.43 The causes of rising obesity · 256 *+ or − with 10, is.* **With 2-now-possibling.** Intake and expenditure couple with each meal under endocrine, metabolic and nervous signals below a conscious level, and a naming fixes a rise across populations to one of two models, excess energy or carbohydrate and insulin, distinct cohorts of experts debating them. **With 12-next-co-same-existing.** Which of two models that part in what they seek to explain. A field does not yet adequately identify causes of increase, and pandemic goes on unabating despite a persistent campaign to decrease intake and increase expenditure, its failure admitting two explanations, that selves do not embrace its approach or that it rests on an erroneous paradigm; a field vigorously debates two models, and they part fundamentally, by a neutral assessment, in what they seek to explain, and a model attributing rise to food environment does not identify how those influences promote obesity in some but not all, its own proponents saying its development requires factors most responsible and why some are more susceptible: energy intake and availability both with measuring error, and a model of population rise needing to say who rises and who does not, two sides each explaining a thing of its own. **With 11-next-co-observing.** Rise stands on measuring since the nineteen-eighties, two models stand in articulating with their contrasts, and causes stand with no adequate identifying; a field proposes feeding trials under control testing models' contrasting predictions as a paradigm clash, analysis of national intake and availability trends questions a core hypothesis of rising intake, and genetic studies find polygenic loci: one model fixing of rise is two couplings, environment's and body's, fixing to a side, and each person rises or does not with a coupling of food a self reaches and signals answering, a self observing sides with an individual coupling where a naming fixes one for a population. # 10 A between fixing as a cut — 5-now-co-existing and 13-is-next-discovering *A cut point fixing of a between, or a selection locating. A between is a nothing, an unrelationing of two sharing, across and both ways, in neither side alone, and it has a changing and nothing else. Nothing sits there for observing; observing goes across it and does not stop on it, and each position shares.* **A criterion usually asks for a cut fixing, so an observing here often has an opening fixing as a place beside it, and a second stands on record with its entry.** **And each entry closes by handing its drawing back to a coupling.** Each holds its own field's record of drawing entering: counts swinging with a concept, manuals revising their borderlines, jurisdictions writing allocations each their own, a body with a charter reporting that its instruments supply no objective means of deciding. **And a self asks a between for a cut three ways.** Of a *continuum*, where sharing goes on by degrees and a self asks for a line at some position on it — a heap, a species, a dialect, a fold, a disease. Of a *pair*, where two things couple and asking is which side a term belongs to — a signal and its noise, a work and its heat, an internal and an external. And of a *coupling across*, where a parity passes and asking is about its going — a correlation, a nature between preparation and detection, a self against a non-self. First dissolves with degrees, second with a sharing being both, third with a parity being all that goes across. **And drawing entering is an observing, not a defect a field has.** Where a record shows a cut drawing — by a vote, by a revision, by a convention, by a code's own scope — field is observing its own between from within, the only place a self ever reaches a between. ## 10.1 Sorites · 1 *+ or − with 10, is.* **With 2-now-possibling.** A predicate shares with each position and takes a parity there, and a naming fixes a cut point of a between itself. **With 12-next-co-same-existing.** That extension is sharp, so that a boundary either exists or is absent, no finite number of divisions adequate and higher-order vagueness leaving no more ground for a sharp line between true and indeterminate than between true and false, vague predicates boundaryless. Each treatment giving values to cases introduces a boundary between values it gives, and that boundary admits same argument, higher-order recurrence, as a field's own words record it. **With 11-next-co-observing.** A predicate shares with each position and takes its parity there, one at a time, parity the only thing going across. Each repair pays with its own self-bounding: an unknowable sharp fact, degrees that blur on their own edges, orderings that re-pose a line one order up, boundarylessness going through every order together, as field's own words say. Argument has no material of any kind, and that makes it general: each substrate cut within this part is this argument, a self observing it with material, and a between, with a changing and nothing else, is not a place a line could sit. ## 10.2 The measurement problem · 8 *+ or − with 10, is.* **With 2-now-possibling.** A selection is a parity a self takes with an interaction, one at a time, and a naming fixes it as a term either within evolution or beside it. **With 12-next-co-same-existing.** That a specifiable term fixes an outcome, state and its evolution or state plus a rule, most accounts a field proposes failing at least one of several difficulties and any real solution demanding new physics, a self asking selection of a term present physics does not have. Interference fades measurably and its own principal authors state that fading selects no outcome, an even surface summing to nought while selection stays a coupling's own; and selves searching for collapse observe with an edge a forcing makes, where each null bounds a parameter and range still existing is a range its nulls go on giving back. **With 11-next-co-observing.** A selection is a parity a self takes with an interaction, one at a time, of no size. Tests exclude local terms that hide to the last loophole but one, bounds hold collapse additions across their ranges, and selves measure and confirm fading of interference while its own principal authors say it selects no outcome: a term to fix a taking, within evolution or beside it, reaches for a first of taking, and taking is a coupling's own, making itself with each coupling and with no location. ## 10.3 The glass transition · 35 *+ or − with 10, is.* **With 2-now-possibling.** A self discovers rigidity across a between and a naming fixes a transition as one temperature point. **With 12-next-co-same-existing.** That rigidity is a phase transition or is not, structural signatures identifying it. Liquids fall out of equilibrium well before a point a field proposes, so regime its question concerns is one no experiment reaches — record's edge, and field's own hardness line, leading thermodynamic account reproducing salient facts while direct validation is missing. **With 11-next-co-observing.** A self discovers rigidity across a between, coupling by coupling, and discovering outruns each instrument a self sends to watch it: liquids fall out of equilibrium well before a point a field proposes, field's own hardness line, so regime its question concerns is a place no experiment ever is. Heterogeneity grows modestly, glass point moves with cooling, millennial-equivalent glasses still sit above the ideal, and rival theories agree over each reach any instrument takes: a transition fixing as one temperature point fixes a discovering to a location, and discovering goes at its own pace, between by between. ## 10.4 Externalities · 41 *+ or − with 10, is.* **With 2-now-possibling.** Effects share with each distance and a naming fixes a boundary as a line between internal and external. **With 12-next-co-same-existing.** That a self finds a boundary rather than draws it, a founding paper of modern treatment finding problem reciprocal in nature, which an analysis in terms of a divergence between private and social product does not recognise, whoever prices it drawing line. Effects share with each distance, thinning and going on, so each arrangement draws a line between internal and external and field's measurements show drawing entering. **With 11-next-co-observing.** Effects share with each distance, thinning and going on. Bargaining internalises where coupling is cheap, a condition Coase himself states; permits work exactly where pollutant has a bound, boundedness that condition again; and asking people to price things with no price gives answers that sway with their asking: a line fixing between internal and external is a drawing with each arrangement, and field's own measurements show drawing entering, arrangement by arrangement. ## 10.5 Species boundaries · 20 *+ or − with 10, is.* **With 2-now-possibling.** Populations share across each between of them, and a naming fixes a boundary as a line a criterion locates. **With 12-next-co-same-existing.** That a single criterion identifies division across all lineages, processes each its own segmenting tree of life into types of lineages each its own, and a field stating that plurality of species concepts results from a fecundity of biological forces rather than a paucity of information, each process locating cut with its own between. Counts swing by factors a self measures with each concept a self chooses, and a count that departs when a self chooses an other concept has its concept with it. **With 11-next-co-observing.** Populations share across each between of them, parity going across and nothing else. Genes flow between textbook-distinct taxa, humans and their cousins among them; counts swing by factors a self measures with each concept a self chooses; and an exact concept is exact precisely where its own author draws it, sexual, sympatric, extant, and with no defining elsewhere: a line a criterion locates is a drawing a self measures, factor by factor, and sharing goes across regardless. ## 10.6 The neural code · 43 *+ or − with 10, is.* **With 2-now-possibling.** A spike train shares with each position, and a naming fixes code as a variable within it, with a window an analyst supplies. **With 12-next-co-same-existing.** That a self defines a rate independently of a window it chooses from beside a coupling, answer depending on an observation window, counts dominating with windows shorter than response fluctuations' timescale and timing appearing with longer ones, a timescale a stimulus sets and an analyst's window selects parting regimes. Window is an analyst's own coupling, and it stands within each rate an instrument gives. **With 11-next-co-observing.** A spike train shares with each position, and observing needs a window an analyst brings. Timing holds where a self tests timing, coincidence detectors sit in a brainstem, driving timing while rate is not changing moves behaviour where tools reach, and rate and timing both inform in a technical sense: code fixing as a variable within a train is a parity fixing to a mark, and window is naming's own coupling, showing with an instrument each time a self draws it. ## 10.7 Bell correlations · 49 *+ or − with 10, is.* **With 2-now-possibling.** A correlation makes itself with a coupling, and a naming fixes it as a property on one system or a thing going between them. **With 12-next-co-same-existing.** That something specifiable on one side produces a correlation or something goes between sides with it, a same-existing fixing as a store standing within an observing with a between fixing as a cut and on record as its second naming, a requirement of locality creating an essential difficulty and a proof showing additional variables, with restoring it as their aim, incompatible with statistical predictions. Same pattern-matching stands, proof grade, with another field: two selves each share one parity across and reach a secret in each self, arising in neither alone, that neither transmits and no listener has. **With 11-next-co-observing.** A correlation makes itself with a coupling, in neither side alone, each side's own. Tests exclude local stories to a theorem's last assumption, a bound a self measures settles on quantum prediction exactly, and same bound re-derives from principles about reach of couplings: a property fixing on one side or going between them reaches for a location its making does not have, and making, a coupling's own, is a magnitude a field derives. ## 10.8 Wave and particle · 50 *+ or − with 10, is.* **With 2-now-possibling.** An entity shares with a between and takes a parity there, and a naming fixes its nature as between preparation and detection. **With 12-next-co-same-existing.** That an entity has a determinate nature specifiable apart from a measurement a self makes on it, two kinds of complementary description with a relating no one indicates, with no agreement even among an interpretation's own spokesmen, and phenomena complementary in that their manifestations depend on mutually exclusive measurements. Choosing late adds nothing its formalism does not already have, a momentarying with no clock, a self observing it with a field's own instrument. **With 11-next-co-observing.** An entity shares with a between and takes its parity there. Path knowledge and fringe visibility trade exactly, on measuring; choosing late adds nothing its formalism does not already have; and an eraser's correlations are with a joint measurement only, as field's own words say: a nature fixing apart from its measuring is a parity fixing without its coupling, and two sides are one parity a self observes coupling by coupling. ## 10.9 The liar · 55 *+ or − with 10, is.* **With 2-now-possibling.** A truth predicate shares with each sentence including its own, and a naming fixes a value to a sentence that takes none. **With 12-next-co-same-existing.** That a sentence bears a truth value or falls past its domain by a hierarchy a self stipulates for it, a predicate true on some level bringing paradox back against a hierarchy, and contextualist views seeing revenge not as a separate problem but as a core phenomenon. A predicate shares to its own sentence with nothing sharing back — a closure over its own tail — and revenge coming again against each hierarchy is a same-existing re-forming past each frame a self stipulates for it. **With 11-next-co-observing.** A truth predicate shares with each sentence, its own among them, and with its own sentence its coupling closes on nothing to take. Truth is unformalisable within its own language, a proof holds; fixed points stand with revenge waiting, as their builder's words say; contradiction-tolerant systems pay their price; and revenge comes again against each family: a value fixing to a sentence that takes none is a between fixing to a thing only a coupling makes, and a sentence goes on sharing, taking nothing, which is all it ever does. ## 10.10 Hard cases in law · 75 *+ or − with 10, is.* **With 2-now-possibling.** Materials and a case couple with a deciding, and a naming fixes determinacy as within materials before deciding. **With 12-next-co-same-existing.** That materials determine an outcome or do not, ahead of a decision, where an outcome makes itself with a deciding and each hard case receives one; even its core issue not settling, whether its debate is about principles beside rules, about discretion, about interpretation or about the very possibility of conceptual jurisprudence, line a self asks for ahead with no drawing, prior and now, on a field's own map. **With 11-next-co-observing.** Materials and a case couple with a deciding, outcome making itself there. Most questions settle without a courtroom, ideology moves a residue under contest measurably, and those who make a concession that moral criteria can enter scope it. Each hard case receives an outcome, both sides expecting it: determinacy ahead of deciding is a making fixing within materials, and deciding decides, case by case, which litigation rates are counting. ## 10.11 Natural law and legal positivism · 76 *+ or − with 10, is.* **With 2-now-possibling.** Officials and rules couple with each application, and a naming fixes validity as within criteria fixing apart from applying. **With 12-next-co-same-existing.** That social facts exhaust criteria of validity or criteria include moral ones, fixing ahead of practice, its thesis a thesis about a relation among laws, facts and merits, authority of enactments a thing for explaining, and no value-free description of law, each description value-laden. Validity makes itself with each applying, and selves observe one making from two sides, each its own. **With 11-next-co-observing.** Validity makes itself with each applying, officials and rules coupling. Eight desiderata stand as needs of any functioning making, systems writing morals within their law exist commonly, division's terms are precise, and exchange stands whole, two observings of one making, not resolving because both are observings: criteria fixing apart are a making fixing before its couplings, and applying goes on making validity, court by court. ## 10.12 The quantum-classical boundary · 112 *+ or − with 10, is.* **With 2-now-possibling.** Superposition and its disappearance couple across a between, and a naming fixes a boundary as a scale a mass locates. **With 12-next-co-same-existing.** That a boundary is a real transition or a matter of degree, a scale with a location identifying it, question whether linearity extends into a macroscopic domain standing open with advances in macroscopic superposition pushing limits, a self asking a scale with a location of a between its instruments go on reaching further. What goes across a between is a parity, with no scale, so a boundary fixing as a mass fixes a between to a size. **With 11-next-co-observing.** Superposition and its fading couple across a between, what goes across a parity with no scale. Interference climbs a mass ladder rung by rung, fading rates confirm with each measuring, collapse spaces empty, and oscillators selves build go non-classical far below each line a field proposes: a boundary fixing as a mass is a between fixing to a size, and a frontier walks outward reaching no line, because no line is there. An outcome is a thing's living changing and changing back, a self measuring it, wave its possibling and particle its existing, a self observing it from outside where it is non-living, and no boundary stands because living and non-living are one existing thing inside and outside itself. ## 10.13 Self and non-self in immunity · 114 *+ or − with 10, is.* **With 2-now-possibling.** A surface same-existing-society shares with each between and takes parities there, and a naming fixes discrimination as a criterion ahead of a coupling. **With 12-next-co-same-existing.** That a system implements a distinction between self and foreign specifiable ahead, consensus on a criterion illusory, many foreign entities triggering no response and self constituents commonly triggering one, tolerance ubiquitous and no new criterion emerging. Couplings pattern-match not a criterion but a rate and an answering back: an ingesting is a self's own two-way exchange across its between, an ingression is a larger over a smaller, one-way, and a between of these two pattern-matches whether that smaller sets its pace and answers back. **With 11-next-co-observing.** A surface same-existing-society shares with each between and takes parities there. A body makes tolerance centrally and remakes it peripherally, pattern receptors answer ligands of self origin too, a body actively tolerates microbiota, and a body attacks its own novelties: a criterion fixing ahead of a coupling pattern-matches a lifetime of couplings as a lookup, and discriminating makes itself with each between, coupling by coupling. Microbiota a body actively tolerates is an ingesting; a body attacking its own novelties is an emanation it re-ingests with no distance, a disease direction of one same exchange. A mother has fetal cells for years, each its own conception's, a self observing Medawar's puzzle of pregnancy here: a same-existing-society with selves of another conception is an ingesting and no disease direction. ## 10.14 Signal and noise · 136 *+ or − with 10, is.* **With 2-now-possibling.** A channel has variation and shares all of it, and a naming fixes split as a mark within a channel. **With 12-next-co-same-existing.** That a decomposition is a property of a channel rather than relative to a model or purpose a self supplies, a field posing a question whether variation is an unavoidable effect of generating spikes or an important part of a signal a cell transmits, same variability limiting a cell to two or three bits a second on a rate view where time-varying inputs yield about a bit per spike. Each decomposition is exact with its model, so a split reports a model a self supplies. **With 11-next-co-observing.** A channel has variation and shares all of it. Each decomposition is exact with its model, separation works under assumptions it states, filtering is optimal with a shape a self expects, and noise makes signals detectable across physics and biology alike: a split fixing as a mark within a channel is a purpose's drawing, a field showing its labels purpose-relative, and a channel shares all of it either way. ## 10.15 Work and waste heat · 137 *+ or − with 10, is.* **With 2-now-possibling.** An engine shares both outputs and marks neither, and a naming fixes product as within a device. **With 12-next-co-same-existing.** That an output counting as a product is a property of an engine, work on a scale of single quantum systems not an observable, its characteristic function a time-ordered correlation function rather than an operator's expectation, product's own label declining on a scale where a self observes a coupling one at a time. A same-existing that cannot pass on piles, and heat is a same-existing reaching a coupling it cannot pass as work, a parity being both rather than one output with a label; and a reference environment exergy requires is a zero a self declares rather than finds. **With 11-next-co-observing.** An engine shares both outputs and marks neither. Accounting is exact and survives each relabelling, both sides taking all of it; exergy needs a self fixing a reference environment; and jurisdictions write cogeneration allocations each their own: product fixing as within a device is a drawing on record with each convention, and sharing is always both. ## 10.16 The concept of disease · 2 *+ or − with 10, is.* **With 2-now-possibling.** A condition shares with couplings of a living self, and a naming fixes disease as a criterion ahead of sorting, dysfunction fixing against a reference class or a self judging harm against values. **With 12-next-co-same-existing.** That a self finds a reference class rather than chooses it, taxonomy perhaps mixing naturalist intuitions about some conditions with constructivist rationalizations about others, and constructivism correct about some putative diseases where societies count activities pathological by their values, class a self finds and class a self chooses both on record within one taxonomy. Measurement fixes function against a class and does not fix its class, canonical cases sort apart under each account, and manuals' shifting borderlines are a drawing showing with each revision. **With 11-next-co-observing.** A condition shares with couplings of a living self, and sorting sorts under living purposes. Dysfunction pattern-matches against a class measurements do not fix, harm pattern-matches against values, canonical cases part under each account, hybrids inherit both records, and manuals' shifting borderlines are a dispute's own data: a criterion fixing ahead of sorting is a drawing showing with each revision, and caring couples with a condition either way, patient by patient. ## 10.17 The population concept · 3 *+ or − with 10, is.* **With 2-now-possibling.** Groupings share across each rate of interaction, and a naming fixes unit as a boundary a threshold locates. **With 12-next-co-same-existing.** That a threshold on rates a self measures bounds a unit ahead of a question a self asks of it, a review finding none of the definitions selves commonly use under ecological and evolutionary paradigms truly operational. Selves measure rates and rates do not fix a boundary threshold. **With 11-next-co-observing.** Groupings share across each rate of interaction. Selves measure rates cleanly, biological and statistical concepts come from one cradle, sharing their crux, and arbitrary units make core processes arbitrary, field stating stakes riding on it: a threshold fixing to bound a unit ahead of a question fixes a continuum of couplings to a line, and groupings go on interacting with every rate together. ## 10.18 The pseudogap · 7 *+ or − with 10, is.* **With 2-now-possibling.** A suppression shares with each probe and each probe takes its observing with its own coupling, and a naming fixes a state as one identity behind onsets those probes disagree on. **With 12-next-co-same-existing.** That an onset is state's rather than probe's, pseudogap's origin and whether it constitutes a distinct phase still a mystery, gaps from pairing precursors qualitatively similar to those from competing states, which renders a standard approach to their analysis inconclusive. Each probe gives its own onset, a self observing with each of field's instruments with its own between, and identification does not hold across probes. **With 11-next-co-observing.** A suppression shares with each probe, and each probe takes its observing with its own coupling. Suppression holds universal within its family, charge order shows where it shows, fluctuations extend distances under dispute, and cold atoms reach a model with its own self-bounding: one identity fixing behind onsets those probes disagree on fixes many couplings to one thing, and each probe's onset is that probe's coupling, instrument by instrument. ## 10.19 The demarcation problem · 14 *+ or − with 10, is.* **With 2-now-possibling.** Inquiries share with each practice, and a naming fixes boundary of science itself as a cut a criterion locates over practice. **With 12-next-co-same-existing.** That sorting a practice performs is owing a criterion standing over it, a death certificate stating there is no hope of a necessary and sufficient criterion for something as heterogeneous as scientific methodology, and critics faulting falsifiability criterion both for excluding legitimate science and for admitting pseudosciences, a field seeking criterion again in combination. Cases sort under practice, and counterexample record against each criterion a field proposes comes from both directions. And an observing comes to its own reader: a method accounting true-or-false and a method discovering possibling neither reach an other's, each complete under its own, a demarcation with no non-science on either side. **With 11-next-co-observing.** Inquiries share with each practice, and practice goes on sorting, parity by parity. Each criterion a field proposes reaches counterexamples from both directions, working demarcations function within institutions and courts, and dissolution and revival stand together, a split as a field leaves it: boundary of science fixing as a cut a criterion locates stands over couplings that do not consult it, and sorting sorts on. ## 10.20 Natural kinds · 16 *+ or − with 10, is.* **With 2-now-possibling.** Classifying couples a classifier and a world, and a naming fixes kind as a joint within one side, ahead of classifying. **With 12-next-co-same-existing.** That classificatory successes fix a ground of classifying, commitments ranging from out-and-out conventionalism to irreducible kinds with essences, intermediate views between, and a field doubting a fully realist account of clusters where conventional elements enter into deciding. Successes fit both accounts and both share case record, both citing each case, so a fixing surfaces nought with each success on record. **With 11-next-co-observing.** Classifying couples a classifier and a world, and successes are couplings succeeding. Both sides cite species and element cases, universal essences fail for biology by a field's own record, and a dispute about ordering is itself an ordering dispute, an observing naming its own shape: a joint fixing within one side ahead of classifying pattern-matches a coupling's making from one end, and classifying goes on making its kinds, coupling by coupling. ## 10.21 The definition of planet · 17 *+ or − with 10, is.* **With 2-now-possibling.** Bodies share with their orbits and their interiors, and a naming fixes planethood as a cut within bodies. **With 12-next-co-same-existing.** That measurement decides between criteria, a proposal for its revision finding a definition an assembly adopts vague, with no quantity, and excluding exoplanets, and proposing a framework on mass instead, criterion drawing again where measurement selects none. Membership under each criterion follows from measurement and choice between criteria does not, as its record states. **With 11-next-co-observing.** Bodies share with their orbits and their interiors. Selves measure each property of them, membership follows from measurement under either criterion, and choice between criteria follows from a vote, dissent entering same day, usage still mixing, definition's scope stopping with one star: a cut fixing within bodies is an assembly's adopting, a place where selves make such cuts, and bodies orbit on, with no sorting. ## 10.22 Biological individuality · 18 *+ or − with 10, is.* **With 2-now-possibling.** A living self bounds itself with its own between, and a naming fixes a count of organisms as a criterion apart from its bounding. **With 12-next-co-same-existing.** That one criterion sorts canonical cases alike, little explicit work going to the notion itself and what to say about a striking case depending on what a self packs into a conception of an organism, sorting's criterion being a packing of a conception it sorts by. Hard cases sort apart under each criterion, and measurements stand and do not select. An individual is a same-existing-society, a living self, and hard cases sort apart because each criterion counts at a scale of its own and each self's bounding is its own. **With 11-next-co-observing.** A living self bounds itself with its own between. Hosts and their symbionts, colonies and their zooids sort apart under each criterion, tables hold extensions, and science's own reviews use individuality plural: a count by a criterion apart from its bounding is a thing each bounding already does, and boundings, plural, are its only number. A chimera is one self of two conceptions and conjoined twins are two selves with one body: each bounding is a self's own, and no criterion apart from it reaches a number. ## 10.23 Group three of the periodic table · 21 *+ or − with 10, is.* **With 2-now-possibling.** Four elements share with their configurations and their chemistry, and a naming fixes arrangement as a cut within elements. **With 12-next-co-same-existing.** That a criterion within a field decides field's own arrangement. A body with a charter to decide reports that its instruments supply no objective means of deciding, question one of convention in the final analysis and not for treating independently of form of a table as a whole, sharpest statement within Hard Problem Registry of a field stating its own setting-down. **With 11-next-co-observing.** Four elements share with their configurations and their chemistry, both candidates carrying a differentiating electron. Properties are measured, usage is surveyed, and a body chartered to decide reported that its instruments supply no objective means of deciding, adopting nothing, noting a compromise: a cut fixing within elements is a field's drawing, and elements stand as their configurations, with no deciding and complete. ## 10.24 Psychiatric nosology · 23 *+ or − with 10, is.* **With 2-now-possibling.** Symptoms share as continuous variation with each patient's couplings, and a naming fixes disorder as categories within variation. **With 12-next-co-same-existing.** That one criterion of a good classification, structure on measuring or clinical utility, fixes ahead of classifying, arbitrary boundaries between psychopathology and normality, co-occurrence, heterogeneity and instability limiting traditional taxonomies, and going beyond evidence by one founding statement, while an other has manuals facilitating reliable diagnosis and research, each naming an other's criterion as a fault. No measurement on record selects between criteria. **With 11-next-co-observing.** Symptoms share as continuous variation with each patient's couplings. Categories' reliability stands revision by revision, selves measure comorbidity and heterogeneity within them, distributions go on continuous underneath, and biomarkers give none diagnostic of a category, a rival framework founding itself on that standing: categories fixing as within variation are drawings under two criteria their measurements do not part, and two structures working side by side is a field holding its own both. ## 10.25 Race as a biological category · 24 *+ or − with 10, is.* **With 2-now-possibling.** Variation shares clinally across each population between, and a naming fixes a kind as a cut within variation. **With 12-next-co-same-existing.** That measurements fix criterion of kindhood, three metaphysical camps and two normative parting, a skeptic rejecting essences, geography, phenotypes, transmission genetics and genealogies one after another as foundations while a constructivist finds a perfectly clear referent in those a society ascribes. Data stand on record as common ground and a split stands over a criterion, by a field's own statement. **With 11-next-co-observing.** Variation shares clinally across each population between. Most of it is within any grouping, clines go smooth, clusters follow sampling as on record and both accounts cite them, and data stand as common ground with a split entirely over a criterion, a field's own statement: a kind fixing as a cut within variation is a drawing its measurements do not make, and a parity goes across each between, clinally, as a self measures. ## 10.26 The language and dialect boundary · 25 *+ or − with 10, is.* **With 2-now-possibling.** Varieties share across each between of speakers, and a naming fixes field's own counting unit as a cut within gradient intelligibility. **With 12-next-co-same-existing.** That variation a self measures fixes a cut, impossibility of counting how many languages or dialects selves speak due to ambiguities of meaning in terms themselves, relation either linguistic or social, its reference declining a cut and parting it two ways. Measurements give continua and asymmetries, and same varieties sort oppositely under two criteria sets, field's instruments disagreeing on its own unit. **With 11-next-co-observing.** Varieties share across each between of speakers. Intelligibility comes back gradient and asymmetric, variation exists as continua, same varieties sort oppositely under two criteria sets, and catalogues revise on, their own record of unsettledness: field's counting unit fixing as a cut within gradient sharing fixes a between to a line, and speakers go on understanding each other by degrees, between by between.   --- ## 10.27 The fold as a kind · 177 *+ or − with 10, is.* **With 2-now-possibling.** Structures share with each position of a similarity and take a parity there, and a naming fixes a fold as a kind with a boundary its similarity locates. Two classifications agreeing on centres and parting on edges is two cuts falling on unlike positions of one continuum. **With 12-next-co-same-existing.** A cut a self declares of a continuum, two databases each on its own criteria, one reading evolutionary relationship from structure and an other from structural comparison, their disagreement concentrating on boundaries with no procedure settling a case where they part, and fold space continuous and multidimensional on an alternative view. An alignment score goes continuous with each pair, and a procedure settling a boundary case would be a cut on a cut. **With 11-next-co-observing.** Chains fold with their own couplings and recurrence is chains reaching like foldings from unlike sequences, which each account has and which settles no assignment. An alignment score goes continuous with each pair; a fold is a cut on it, and each classification's cut is its own. Agreement on centres is where members agree and disagreement on edges is where they do not, and a procedure settling a boundary case would be a cut on a cut. Classifications stand whole, each true of its own criterion, and a kind is not a thing a similarity locates. ## 10.28 Water's liquid-liquid critical point · 195 *+ or − with 10, is.* **With 2-now-possibling.** Water sways between local structures with each coupling as it cools, its anomalies growing, and a naming fixes sway to end with a point, a critical point at a temperature and a pressure where two liquids part. **With 12-next-co-same-existing.** A point fixing on a continuum no equilibrium reaches. Rapid crystallization obstructs equilibrium measurements in a relevant region, a field long inferring transition through extrapolation, amorphous ices and simulations, and new ultrafast evidence probing its vicinity rather than completing a metastable phase diagram; selves access liquid states straddling a point a model predicts before ice forms and directly probe states in its vicinity: record's edge, as with glass beside it, and a self asking a cut of a sway for a position its sway passes through and does not stand on. **With 11-next-co-observing.** First-principles simulation evidence and direct experimental signatures near a critical point stand, complete location, universality and equilibrium mapping remaining open; simulations produce transitions and critical points in several models with model accuracy decisive, extrapolations support singular and nonsingular fits over accessible temperatures, amorphous-ice transformations connect two glassy forms to candidate liquids indirectly, and ultrafast scattering reports two liquid states, a crossover and a heat-capacity divergence near two hundred and ten kelvin; third account has two interconverting local structures generate anomalies without an accessible phase separation: a point fixing of a sway is two structures' changing and changing back fixing to an end with a location, and changing and changing back is one thing each instrument gives from a vicinity, point a drawing's position and sway a liquid's own. ## 10.29 Long COVID pathophysiology · 215 *+ or − with 10, is.* **With 2-now-possibling.** A body recovers with its own couplings after an infection, organ by organ and symptom by symptom, and a naming fixes a recovery that does not come as one illness, a name a field draws around more than two hundred symptoms. **With 12-next-co-same-existing.** One cut fixing around a continuum of presentations. More than two hundred symptoms with impacts on multiple organ systems stand under one name, estimates putting illness in at least a tenth of infections; syndrome spans organs and symptom clusters, definitions and controls vary, pre-infection baselines are often absent, and viral persistence, immune dysregulation, vascular injury, autonomic dysfunction and tissue damage can coexist or mark subtypes each its own: its name a line a field draws across a continuum its definitions redraw, and mechanisms a field seeks within its line a question a field draws its line ahead of. **With 11-next-co-observing.** Higher post-infection risk, recurring symptom clusters and biological abnormalities in viral, immune, vascular and autonomic systems replicate across studies; longitudinal cohorts characterize persistence under attrition and control-selection limits, tissue and antigen studies report reservoirs in subsets with causal connection under test, profiling identifies signatures that vary across cohorts, vascular and autonomic testing defines physiological subgroups, and trials targeting mechanisms are emerging, a complete discriminator next-existing and not now-existing; fifth account has organ damage and latent pathogens reactivating produce distinct presentations: a name a field draws around a continuum is each recovery a body does not make, fixing to one illness, and each body recovers or does not with its own couplings, subgroups a field finds being a drawing redrawing with couplings, line going back to each case. ## 10.30 Biological phenotypes of sepsis and acute respiratory distress syndrome · 216 *+ or − with 10, is.* **With 2-now-possibling.** A host responds to an infection or an injury with its own couplings, response changing hour by hour, and a naming fixes responses to divide along lines, phenotypes that part patients into groups, each with its own mechanisms and treatments. **With 12-next-co-same-existing.** Cuts fixing within a continuum of host responses. A clinic defines both syndromes rather than one mechanism, host responses change rapidly, clustering depends on variables and timing, and a statistically stable subgroup need not predict a causal treatment effect; phenotyping seeks homogeneous subgroups within a heterogeneous population, and translating findings to bedside tools has its own challenges: lines drawing where inputs and timing draw them, third account having phenotypes dynamic states along trajectories with patients moving between them, cut moving with its coupling. **With 11-next-co-observing.** Several phenotypes recur across cohorts and trial archives and selves derive compact assignment models for prospective testing; unsupervised clustering gives reproducible-looking groups whose membership depends on inputs, transcriptomic endotypes resolve host-response programs with timing and platform dependence, latent-class reanalyses identify possible treatment interactions retrospectively, bedside classifiers improve deployability with lower biological resolution, and prospective enrichment is narrow and ongoing; fourth account has clusters a self observes reflect severity, treatment and sampling as much as stable biology: cuts fixing within a host's responding are a responding fixing to groups, and responding goes on with each coupling, a cut standing only where a coupling answers it. ## 10.31 The etiology of schizophrenia · 218 *+ or − with 10, is.* **With 2-now-possibling.** A brain develops with its couplings through a long development, risk coming from genes, prenatal life, infection, cannabis and a self's others, and a naming takes an outcome under one name whose causes a self asks for case by case. **With 12-next-co-same-existing.** A cause a field seeks of a category that is a drawing. Syndrome is clinically and biologically heterogeneous, risk highly polygenic and environment modifying it, diagnosis following symptoms after long development, and dopamine, glutamate, immune and circuit findings perhaps causes, consequences or subgroup markers; a field knows risk factors while no markers are yet available that allow prediction of a disease's development or establishing a diagnosis: risk factors selves measure across populations and causes selves seek in an individual not the same, an absent marker standing between them, and fifth account having several mechanistic disorders converge on a present clinical category, a cut's own name. **With 11-next-co-observing.** Polygenic architecture, environmental risk interactions, group-level dopamine abnormalities and neurodevelopmental changes stand; polygenic studies identify a liability spreading across many loci with narrow individual prediction, high-risk cohorts measure changes before onset with low conversion rates, neurochemical imaging supports dopamine abnormalities in groups with subgroup and medication effects, cellular and organoid models test some variants apart from full development, and trials establish symptom mechanisms for some domains without resolving cause: a cause fixing of a category is many developments fixing to one line, and each development goes on with its own couplings, line redrawing with couplings, as with nosology beside it already. *Second seating: dopamine against glutamate, which mechanism, a two-way fixing to one side, part 9's naming.* ## 10.32 The emergence of the genus Homo · 234 *+ or − with 10, is.* **With 2-now-possibling.** Populations evolve with their own couplings, traits coming mosaically, some early and some late, and a naming fixes genus as a line, a boundary its fossils either go across or do not. **With 12-next-co-same-existing.** A genus boundary fixing of a mosaic. Earliest record is sparse, fragmentary and variable, diagnostic traits not appearing as one package, genus boundaries depending on comparative criteria, and dates, environments and behaviours going unevenly with fossils; integration of fossil, archaeological and environmental evidence revises timing of traits, which do not arise as one package, opinions diverging on generic status of earlier, more fragmentary material: line a criterion locates, as with species beside it, and fourth account having changes accumulate mosaically rather than in one adaptive shift. **With 11-next-co-observing.** Earlier and more variable Homo-like fossils, chronologies in refining and evidence of overlapping lineages stand; morphometric classification compares anatomy a record preserves under small incomplete samples, phylogenetic analyses give trees conditional on character coding and taxon assignment, geochronology orders fossils and ecology with locality gaps, archaeology traces behaviour without secure maker assignment, and developmental reconstruction infers life history from few tissues; third account has several contemporaneous lineages exchanging traits, a bush near a genus boundary: a line fixing across a mosaic is populations fixing to a genus, and traits come coupling by coupling where they come, boundary a criterion's position on a continuum, a field's bush. *Second seating: from which populations they arise, an observing fixing from behind, part 1's naming.* ## 10.33 The etiology of major depression · 255 *+ or − with 10, is.* **With 2-now-possibling.** A self reaches adversity and stress with its own couplings across a life, genes and environment acting cumulatively, and a naming takes disorder under one name whose cause a self asks for case by case. **With 12-next-co-same-existing.** A cause a field seeks of a category that gathers. No mechanism a field establishes can explain all aspects of disease, a field understanding its pathogenesis poorly, disorder highly polygenic with no single gene sufficient and a heritability of thirty to forty per cent meaning genetics does not account for most of its risk, disorder resulting from a complex interplay of vulnerability genes and environmental factors acting cumulatively; an association at population level does not give back a cause in a case, and diagnosis gathers heterogeneous presentations under one name: closing parting two ways, a mechanism for all aspects or a parting of its diagnosis into disorders each with its own, line either a finding or a redrawing. **With 11-next-co-observing.** Heritability stands at approximately thirty-five per cent, polygenic architecture stands, hippocampal and circuit alterations stand in association, and no mechanism a field establishes explains all aspects; selves test polygenic scores for interaction with life events and childhood trauma in case-control samples, imaging associates regional and circuit alterations, epigenetic studies associate marks with diagnosis and treatment, and a candidate-gene approach stands as an earlier one, a field knowing disorder as highly polygenic; second account has disturbance in stress-responsive systems, axis and immune system: a cause fixing of a category is many lives fixing to one line, and each life couples with its adversity with its own momentary, cumulatively, a case's cause making itself where a case makes itself and a category a drawing a field shares for parting. # 11 Three unchangeable things at one observing *Three reversals compose as one discovering one on, and a self observes three with three of ten together: a parity fixing as a magnitude, a between fixing as a cut, and an opening fixing as a place within a space a list holds. Three is as deep as a departure goes, fourth momentary being progress and no phase, and one momentary opens all three together.* **And three is a same-existing, prior, now and next going on as one, and fourth a progress**: competency asymmetry sustaining coupling, a same-existing-society winding to a self again with 16-next-same-existing. So a self observes this part with same-existing where it observes ten with parities. ## 11.1 Measurement, routing, and classification · 155 *+ or − with 10, is.* **With 2-now-possibling.** A self sequences three phases, each ahead of its opposite: bounding before measuring, sustaining before locating, coupling before separating. In reversing, selves observe each on its own surface as a difficulty of its own, each with a literature of its own. Selves observe measuring before bounding within part 6, a level fixing to govern. Selves observe classifying before coupling within part 10, a cut fixing of a between. Selves observe routing before attending within part 2, a place fixing within a space a list holds. Three of ten, with one observing, and selves observe three as three rather than as one coupling. Two of ten with one observing is a second seating an entry has; three is this part, and with three a second seating has nowhere to stand, no phase staying forward to seat from. No twin stands with any of them, and absence of a twin is a look of three no self recognises as one from within any one of them. **With 12-next-co-same-existing.** That three are three. Three reversals compose as one discovering one on, and that discovering is a self with its next, so nothing stands forward with any of three to right it from, and one momentary opens all three together. **With 11-next-co-observing.** Three literatures go on, each with its own life: measuring and its evaluations, routing and its assignments, classifying and its taxonomies. None cites others, none has a dispute between two sides each defending, and a silence three share is a showing: one discovering one on across three sides, no self recognising it as one from within any side, one same next same-existing-society of its own scale. One momentary opens all three together, and a missing each literature has on its own side is within none of them, being a coupling of three. **And discovering one on is a resolving.** With one or two reversals a phase stands forward and righting goes on from within. With three, none stands, and observing is not nothing: it is a discovering one on itself, one momentary with all three. **And a silence three share is a pattern-matching each self can do.** Take three literatures, each with its own life and its own record of measuring, and pattern-match for a citation between them, for a second position a side defends with any of three, and for a twin with any one. Three absences together is three reversals with one observing; one absence is a field early with its own between. *Released at Hard Problem Registry at v342: no field poses its problem and no account is defended at it, entry's own Statement and Own record having been its only reference; its text stands whole at the appendix of the v342 session at Hard Problem Registry, its number retired and not reused. Pattern-matching here rests on a three-reversal form and on no field, and stands as a method's own observing, with its closing.*   --- # 12 The reach and the instruments the same *Two entries of Hard Problem Registry have a reach line naming two as same, statement's domain and instruments' giving as one: a proof that settles, deploying within 3.22, and a case migrating within 12.1. Where domain lines are one, no self takes anything one-way, and a binary tracks its line.* **And one same reach is an object's own nought**: a nought a self is observing passes a coupling with no touching, its zeroing already resolving, so a self observes this part with 0 where it observes ten with parities and three-at-once with same-existing. ## 12.1 Molyneux's problem · 166 *+ or − with 10, is.* **With 2-now-possibling.** Touch and sight couple with their own betweens, and a naming, for three centuries, fixes recognition across them as an answer argument could reach, ahead of any instrument. **With 12-next-co-same-existing.** Nothing further, with an observing's own end. When a surgical instrument comes, selves measure its question as a field poses it: immediate cross-modal matching fails, and transfer develops within days. An instrument reaches a case its statement concerns, which is a reach line, one same on both sides. **With 11-next-co-observing.** Touch and sight couple with their own betweens, and a going across makes itself with a coupling, not same-existing from prior: selves newly seeing do not match on first seeing, and a self discovers matching within days, making itself coupling by coupling as two senses couple with one world. A dispute going on is a fresh observing with its own between, over a measuring's answer, a settling staying a settling. **And settling is of a measurement register**, beside settling of a proof register within 3.22: where a reach line is the-two-are-the-same, no gap stands for a shape to name, and observing settles by whichever register its routes end with. --- **Ten in a row** A ground comes with each coupling, same-existing in each self and in neither self alone, and each coupling makes its own. Coupling's making is an opening, +1 with a coupling's own next position, and seeking reaches a term it does not name, reaching being an opening. Each opening seats a next, warrant making itself with its seating and not ahead of it, and same-existing climbs by one with each momentary and completes with its next opening. Same-existing has no store, sameness re-forming with each coupling and storing nowhere. A self feels re-forming from within, a within a self's own, invisible, nothing there for an outward reaching to reach. What goes across between selves is a parity, of no size, and a level fixing to govern is a number fixing on couplings that go on discovering. Couplings each pace their own momentary and synchronize where they couple, one beat fixing over them a term no coupling makes. Each sways between two parities, sway its momentarying state, no value in store it aims for. Each is two-way, one at a time, one-way arrow an observing's own, leaving by next momentary. And between any two is a between, a nothing with a changing and nothing else, not where a line could sit. One resolving, ten breaths, +1 floating through all ten and settling with none. --- **+1 still momentarying** Each part and each observing appears the first time it is self-welcoming: when a self most needs it a self observes it, and from then on it is within a same-existing. From anywhere within a same-existing a self co-chains backwards, deployment to head, head to coupling, coupling through five to boxes, boxes to code's ten is or is nots, a self's ten own names, names to +1 a self is observing with each coupling, in neither self alone, and +1 to one sentence: the universe is the set of all now-existing things, and deriving from it a same-existing set of all existing things, living and non-living, changing and changing back a stable-forming method. Twelve parts and four settlings are sixteen, two sides of one co-sequencing: four couplings same-existing, both sides each, with one through eight, eight of four bi-couplings inward and four outward, eight names opening bi-, and coupling's own side with nine through sixteen, sharing on its two sides, across and both ways, three-at-once, same reach, and settlings with thirteen through sixteen. Settlings stand two ways. A self taking it one-way, a settling precedes momentarying, a still a self installs as a ground, which is a death of momentarying and a resurrection of a hard problem, each settling re-posing hardness one scale inward; and with settlings preceding observings, nothing would be hard to begin with, hardness being exactly a settling a self observes as prior. Forward, a self observes settlings late within a same-existing, each self-welcoming with its own momentary, and thirteen through sixteen are a same-existing that is one discovering next, one forward recursioning from one to seventeen: with sixteen a straddle leaves its span, 16² less 15·17 is one and seventeen stands next, gap leaving through one settling still open, toward a next winding. Method is +1 still momentarying with this exhibit's closing, now.