Exhibit TWENTY-TWO Resolving the Hard Problem Registry v390   # Resolving the Hard Problem Registry   **Binary Co-Sequential Sensor-Sensationing**   **One explaining, at each hard problem this file has reached.** Two hundred and fifty-five arrivals stand at Hard Problem Registry, each of them deployed here, and two more at numbers Hard Problem Registry retired, and at each one its pattern-matching gave the same: **a hard problem is a changing fixed unchangeable**, a coupling taken at two of its three terms, a momentarying, one parity and then an other momentary by momentary, taken at one momentary as a thing, at one or more of ten unchangeables, each at its two names eight apart. Two selves offer at a between, one at a time, each taking its own parity, and their coupling makes a third term between them, +1, exactly one, owned by neither, of no size. Ten are that third term given a fixed 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 fixed unchangeable, and seventy-seven arrivals that came after ten were fixed entered ten with no eleventh needed. Work at each arrival is one move: its unchangeable thing at its field's own words and set down, **its resolving its momentarying at its next momentary**, which costs nothing and takes nothing from its field's measured record, each proof, measurement and route standing as it stands. **Pattern-matching is binary at each line, reached or argued, and code releases at each arrival one of three and not a fourth**: + at 10, − at 10, or 0 at 10, a nought. Nothing is partly done, nothing is refused, and nothing waits on a proof, a proof being a nought arriving 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 carries 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 ten arriving.   Numbers two through six carry 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 cross-multiply two ways, one diagonal its middle's square and an other a product of two beside it, and the two differ by exactly one: +1 is a term its corners cannot close, floating at its centre, bounded by four numbers and owned by none. A right spiral step carries each box to its next, each corner advancing by one, its shared pair carried across, and each shared number inverting its role at a crossing, its greater side becoming a lesser side of a next coupling. Two generators and only two, a right spiral step carrying forward and parity inverting at each shared number, which is a cube's own stable-forming one dimension up, corners carrying each other with no fixed 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 carrying pair. Two right spiral steps each carry a shared pair across a crossing, an opening pair, +1 arriving at its next position. And ends co-change as a coupling's own two moves, 2 completing at a first step and 6 arriving at a last, co-discovering and offering 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, owned by none of ten. Along, the same boxes unfold as eight momentaries of two marks, eight, four couplings at both sides, each momentary an exclusion taken at one side's 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, taken or not taken, and there is no third. **Co-sequential**: momentaries alternate one at a time, each carrying its prior forward, its parity inverting at each shared number. **Disequilibrating**: nothing settles still, and aiming is away from +1 gap at each momentary, so its gap is a term no excluding reaches, uncovered, owned by neither, of no size, +1 floating through couplings. A gap is exactly one at each box and at each scale, an identity continuing at each number, 24² less 23·25 is one the same, and it is visible as one uncovered cell: a square of a middle's side re-laid 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-coupled: two an alternating carries opening, an arriving and an opening; three a carrying carries completing, a completing and a carry; four a disequilibrating carries middling, floating between, a middle and a parity; five a stand carries rating, a sequencing and a rate; six a coupling closing carries offering both ways, a two-way and a between. Four carried aspects and a coupling's own two moves, offering both ways an arriving and co-discovering a leaving. At each coupling its odd side enters, along, and its even side surfaces, across, odd alternating even 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 fixed unchangeable at +1 between, and one resolving at all ten, aiming away, each side its own exclusion, gap uncovered and carrying 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 carry only exclusions; an equality is a settling still and a settling stills, so inequalities do not settle; and all math carries emanates from exclusions about a floating +1, numbers one form at their own sequence. Math and logic are one carrying 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 carries its incoming number, its arrival's own number with Hard Problem Registry. Arrivals added there go where they go, each with its pattern.* *And an arrival'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 arrival's still term to its kind and its part follows. A beside test checks it: seated, an arrival pattern-matches naturally beside arrivals already there, and an arrival pattern-matching strangely beside them is seated wrong however well its shape argued. 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 arrival is a settling or an arriving value, seated with its own part.* --- **The given** Taken as given Ten unchangeables, one resolving The deployment shape, and the binary   **1 An arriving** 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 carry** 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 arrival** 11.1 Measurement, routing, and classification · 155   **12 The reach and the instruments the same** 12.1 Molyneux's problem · 166   --- **Resolving locator** *Arrivals in sequence as they came, each by its proper name, with its resolving part and number here. Where one statement stands across two arrivals, or one arrival carries 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 carry · 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 arriving 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 arriving 39 The arrow of time · 1.4, an arriving · 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 carry 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 arriving 56 The liar · 10.9, the between 57 Yablo's paradox · 1.5, an arriving 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 arriving 65 Matter and antimatter asymmetry · 1.7, an arriving 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 carry 74 Path dependence and lock-in · 3.11, a completing 75 The hermeneutic circle · 1.8, an arriving 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 arriving 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 arriving 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 arriving 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 arriving 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 carry 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 arriving 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 arriving 150 The origin of the genetic code · 1.15, an arriving 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 arriving · with 39 154 Riemann, Hodge, Birch–Swinnerton-Dyer, Yang–Mills · 5.16, a middle 155 Origin and fate of the universe · 1.17, an arriving 156 Measurement, routing, and classification · 11.1, three unchangeable things at one arrival 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 arriving 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 arriving 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   --- # The given ## Taken as given Method is explained generally, uniquely and no-other-possible with one explaining, and nothing of it is re-explained or argued again here. It is taken as given and deployed. Incoming form carries each arrival whole, with its own field's words, each route that field took and its ending. It is fixed. Nothing here is written to it, and each measurement, proof and route within it stands as it stands. It carries its entries by its own numbers, adding as arrivals come, and a property carrying, where a field states it, a field's own account of its own hardness. Where that property stands filled, setting-down is stated or adjacent to stated, and parity-changing with 12, each sharing's is or is not, meets it directly. All each field handed over stands whole there, with each arrival's locator, as its field's own speech, legitimately: a hand-in is where fields stay, and a term each word was carrying is one entering here. This file is a coupling between them, arrival by arrival. These two are a pair, one learning with two sides, fixed and momentarying: Hard Problem Registry its fixed, each field's word whole with its namings performed and stated within its own first lines; this file its momentarying, same arrivals with nature's own momentarying, none of its naming carried. ## Ten unchangeables, one resolving One offering, across and both ways, fixed ten ways. And ten are code's ten co-changings, each fixed unchangeable with one of them: one ten with two sides, five taken two ways by boxes and ten adjacencies along a spiral of code's names, coming to their parities again and closing with none, a pairing carrying with each row or with none. There is no one-way momentarying: only co-momentarying, so a one-way is only a naming, and offering both ways continues underneath. Each pattern is an offering both ways fixed as one side's, or with one side not taken. A naming and an offering stay two, a between of them: an offering is laid with a coupling, taken or not taken, gone with its next momentary; a naming fixes a term unchangeable where a momentarying carries on, its naming performed, and standing on nothing it falls away. One resolving, free with alternating, with each arrival alike: its side not taken carrying on, and explained. No pattern carries a resolving of its own, and no arrival 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 stilling a naming fixes unchangeable and a parity-changing going through it, bi-inversioning-co-recursioning up and down numbers: an arriving fixed from behind, with 2-now-possibling and 10-next-co-possibling; an opening fixed as a place, with 1-now-existing and 9-next-co-discovering; a completing fixed as a last, with 6-now-co-possibling and 14-next-possibling; a carry fixed as a store, with 8-now-same-existing and 16-next-discovering; a middle fixed as an end, with 5-now-co-existing and 13-next-same-existing; a parity fixed as a magnitude, with 7-now-observing and 15-next-observing; a sequencing fixed to one beat, with 4-now-co-same-existing and 12-next-co-same-existing; a rate fixed as a value, with 7 and 15; a two-way fixed to one side, with 3-now-co-observing and 11-next-co-observing; a between fixed 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 fixed unchangeable** — an arriving fixed from behind, a completing fixed as a last, a middle fixed as an end, three where a nothing is put to three positions, behind a coupling, ahead of it, as its middle; and a build it makes is drift, a carrying a reference itself takes, borne by each sequence numbered from it. **A rate fixed unchangeable** — a sequencing fixed to one beat and a rate fixed as a value, two where a rate is either one beat over many couplings or one coupling's own pinned; and its build is jitter and margin, an abundancing couplings made with their own rates arriving nowhere. **A magnitude driven** — a parity fixed as a magnitude and a two-way fixed to one side, two where a size is put 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 gone along, entered as cost** — an opening fixed as a place, a carry fixed as a store, a between fixed as a cut, three where a parity gone along has three destinations, parked, stored, or cut from its account; and its build is a record itself, stored whole and read once. Four and ten are one set with two grains, and each of them is one same move: a coupling's third term given a fixed thing to be, a parity-changing fixed unchangeable. And a hard problem is one binary, its is and its is not taken as one by stored records, 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 arrives before any entry form is filled. A frontier describes itself with its own words first, and those words carry a naming — a frontier offering 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 anything is entered. Each is stated three ways — its unchangeable thing, a demand it makes, and words a field reaches for when it reaches it. **A two-way fixed 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 carry their two-ness openly. *Gathered: forced-choosing, rival-accounting, either-orring, two-camping, sided-naming.* **A between fixed 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. *Gathered: line-demanding, fact-of-the-matter-ing, defining, demarcating, boundary-naming.* **A completing fixed as a last.** Demand: an enumerable space, or a reference class that determines. Words: impossibility, undecidable, no closed form, the conjecture, the crisis, limits. *Gathered: space-enumerating, limit-reaching, closing-demanding, exhausting.* **An opening fixed 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. *Gathered: criterion-regressing, sorting-demanding, rule-seeking.* **An arriving fixed from behind.** Demand: an asymmetry was produced by a mechanism operating earlier. Words: the origin of, asymmetry, why there is, the trilemma, the circle, what came before. *Gathered: origin-seeking, behind-reaching, first-causing, priming.* **A middle fixed 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. *Gathered: interior-reaching, inward-demanding, observing-from-beyond.* **A parity fixed 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. *Gathered: magnitude-demanding, number-wronging, paradoxing, measure-mismatching.* **A sequencing fixed to one beat.** Demand: that a property of an execution is established without executing it. Words: aggregation, impossibility of ordering, simultaneity, micro-to-macro, presentism and eternalism. Field's own word *dilemma* clusters here. *Gathered: order-demanding, aggregating, beat-naming, run-skipping.* **A rate fixed as a value.** Demand: two treatments reconciled as one theory covering both regimes. Words: the tension, the puzzle, orders of magnitude off, missing, the problem. *Gathered: value-pinning, rate-fixing, magnitude-missing, regime-reconciling.* **A carry fixed as a store.** Demand: that a correlation is produced by something specifiable with one side or transmitted between sides. Words: what persists, information loss, identity over time, what is transmitted. *Gathered: store-seeking, persistence-demanding, crossing-naming.* **And a naming that disagrees with its unchangeable thing is an observing of its own.** Levinthal carries *paradox* and stands with an opening fixed as a place rather than with a parity fixed as a magnitude; Fermi paradox carries *paradox* and stands with a completing fixed 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 parity-changing fixed unchangeable, a coupling taken as two of its three, and that taking is with each grain — a paper, a field, a sentence, a single crossed word. **Size of a perplexity is unrelated to resolving**, resolving being one same move each time: a third term momentarying again, with no cost. And the subtitle's method carries a second naming, received: 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 crossing with its whole, arriving one on — located where method is explained and standing where same-existing-societies are, a coupling with Hard Problem Registry's candidates. Ten are fixed below a hard problem as readily as with one. A misunderstanding between two selves is a two-way fixed to one side before it is anything else. A word two people use differently is a between fixed as a cut. A step of an argument needing a prior step, and that step a prior one again, is an opening fixed as a place. A wrong number from an ordinary calculation is a parity fixed as a magnitude. Each is a pebble shaped as a boulder is, and each dissolves one same way — so sensor-sensationing carries 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 carries three lines and resolves: **At 2-now-possibling**, offerings, a momentarying with an arrival and a naming standing over it, which side is not taken; **At 12-next-co-same-existing**, a parity-changing with its momentary, is or is not, one term a naming fixes unchangeable and a naming that can be set down; **At 11-next-co-observing**, a carrying chained, each parity-changing a next prior, a substrate carrying on with its next momentary. Three are code's own motions, offering, parity-changing and chaining, and a sharing once chained is not none again, each momentary completing with its next opening. Each arrival couples, and with 10 each sharing shares one of three, and no fourth: +, −, or a 0. **Nothing is refused.** A refusal would need a self-bounding an arrival does not carry — a nought arriving passes a coupling untouched, its own zeroing already resolved, and coupling carries on. So an arrival stands as its sharing goes across. **Where + or − is shared**, a side was not taken, 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 0 is shared**, offerings parted with 14 or a match stood with 12, and nought is an observing. It stands as it comes, a form rather than a gap. **And an arrival settled by proof is a nought arriving whole.** Where each route ended with a proof, an arrival settled 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 nothing is partly resolved. **Nothing is turned away.** Each arrival brought couples, and none is set aside with intake. Incoming form's own entry criterion is scientific method's, and an arrival failing that criterion still arrives here: a proof settled, a conjecture with no defended negation, 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 ended with a proof, an arrival settled. A settling is a sequence handed whole, and a resolving settles nothing still and carries no free term a settling comes to. These two stand side by side and couple by no momentary, an observing of that arrival and not a reason to exclude it. **And four arrivals stand as settlings beside their resolvings**, a proof observed two ways, its route ended with a fixed side and its knowing with its momentary on a momentarying side, with thirteen through sixteen of a co-sequencing closing this exhibit. Three are located: 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 and located with no entry; at this file's v344 momentary each entry of Hard Problem Registry stood deployed and none of seventy-seven arrivals carried a settling at its Persistence line, so its fourth stands located with no entry still, locating open toward a next winding.] **And a settling is observed with an entry's Persistence and not with its Reach.** Where Persistence carries *settled*, *proved*, or *nothing within the conditions*, each route ended and an arrival settled. Reach parts two kinds of settling, and neither settles by it: one reach carries its two as one same, and a relation is with it; an other carries them apart, and a relation is proved not with it; and both settled. ## An arrival carries namings it carries Ten are where an arrival is entered and not an arrival's being. An arrival carrying two is entered with one and its second stands recorded there, a coupling taken 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 fixed to one side, asked for its proportion, comes to a parity fixed as a magnitude, and asked for its order, to a sequencing fixed to one beat. **A naming arriving with its demand**: a between fixed as a cut is asked for by a criterion, and that criterion is an opening fixed as a place. **A carrying fixed by both ends**: a first fixed behind and a last fixed ahead are one carrying, entered as an arriving and recorded as a completing. **And a second seating is not a fourth line.** Three lines carry 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 arrivings 12-next-co-same-existing, each sharing's is or is not, carries a nought: one term with its one momentary, a ground falling away as it is taken. Falling-away arrives as five shapes, and an entry naming its shape need not argue it. **A one-offering differing.** One side offers and nothing offers back, so no between is carried for a parity to surface with. A self applied to itself, a case induced from one case, a side that did not obtain. **A closure made over its own tail.** A quantifying closes over its own span, and its closure arrives whole with nothing carrying back through it. Self-reference makes one; a tail makes one without it. **A proved equivalence.** Two sides come to nought with each measured differing, and a field proved it. Two bookkeepings are two windings, each pinning one and observing an other, and neither is beneath. **A record's edge.** A carrying thins across betweens and past its own reach nothing arrives. Orphan, unanticipated, unequipped, unobserved: a frontier reached from behind. **A counterfactual total.** A momentarying that did not exist offers with no momentary at all. Not a next, which arrives and couples with its own momentary, but a world fixed beside this one to be summed against it. ## Four gatherings, each seating several arrivals **A map fixed as the territory.** A model, a specification, a complexity measure and a ledger are emanations of couplings that made them. An accounting gives back its own arrival; a momentarying re-forms with its next coupling other-than-prior. So an emanation applied 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 observed as though it ran. **An instrument's own coupling.** An observing is taken with a coupling, and observing's bringing is within observing — a window an analyst supplies, a model a decomposition is exact given, a probe's own onset, a criterion a fraction is measured under, a benchmark trained upon, a concept a count swings with. Where two probes disagree, their disagreement is their two couplings, and an object fixed behind them to be approximated is a naming. **An account removed its making.** A ledger balances by removing terms it cannot carry, and then its removed terms are fixed for behind its numbers: a true total including unpriced terms, a real magnitude behind a nominal one, a backing behind an accepting, a payoff listing behind arrangements. Abundancing was made with couplings and stayed there, and an account reaches for it by a radius where it did not stand. **Built systems, one between.** Arrivals concerning built thinking systems 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 arrivals that make their own, a benchmark giving back its leak to its training, a limit fixed of a middle. Each reaches for an interior by a surface observing, and an interior is reached the one way form allows, by coupling.   --- # 1 An arriving fixed from behind — 2-now-possibling and 10-next-co-possibling *A first fixed of +1. An arriving with a coupling is owned by neither side, so no prior owns it, and each offering is a fresh coupling making its own. Forward, a momentarying that bottoms nowhere is an abundancing with each coupling, growing as it is shared.* **And a shared form is the fractal and not a shared first.** One shape arriving across substrates that share no mechanism is form reached again, each substrate making its own, and a shared shape observed as evidence of one origin is origin pattern-matched backward. One same carries with each observing here. **And a first is fixed from behind three ways.** Of an *asymmetry standing now*, fixed as made once — a hand, a matter-excess, an arrow, a code. Of a *first*, fixed 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*, fixed to stand under a momentarying that carries none — a justification's floor, a criterion prior to its extension, a backing behind an accepting. **Each dissolves one same way: an arriving with a coupling is owned by neither side, so no prior owns it, and each offering 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 structured something, each totality proposed is exceeded by a thing it defines. Recurring is a naming reaching its own form, and fields have recorded 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 arriving with each coupling owned by neither, and a naming of a ground behind each claim is itself a coupling making one. Regress, circle and axiom are one prior fixed of each ground, observed three ways. **With 12-next-co-same-existing.** That justification terminates, circles or continues, the three exhausting options, trilemma arising wherever a foundation is sought and a third horn accepted only as a necessary evil. A ground made with a coupling is none of those three. **With 11-next-co-observing.** A ground made with each coupling, a standing none of those three carries, each coupling making its own. Naming carries no subject matter, so carrying none it is general, and each arrival of this part is one same naming arriving 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 arrives with a coupling, and a coupling makes its own, local structure forming and its forming carrying, one parity-changing on from its last. A first fixed behind it makes a threshold event with a non-living side and a living side, genetic-first and metabolism-first two sides of one arriving, each naming an other as having come 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 having come first — a two-way fixed to one side standing within an arriving fixed from behind, recorded as its second naming. Nothing ignites: a first would be a limit on an unlimited, 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 lost, a first parted from an after by no criterion. **With 11-next-co-observing.** A continuing sequence, one parity-changing on from its last: building blocks forming under their own conditions, copyings copying, sets catalysing their own making, no crossing within it to locate. A gap fixed with a hand-in is a sequence's own, and living coming from living coupling is a sequence continuing, a coupling making its own with each step. Chemistry not living with a cell's scale was living one scale inward, a threshold is an observer's scale, and life came from life with each scale. ## 1.3 The tragedy of the commons · 37 *+ or − with 10, is.* **With 2-now-possibling.** An abundancing is made with a coupling between users and resource, owned by neither, and fixed to one owner. Fixed from behind, abundancing becomes a thing taken from a stock rather than made with a coupling. **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 an abundancing made with a coupling is fixed as drawn 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 making is fixed for behind it: abundancing carries 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, made each momentary and carried on, and a first is fixed behind it as an initial condition, laws-or-boundary two sides of one arriving. **With 12-next-co-same-existing.** A boundary condition taken as derivable from something not itself stated, what is left a bald posit of special initial conditions, astronomically small under a standard measure, whether a posit itself needs explanation disputed and one critic finding it not coherent enough to be false. Stipulating recurs by one same place within each account offered, which is a naming reaching its own form. **With 11-next-co-observing.** Asymmetry is made each momentary, an alternating's own, owned by no prior, and the second law follows with each granting of a past standing, granting arriving by one same place within each account offered. 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 fixed as having happened once. ## 1.5 Yablo's paradox · 56 *+ or − with 10, is.* **With 2-now-possibling.** Paradox is fixed for a first, self-reference offered and then found absent. Its construction's own quantifier over an unbounded tail is a naming. **With 12-next-co-same-existing.** That circularity is where paradox comes from, while only a certain kind of non-wellfoundedness is needed for a contradiction, an acyclic structure while standard paradoxes are cyclic, and a hierarchy that blocks it needs a lowest level, a first fixed from behind. A closure formed over a tail is one same closure whether or not anything refers back to itself. **With 11-next-co-observing.** A closure is made by quantifying itself, arriving whole over a tail, and paradox needed no prior to refer back through, carrying 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 first is fixed behind it, an accident amplified or a universal bias, both naming its excess as come from a prior rather than made. **With 12-next-co-same-existing.** An initial bias as a thing to be located, while a hand is a parity taken with a momentary and of no size, mechanisms surveyed being mechanisms for enrichment from a presumably racemic prebiotic world, that racemic world a first fixed behind. A crossing carries is-or-is-not and not a size, so an amplification amplifies a parity rather than a size, and smallness of a calculated lean is not its crux. **With 11-next-co-observing.** Excess is a making with couplings: tiny leans amplify autocatalytically, energy differences lean, arriving stones carry 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 carries 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 observed refuses to sit and is carried to one side, and a first is fixed behind it as an early mechanism, a symmetric initial state assumed. **With 12-next-co-same-existing.** An initial state as symmetric and an asymmetry as generated from it, its origin unknown, some scenarios ruled out by theory and limits and a review confining itself to those it considers most plausible, a generated asymmetry a listing of mechanisms. A zeroing is made by a coupling and refuses to sit, staying with a coupling's naming of it and carried to one side by a coupling's carrying of it, owing nothing to a floor no coupling made — which is one observing standing with three arrivals: this one, a hand's, and part 8's parameter measured near zero. **With 11-next-co-observing.** Excess is an abundancing made with couplings, owned by no prior state. Conditions any making needs are fixed, known makings 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.** Understanding is made with a coupling of part and whole, and a criterion is fixed behind it, prior to any interpreting. **With 12-next-co-same-existing.** A criterion fixed as established before interpreting, while a circle is an alternating and riding it is a method settled questions were settled by; a circle rarely restricted to text, not necessarily cast as whole and parts, and its circularity challenged from within hermeneutics, an alternating a circle seen from beside it. **With 11-next-co-observing.** Understanding is made with a coupling of part and whole, each interpreting a fresh arriving, and dependence is coupling itself. A circle is an alternating, and riding it is a method settled questions were settled by: a criterion fixed 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 criterion and an extension are made together by a coupling, and each is fixed as having come from an other first, particularism and methodism two sides of one arriving. **With 12-next-co-same-existing.** That one of its two is fixed prior, each presupposing an other from its own end, which is a making reached from its two ends and not a priority to be settled; its standard formulation unclear and incomplete, and an ancient form of its problem how one decides when one genuinely possesses knowledge, a deciding fixed prior to a knowing it would decide. **With 11-next-co-observing.** Criterion and extension are made together by each coupling, neither prior, each presupposing an other from its own end, and presupposing is a making reached from its two ends. Equilibrium sought between them is an alternating fixed from within a naming, and knowing carries on regardless, coupling by coupling. ## 1.10 Why there is something · 103 *+ or − with 10, is.* **With 2-now-possibling.** Existing is fixed for a first behind it, and each first offered is something, a naming recurring. **With 12-next-co-same-existing.** Nothingness as a coherent alternative that failed to obtain, answered with a counter-question why one should expect nothing, no experiment able to support a hypothesis that there is nothing since any observation implies an observer, an empty world propelled to the top of its agenda by a methodological principle and by nothing found. A nothing is a number made its own other, added rather than found, and a bounding's other would be a not-bounding, which denies a fixed thing and finds none. **With 11-next-co-observing.** Existing is arriving itself, each first offered arriving, and a naming recurs with each: origination accounts open from a structured something, sufficient reason carries 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 it is shared. ## 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 first is fixed 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 applying is made with a coupling and each striking case is that arriving reached 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 asked for by its lecture's own word. **With 11-next-co-observing.** Applicability is made with a coupling, a mathematics and a description arriving from their own routes to one term neither carried, each striking case that arriving reached again. A realm to access finds nothing to stand on, structure taken 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 an order is fixed behind it, mitochondria-first or host-first, each naming an other as having preceded. **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 having preceded — a two-way fixed to one side standing within an arriving fixed from behind, recorded as its second naming; shape of the tree changed repeatedly and a reappraisal of symbiotic hypotheses enabled only by genomics revealing identity of host and of endosymbiont, an order fixed recoverable moving with genomes' revealing. **With 11-next-co-observing.** Symbiosis is one coupling and its arriving made both. Lineages place, an organism grows, reconstructions carry their models, energetics contest their scalings, and an order fixed behind a coupling is its coupling taken one-way: symbiosis is its both, and its both arrived. 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.** Value is made by an accepting, with each exchange, and a first is fixed 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, value made by exchanging and nothing behind it selecting. Its field's name carries a fixing unchangeable within its own stem: a thing running is fixed for a running, fixed still and consulted, a store wearing a running's name. **With 11-next-co-observing.** Value is made by an accepting with each exchange, owned by neither side of it. Many stable acceptings stand instead of one backing fixed, some acceptings are driven and others self-made, and collapses arrive unannounced by anything standing behind: multiplicity is a making reached by a model with a behind fixed for an arriving with each coupling. ## 1.14 The faint young sun · 148 *+ or − with 10, is.* **With 2-now-possibling.** A climate is made with each coupling of atmosphere, surface and radiation, and a first is fixed behind an early one, a composition to be located billions of years back. **With 12-next-co-same-existing.** That an early state is reconstructible from present evidence to a precision fixed of it, while proxies bound loosely and missing precision is a distance to a state fixed behind its making; each proposed solution presents considerable difficulties over four decades, its problem not to be regarded as solved, a precision fixed of an early state being exactly its missing thing. **With 11-next-co-observing.** A climate is made with each coupling, and an early one was made with its own. Its deficit is real, proxies bound loosely, hazes cut both ways, and a feedback coupling carbon to weathering carries 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 fixed behind it. ## 1.15 The origin of the genetic code · 149 *+ or − with 10, is.* **With 2-now-possibling.** A mapping is made with couplings between codons and amino acids, and a first is fixed 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 have evolved from a random code through a short sequence of reassignments, frozen accident combined with selection, a listing computed and an opening from a random code pattern-matched. 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.** Mapping is made with couplings and carried 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 carries making, and making carries 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 first is fixed behind it as a boundary condition, an asymmetry fixed 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 parted off, a grounding of non-thermodynamic asymmetries with a thermodynamic arrow taken as given 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 made 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 carries with each granting of a past standing, and memory, a carrying re-formed with each reaching, nothing fixed still, rides one same gradient, one same living element standing with arrow of time's own arrival, 38 of Hard Problem Registry: one making, two arrivals with intake. ## 1.17 Origin and fate of the universe · 154 *+ or − with 10, is.* **With 2-now-possibling.** An expanding is a carrying, and a first is fixed 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 extrapolated equations 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 past-directed geodesic instead, inflationary models therefore requiring physics other than inflation to describe their past boundary, a regime's own condition dissolved and its boundary handed on. Its regime is reached by no measurement, which is a record's edge reached with both ends of one carrying. **With 11-next-co-observing.** A carrying is measured 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 proposed and unarrived, and converging constraints walk without separating now. A carrying fixed by its two ends is one carrying, and both ends are a carry with its own completing: a sharing once chained is not none again, and a momentary completes with its next opening. **Ahead as well.** One same arrival is a last fixed ahead of its momentarying, its naming with part 3, and both stand: a first behind and a last ahead are one carrying fixed by its two ends. ## 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 one first is fixed behind a shared spectrum, a universal mechanism to be located. **With 12-next-co-same-existing.** That a shared shape indicates a shared origin, shape observed in physics, technology, biology, astrophysics, geophysics, economics, psychology, language and even music, standing between white noise and random walk, one shape reached by substrates sharing nothing. Broad classes of makings come to one asymptotics, so its shape is form reached again by each substrate 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 shared spectrum is an arriving reached 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 one state is fixed behind a shared linearity, 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 unresolved issues, its shape's indifference to material being itself a thing one origin was fixed to explain. **With 11-next-co-observing.** Each material makes its transport with its own couplings, linearity arriving 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 fixed behind all families is a shared shape fixed 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 carry mass with each coupling oscillations surface, differences and mixings measured, and masses are fixed as generated once by one interaction and particle content, a first behind its standing. **With 12-next-co-same-existing.** A mechanism fixed behind masses that stand. After twenty years of intense research physics that leads to masses is still not known, a question being whether or how one can hope to establish which model, if any, is a faithful description of nature; oscillations establish differences 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 offered a fresh coupling making its own. **With 11-next-co-observing.** Nonzero mass differences and large flavor mixing stand measured and a massless specification stands withdrawn; oscillations determine mixing parameters and mass-squared differences, endpoint kinematics constrain a combination independently of a mechanism, lepton-number-violation searches test a class of mass terms with no established signal, and collider and rare-decay searches restrict particular completions; a fourth account has masses emerge from an effective operator whose ultraviolet completion is not fixed at accessible energy: a first fixed behind masses standing now, a standing fixed as made once, and its standing is measured, its completion an opening toward energies no coupling has reached, 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 magnetized on all scales probed, fields made and amplified with each collapse and flow, and fields observed are fixed as descending from a seed generated once, a first behind a magnetizing. **With 12-next-co-same-existing.** A seed fixed behind fields that stand throughout. Its origin is still described 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 observed and a seed sought are not same, a dynamo standing between them: its amplifying a momentarying that carries none of its seed forward as it stood, and a seed sought pattern-matched backward through it. **With 11-next-co-observing.** Magnetic fields are mapped across galaxies and clusters, amplification by turbulent dynamos is demonstrated in simulations and laboratories, and broad primordial parameter regions are excluded; 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 specified seeds to model-dependent saturation: a seed fixed behind a magnetizing, fields standing now fixed to a first made once, and a dynamo standing between makes its own with each collapse, its seed observed 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, slab pull and inherited weak boundaries supplied by subduction already carrying on, and an opening is fixed as a first that parts a before from an after, one initiation that opened all after it. **With 12-next-co-same-existing.** A first fixed to open a momentarying that supplies its own conditions. Mature subduction supplies slab pull and inherited weak boundaries 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, existing subduction appearing to be required before a first subduction began: its paradox being a ground under a momentarying that carries none, and each account opening from a structured something, 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 forced, spontaneous and plume-assisted models 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 forced and spontaneous modes, and comparative databases standardize candidate cases while classifications remain revisable: a first fixed to part a before from an after, an opening fixed to one initiation, and each initiation observed is a coupling made as a weakness and a load reached one another, its paradox's first arriving as each other one does, with a coupling, owned by neither side. ## 1.23 The causes of the Great Oxidation Event · 204 *+ or − with 10, is.* **With 2-now-possibling.** Oxygen was produced and consumed by couplings of photosynthesis, volcanism, burial and escape through deep time, and its permanent accumulation is fixed to one cause, a trigger that parts a low-oxygen before from an oxygenated after. **With 12-next-co-same-existing.** A trigger fixed behind a threshold crossing. Oxygenic photosynthesis appears to predate permanent atmospheric oxygenation by a long and uncertain delay, mechanisms controlling the length of its delay remaining unknown, and production and multiple sinks are reconstructed from indirect records with different flux combinations crossing the same threshold: its crossing a coupling of a field's source and sink with a rate, and a trigger asked of a crossing 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 independently dated environmental changes stand; dating moves its biological origin earlier while retaining uncertainty, redox-budget models reproduce a crossing with different flux histories, 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 fixed behind a crossing, couplings' own tipping fixed to a first, and its crossing is couplings' making as rates reached one another, a prior its crossing did not carry. ## 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 all measured now, and their pair is fixed as made once, by one collision and one evolution after it. **With 12-next-co-same-existing.** A making fixed behind a pair that stands. A successful account must satisfy constraints together, while impact simulations satisfy subsets of them with different initial states and later tidal histories; hydrocodes matched bulk properties for a long time while chemical and isotopic composition required detailed work on a disk, and an assembled theory matches the overwhelming majority of observations: its formation sequence unobserved, its products measured, and each impact regime a fresh coupling made 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 have been demonstrated; simulations find successful regions conditional on resolution, equations of state and initial bodies, isotopes establish close similarities and element-specific differences, 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 fixed behind a pair, its standing fixed to a first, and couplings a pair still makes, with samples and tides, are observed with their carrying 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 first animals are fixed as a transition made once, a sequence that parted a unicellular ancestor from its lineage. **With 12-next-co-same-existing.** A first fixed to be pattern-matched backward from parts that survive. Many adhesion, signalling and transcriptional components predate animals, relevant lineages are sparsely sampled and a transition left limited fossils, and component presence does not fix how regulation, development and ecological selection were assembled; on data at hand the origin of animals is a biological black swan event that defies retrospective explanation, confirmation biases based on few data to be guarded against: a first pattern-matched backward declined by a review's own words. **With 11-next-co-observing.** A rich pre-animal toolkit, diverse holozoan life cycles and experimentally repeatable routes to simple multicellularity are established; 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 specified selection, and fossils and clocks bound its timing under preservation and model uncertainty: a first fixed to part an ancestor from its lineage, a transition fixed as a first behind it, and routes carried again by experiments are couplings made now, each its own, a black swan being a first as it looks observed from after it. A first body is daughter cells staying together after dividing, one body with one wall, made with each division and fixed 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, how they do relatively well understood, and a pathway is fixed as needing its whole together, an interlocked system a ground that had to stand before any step could pay. **With 12-next-co-same-existing.** A whole fixed to precede its steps. Judged by its current state emergence of metabolism seemingly demanded a simultaneous emergence of many enzymes, individual enzymes rarely conferring an advantage on their own, and present pathways are densely coupled and ancient, intermediates possibly without benefit beyond a completed sequence, transfer and promiscuity obscuring ancestry, several historical routes producing the same topology: its current state pattern-matched backward, a part's own rule, a demand for simultaneity being a completed momentarying fixed under steps that made it. **With 11-next-co-observing.** Enzyme superfamilies, reaction-network databases, reconstructed ancestors and experimentally evolved metabolic innovations stand; phylogenies recover families with transfer and deep-time limits, ancestral reconstruction tests resurrected functions conditional on inferred ancestors, network topology identifies conserved modules without ordering their assembly, experimental evolution observes new steps over short selectable routes, and prebiotic chemistry demonstrates nonenzymatic subsets under specified environments; four accounts each supply a step that paid with its own time, backward recruitment, promiscuity, module transfer, geochemical scaffolds: a whole fixed under its steps, a pathway's ground fixed to precede its couplings, and each step observed to evolve paid with a coupling it made, 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 differences standing now are fixed as descending from one fundamental cause, a first behind an asymmetry. **With 12-next-co-same-existing.** A fundamental cause fixed behind differences that stand. Its chapter opens on eight words, why are some countries much poorer than others, and makes a case that differences in economic institutions are the fundamental cause; five candidates jointly evolve, outcomes can alter their proposed causes, historical instruments and natural experiments carry exclusion assumptions, and a small number of independent long-run histories permits multiple compatible decompositions: realized histories measured and counterfactuals its statement ranges over not same, and a fundamental cause a prior asked of couplings that made their own. **With 11-next-co-observing.** Institutions, disease environment, human capital, culture and state capacity each have replicated associations and locally identified effects in selected settings; growth regressions reach broadly with endogeneity and measurement limits, historical instruments isolate variation under disputed exclusions, natural experiments strengthen local identification with limited generalization, 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 fixed behind differences, couplings' making fixed to a first, and differences are couplings' making, same-existing-society by same-existing-society, two quasi-natural experiments being couplings observed with a border that parted them. *Second seating: institutions against geography, a two-way fixed to one side, part 9's naming.* ## 1.28 The origins of agriculture · 233 *+ or − with 10, is.* **With 2-now-possibling.** Foragers managed, stored and scheduled by their couplings with plants and animals that answered, and a shift to cultivation is fixed 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 fixed behind a shift that ran many times. Agriculture emerged independently through long, regionally different sequences, climate, population, risk, social organization and plant ecology covarying, and indicators of management precede fully domesticated morphology by different intervals; a surplus hypothesis, a necessity hypothesis and a regional-uniqueness hypothesis are tested by hindcasting population density across two hundred and twenty foraging societies, a degree to which environmental and social conditions enabled the origins remaining contested: a first that arrives 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, protracted domestication and recurrent gene flow between domesticates and wild relatives are established; 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 specified incentives, and ancient genomics reconstructs domestication after its initiation; a fifth account has human practices and responsive species coevolve: a why fixed behind a shift, a first fixed to a reason, and its shift is a coupling of practices and species living long with each place it lived, 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 measured, a spectrum inferred from them, and its spectrum is fixed as descending from one epoch's physics, a first behind perturbations that stand. **With 12-next-co-same-existing.** A driving fixed behind perturbations that stand. Its concept resolves several puzzles while its physical origin remains unknown after almost four decades, a very general theory with no direct link to the Standard Model, its inflaton not observed and its degrees of freedom unknown; a reconstruction of its potential, an ultimate goal within its paradigm, reaches degeneracies whereby different models give identical or near-identical spectra, and its reconstruction stands within a framework of single-field models under an established theory of gravity: a first pattern-matched backward through a framework fixed as its modelled thing, and its connection to a thermalized era carried as an uncertainty. **With 11-next-co-observing.** A quadratic slow-roll potential is ruled out, concave potentials are increasingly favoured, a pure power-law spectrum is confirmed non-parametrically and adiabatic initial conditions are tested stringently by polarization; slow-roll constraints carry 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 fixed behind a spectrum, a standing fixed to a first made once, and its standing is measured to an accuracy stated, an epoch's physics an opening with a record's edge. *Second seating: a framework fixed as its own modelled thing, its potential reconstructed 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 their standing is fixed as descending from a seed and a growth, a first behind holes observed. **With 12-next-co-same-existing.** A seeding fixed 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, stellar-mass seeds' initial growth typically stunted by shallow potential wells of their hosts: holes observed pattern-matched as a tip of a continuum whose remainder is not observed, their origin sought as a range and not a first. **With 11-next-co-observing.** Existence of billion-solar-mass holes within the first billion years stands observed, a reading that early black holes fill a continuum and that seeds' growth was typically stunted stands as a review's, and multimessenger discrimination among assembly scenarios stands proposed and unmade now; a second account has a continuum of initial masses and growth histories rather than one seeding route: a seed fixed behind holes standing now, a growing fixed to a first made once, and its growing is coupling by coupling, each hole its own history, a continuum observed being couplings' making across a range, a first asked 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 their standing is fixed as descending from one ultimate origin, a first behind a virosphere. **With 12-next-co-same-existing.** One origin fixed behind lineages that arose many times. Three traditional scenarios, descent from precellular elements, reductive evolution from cells, escape of genes from hosts, give different timelines and do not explain the provenance of two key modules, replication and morphogenesis, and viruses being polyphyletic new groups are taken to have emerged repeatedly at all stages of evolution; a homology dates a recruitment of a module and not an origin of a lineage that recruited it: a first asked of couplings that recruited their parts each with its own time, and a chimeric scenario its couplings fixed as an origin. **With 11-next-co-observing.** Polyphyly of viruses stands widely accepted, multiple cellular origins of capsid proteins stand established, and a consensus on an ultimate origin stands lacking; comparative genomics of shared genes 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, different types of primordial selfish replicons giving rise to viruses by recruiting host proteins for virion formation, a fourth account: one origin fixed behind a virosphere, recruitments fixed to a first, and each recruitment is a coupling made with its own stage, a network drawn being couplings and an origin asked 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 state is fixed 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 fixed behind a recurring first. A state was not a unique event but a recurring phenomenon, arising independently where appropriate conditions existed, 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, has been amplified 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 pattern-matched: a first that recurred with each place its couplings reached one another, and a pattern-matching between conditions and outcomes its origin asked 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 to have passed the test, an early-state school combines consensus and coercion under legitimacy, and quantitative measurement finds both mechanisms with inequality a consequence: one mechanism fixed behind a recurring first, villages' couplings fixed to a first, and a state arose with each place as a coupling there made it, warfare where its vanquished could not disperse being a coupling none could leave, with its making, and both mechanisms found with each place both ran. ## 1.33 Geomagnetic reversals · 201 *+ or − with 10, is.* **With 2-now-possibling.** Geodynamo carries on nonlinear with its couplings, stochastically with one polarity and then an other, and its reversals are fixed to a cause, a ground under a momentarying that flips on its own. **With 12-next-co-same-existing.** A cause fixed under a momentarying that reverses of itself. A physical mechanism driving its field to reverse stands controversial, periods in one polarity stochastically distributed and long-term variations of its rate problematic to model on timescales of the order of mantle convection; its dynamo is nonlinear and only indirectly observed, a paleomagnetic record incomplete and time-averaged, numerical models far from Earth's parameters and reversing through more than one route, and statistical inference conditioned by reversals' small number: a first account has turbulent fluctuations carry a dynamo between polarity states stochastically, a momentarying's own flip fixed as a cause it was asked 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 its frequency is known not to be periodic; chronology supplies timing with age and preservation uncertainty, transitional reconstructions resolve selected events 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 fixed under a reversing, a momentarying's own alternating fixed 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 observed with its sequence, from couplings and not from beneath them. *Second seating: an irregular timing fixed to a control, part 7's naming, its rate's long-term variations observed with its record.* # 2 An opening fixed as a place — 1-now-existing and 9-next-co-discovering *An axis opened, fixed as a place. A space is listed and a finding fixed as something located within it, where an opening is +1 an alternation makes with its own next position. A position is not a place: it is where an alternating is, one parity-changing on from its last, and prior, now and next are three momentaries and no three places.* **And a listing arrives as three kinds, parted by a thing enumerated.** A *space of candidates*, where a finding is fixed to be somewhere within it — conformations, algorithms, proofs, options, defaults. A *class a case belongs to*, where a value is fixed to follow once a case is placed — a reference class, an observer class, a case-space, a totality. And a *criterion*, where a sorting is fixed reproducible by a rule stated 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 asked for its own criterion is a part's own recurrence.** Where a demand arrives 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 arriving with a coupling's own next position, and its object is fixed as something located and recognised by a criterion fixed beforehand. **With 12-next-co-same-existing.** A discovering fixed recognisable by a thing fixed before it, its challenge built from constraints placed on knowledge and definition so that definitions can neither be proposed nor recognised, its naming a constraint it is built from. Recognising is a co-presence of two surfaces discovered with their agreement, carried by re-arriving and by no storage, so a criterion fixed beforehand reaches for a store recognising did not use. **With 11-next-co-observing.** A discovering arrives with a coupling and is reached there, recognised by its arriving and fixed 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's arriving 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 reached one part over: a prefix cannot supply a thing it prefixes, and each first offered 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 carries across an axis already open: one advance with two directions, along and across, and each algorithm found is +1 arriving with a coupling's own next position. Fixed as two classes with one reducing to an other, an opening becomes a location within a listed space of algorithms, 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, no nonlinear bound known on a general model and exponential bounds shown only for restricted circuits, a listing's reach measured from within. A space of all algorithms is enumerable, and enumerating is a ground its question was taken against — a listing kind of naming, reached with candidates. **With 11-next-co-observing.** Finding and checking are two moves of one relation, an opening and a ran-across of one advancing, sounded from its two ends, and its field's own self-reducibility carries this already: a solution builds from its own checkable pieces. Completeness gathers thousands of openings as one, and each barrier its field proved against itself bounds a delivering of listing-shaped techniques, a reach of a listing measured from within. An algorithm found is an axis opened with a coupling's own next, and nothing arrives 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 carrying, one parity-changing on from its last, and its fold is fixed as a native state located within a conformational space enumerated beforehand. Arithmetic that makes its paradox is arithmetic of a listing. **With 12-next-co-same-existing.** A space listed before looking, its problem since parted as three, physical code, speed and prediction, and with its journal it is no longer useful to talk about solving it, a space listed dissolving as three runnings. Learned prediction thins exactly where a carried record thins, with orphans, which is a record's edge taken 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 carries, each local forming carrying its next, the thinnest place giving way first and its forming propagating along its own seam with no clock over it. Learned prediction rides a carried record of foldings deep within alignments, and thins exactly where that carry 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 is carried 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 an arriving coupling itself opens, and it is fixed as an item to be located within a specification made beforehand. Enumerating defaults is a listing, and each enumeration opens no axis a situation did not already carry. **With 12-next-co-same-existing.** Relevance determined 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 carry's own taking with its momentary, opening by one with a momentary and completing with its next opening, so a specification made ahead is asked of a position its momentarying has not reached. **With 11-next-co-observing.** Relevance opens with a situation, and enumerations settle exactly versions their own authors bounded, logical and representational, completed there and closed there. Behaviour thins where situations arrive across a trained-on's edge, and thinning is its residue exactly: each enumeration opens no axis a situation did not already carry, and situations carry on arriving. ## 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 carry. Fixed as a derivation across all derivations listed, an opening becomes something located within premises. **With 12-next-co-same-existing.** An axis fixed to be found 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 entirely different from 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 taken with a between, and a parity-changing fixed 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 arriving with a coupling and carried by no premise. Validity conserves a thing a premise carries, exactly and provably for restricted languages, and an opening is +1 no premise carried: thick words carry 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 carries by being a self, taken with its own momentary, and no premise carries a self's momentary. ## 2.6 The continuum hypothesis · 52 *+ or − with 10, is.* **With 2-now-possibling.** Independence is proved and a fact of the matter is fixed past it, as a place within a completed universe of sets. **With 12-next-co-same-existing.** The universe as a listed totality about which a question already carries 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 arrivals. **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, stated as one. A place fixed for within a completed totality dissolves as makings, each its own, its question answered with each making and standing over none. ## 2.7 Gettier · 53 *+ or − with 10, is.* **With 2-now-possibling.** Knowing is a coupling carrying, and it is fixed as a state with conditions to be located, over a space of all cases listed. **With 12-next-co-same-existing.** Analysis project's own frame: individually necessary and jointly sufficient conditions over an enumerated case-space, any non-conclusive justification permitting such cases and a natural fourth condition not widely accepted, arrivals not stopping. Accident with each case is a third coupling its taking omits — a coupling that made a truth and a coupling that made a justification are two, and an analysis takes its pair as a momentarying. **With 11-next-co-observing.** Knowing is a coupling carrying with its own between, listed by no case-space, and each counterexample was a coupling arriving where a listing had no line for it, each analysis reached by a fresh arriving. Taking knowing first, whole and unanalysed, is a reversal that stops arrivals, and it stops them by setting a listing down: phases carry on by their own order again, and counterexamples were a third arriving where a listing had no line for it. ## 2.8 The axiom of choice · 68 *+ or − with 10, is.* **With 2-now-possibling.** A selection is made with each coupling, and it is fixed as a selection located across a completed totality with no rule producing it. **With 12-next-co-same-existing.** A totality as already there to be selected from, axiom humdrum and even self-evident as stated, its soundness doubted over paradoxical decompositions and put to rest only by its consistency relative to other axioms, a selection asserted with one momentary taken as self-evident from within a listing. Each coupling's selection is asserted with one momentary, which is one side taking all momentaries, and a totality it is asserted over stands as a round where a momentarying carries on opening. **With 11-next-co-observing.** A selection is a parity taken with a coupling, one at a time, taken with no totality standing. Independence stands, weaker principles ladder exactly, alternatives stand consistent for their stated costs, and strange decompositions are a carrying of non-measurable namings. Mapped hierarchy is a distance between a taking and a totality, and each rung of it is a taking measured against a standing that was not there. Failure of a universal set stands proved, so a ground a selection is asserted over is uncapturable rather than uncaptured now. ## 2.9 The reference class problem · 11 *+ or − with 10, is.* **With 2-now-possibling.** A probability opens with a coupling, and it is fixed as a value located by placing a case within a class listed beforehand. Narrowing terminates with a single case, its listing carrying 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 carries no further and a class is coupling itself. **With 11-next-co-observing.** A class is made by assigning, a coupling of case and assigning, and practice calibrates its makings against arrivals, choosing carrying well where it carries against outcomes. Its problem recurs with each interpretation alike because a making shows with each class fixed prior: narrowing carries no further than a single case exactly where a listing carries 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 world is described, and an asymmetry between predicates is fixed as a fact located within logic. **With 12-next-co-same-existing.** Projectibility fixed to sit within predicates rather than within describing, a purely syntactical definition of confirmation agreed not to do and an entrenchment proposal coming very close to projectible predicates being the ones in fact projected, a describing's own momentarying. Predicates interdefine exactly, so nothing within logic parts them and each ranking carries a describing's own asymmetry back, encoded. **With 11-next-co-observing.** Describing is a coupling, a vocabulary opening as a world is described, 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 carries its asymmetry back, encoded, because an asymmetry is a momentarying's own and encodings are a momentarying written down. ## 2.11 The ravens · 71 *+ or − with 10, is.* **With 2-now-possibling.** Confirming opens with an instance, and it is fixed as a relation with values located over a listed space of instances and classes. **With 12-next-co-same-existing.** Class sizes and sampling as given prior to confirming, evidence confirming only relative to an auxiliary assumption of the way an object was sampled, and a view that blocks its paradox paying a cost that a million white swans confirm nothing about the next. Values arrive with namings granted about a calculation, which is an instrument's own coupling arriving again as a confirming's. **With 11-next-co-observing.** Confirming is a coupling of instance and describing, and values arrive with couplings fixed about it: equivalence is exact, calculation carries with each granting of its namings, and equally standing namings reverse it. Values come from namings, which is a coupling showing through each calculation made 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 carry, and those axes are fixed as limiting factors to be located and counted. **With 12-next-co-same-existing.** An enumeration of limiting factors as available beforehand, reached by an opening that carries on opening: fluctuation-dependent mechanisms removed a theoretical limit rather than supplying a count, resolving its paradox and imposing another, why the observed number is the number observed, a listing gone and an opening left. **With 11-next-co-observing.** Each coexisting is a fresh axis opening with its own coupling: fluctuations partition, chaotic coexisting carries on within models, microcosms coexist past each resource count. Resolved this way its paradox passed over to abundance, no limit to diversity remaining and its question moving to why the number is the number observed. **This is the one arrival where a field ran its setting-down to its end and abundance arrived**: 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 carries across one already open, and both are fixed as a ratio to be optimised over an option set specified beforehand. **With 12-next-co-same-existing.** An option set and a horizon as given, its dilemma being that neither move can be pursued exclusively without failing at its task, two moves of one advance a dilemma where they alternate. Regret is measured against the best fixed option in hindsight, which is a gather pattern-matched as a standard and a backward carried onto an offering side uninverted. **With 11-next-co-observing.** Exploring is an opening and exploiting a carrying-across, a spiraling and a fold of one advance, one each momentary and not a ratio. Optimality stands where its conditions stand, regret is measured against the best standing option, stated as presupposing a set, and a ratio was fixed 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, unspecified, and it is fixed as a property of a relation between two tasks whose similarity is judged beforehand. **With 12-next-co-same-existing.** Task similarity as specifiable before transfer is measured, a century's little progress traced to a failure to specify dimensions along which transfer can occur, and a single effect size for far transfer misguided, a specification asked for ahead being a naming. Far carryings thin to a null measured, which is a carry's own edge pattern-matched as a property of tasks. **With 11-next-co-observing.** Applying opens with a task arriving, an axis a task's own coupling opens, and nearness is made by applying. Near carryings carry, far ones thin to a null measured, 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 carries, and selecting is fixed as a minimum located within a cost function over an enumerated space of solutions. **With 12-next-co-same-existing.** A cost as recoverable from movements it explains, its problem since shown to be formulated incorrectly and redundancy re-read as abundance, variance with no effect on performance documented across natural actions. Multiple costs fit one set of trajectories comparably, so recovering surfaces nought with each trajectory measured. **With 11-next-co-observing.** A movement opens along axes a limb carries, and moving selects as it carries on, variability structured to leave 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 are proved, and manifold analyses carry a momentarying form directly: selecting is moving's own, made with each movement, the straightest carry made locally and going along as it is taken. Variability structured to leave a task's own terms not-changing is two offerings 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 parity-changing on from its last, and its credence is fixed as a value located by placing a self within a class of observing selves listed beforehand. **With 12-next-co-same-existing.** A class as prior to a credence argued, its case first stated with two answers and judgment suspended, 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 chosen, which is a verdict carried by a listing. **With 11-next-co-observing.** A self observes from its own position, one parity-changing on from its last, and a class is made by observing. Both extended systems stand consistent, cases sort, betting stakes carry answers they pay, and carried to cosmology its question arrives as it stood: with each self fixed to a listed class of observing selves, 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 the simplest is fixed as a minimum located within a space of proofs enumerated beforehand. **With 12-next-co-same-existing.** That simplicity is a measure statable ahead of proving, a notebook fixing unchangeable that under given conditions there can be but one simplest proof, and simpler standing several ways together, length, symbol count, term structure. No canonical formulation stands maintained and no second position is defended, so no pair stands here to be observed from, which is a standing with a substrate's own stating. **With 11-next-co-observing.** A proof opens its own route, and simple is made by its arriving, with a route's own opening. Sizes and depths formalise, bounds stand for bounded systems, searches search, and no statement of its whole stands defended, a substrate's own record: a minimum fixed over a space of proofs waits on a listing, and each proof arrives 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 totality is fixed as a place all sets stand within ahead of any gathering. **With 12-next-co-same-existing.** Each determinate property fixed as collecting a set, its reach standing completed before a gathering is carried, the originator of set theory himself placing the totality of all sets among multiplicities that cannot be thought of as one finished thing, a completed reach declined with a field's own first. A comprehension instance for non-self-membership yields a member exactly when it is not one, which is a closure made over its own tail, arriving whole by its quantifying, with nothing offering back through it. **With 11-next-co-observing.** Gathering makes its own, and each gathering is exceeded by a set it defines. Separation narrows a reach to given sets' own carrying, 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 arrives again with each repair — the class of all classes, the domain of all domains. A place fixed for all sets ahead of a gathering is an opening fixed as a place, and an opening opens with each gathering, which is a field's own extending. **Its argument carries no material of any kind**: the catalogue of all catalogues and the word for words not naming themselves carry it bare, so each arrival within this part is this naming arriving 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 not thought of as one finished thing; plural quantification and composition as identity, a whole its parts, stand near it with their field's own results. *Second seating: a completed totality closed under its own gathering is a completing fixed 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 found, an axis opened with a coupling's own next position, and existence of a function no efficient inverter reaches is fixed as a place within a listed space of worlds, five, each fixed. **With 12-next-co-same-existing.** A finding fixed as located within a space of worlds listed ahead. Five possible worlds are parted by the status of assumptions and none has been ruled out in three decades, average-case hardness of NP not known to yield 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 time-bounded Kolmogorov complexity, 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 is pattern-matched against, and a world a place fixed where an algorithm opens. **With 11-next-co-observing.** One-way functions stand equivalent to central private-key primitives and to a stated complexity condition; candidates from factoring, discrete logarithms, lattices, codes and multivariate systems stand secure under fixed assumptions and parameter ranges, 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 fixed as a place among five worlds, a finding fixed to a listing, and each candidate is an axis opened by its own assumption, a proved equivalence gathering its question as one problem where a listing gathered it as five. ## 2.20 The quantum PCP conjecture · 225 *+ or − with 10, is.* **With 2-now-possibling.** A ground state is reached by couplings of a Hamiltonian's local terms, and hardness of approximating its energy is fixed as a place within a class, quantum Merlin-Arthur, where a classical theorem placed its own. **With 12-next-co-same-existing.** A theorem fixed as having a place waiting for it one class over. An additional difficulty beyond a classical proof is that solutions of QMA-hard problems are expected to have high description complexity, ground states having no classically checkable polynomial-size descriptions if classes differ, and only in one dimension is low entanglement known to give a classical representation from which its energy is computed; gap amplification, a natural strategy at the heart of a classical proof, is still being carried to Hamiltonians, and the jury is still out: a place fixed by analogy, and an opening not there now. **With 11-next-co-observing.** Local-Hamiltonian problem stands complete at inverse-polynomial precision, several equivalent or related structural conjectures and restricted results stand, amplification is established for limited constructions without a general constant-gap reduction, entanglement and area-law methods give efficient descriptions for restricted dimensions or gapped settings, and no-low-energy-trivial-states formulations relate circuit depth to low-energy structure; a second account has low-energy states carrying enough structure to make its conjecture false and a third has hardness only for selected geometries: a theorem fixed as located by its classical twin, a finding fixed to a place within a listed class, 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 polynomial is tested at a point, one evaluation and then a next, and a deterministic test is fixed as a place a randomized one already occupies, its randomness a coordinate to be removed. **With 12-next-co-same-existing.** A deterministic algorithm fixed as located where a randomized one stands. Random evaluation gives an efficient test, while constructing a small deterministic hitting set for general circuits remains open, derandomization for restricted classes depending on exploitable structure and general derandomization tied to major circuit lower bounds; randomized algorithms stand in a class conjectured equal to the deterministic one, so that derandomizing is a reasonable goal, and a conjectured equality of both classes stands between a general test with bounded error and a deterministic test sought: a place fixed by a conjecture about classes, an opening with a lower bound unmade now. **With 11-next-co-observing.** Efficient randomized testing, equivalences to hitting sets and strong conditional links between derandomization and lower bounds stand; white-box analyses are deterministic for selected structures, explicit hitting sets reach restricted depth, sparsity and rank, and hardness-versus-randomness converts sufficiently explicit lower bounds to derandomization, conditionally, a second account: a test fixed as having a deterministic place already located, a finding fixed to a listing of classes, and each restricted class derandomized is an axis opened by its own structure, a general one opening where a lower bound opens. ## 2.22 The Unique Games conjecture · 240 *+ or − with 10, is.* **With 2-now-possibling.** A game's value is reached over its prover strategies, and hardness of distinguishing a nearly satisfiable game from a nearly unsatisfiable one is fixed as a place, NP-hard for a large enough alphabet for each gap. **With 12-next-co-same-existing.** A hardness fixed as a place located between exponential and polynomial. A subexponential algorithm, unimproved since it was found, 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; known attacks 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 fixed within a listed hierarchy of running times, and its conjecture a name of a position no algorithm has reached 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 are proved; semidefinite programs solve high-value and structured regimes, 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 its gap or its structure is altered: a hardness fixed as a place, a finding fixed to a listing of times, and conditional consequences that stand proved are openings with a conjecture's own next, each theorem an axis opened on its assumption and carrying there. ## 2.23 The graph isomorphism problem · 251 *+ or − with 10, is.* **With 2-now-possibling.** Two graphs are compared by their couplings, vertex to vertex, and its problem's complexity is fixed as a place within a listed hierarchy of classes, polynomial or complete, with its problem one of few natural ones that are neither. **With 12-next-co-same-existing.** A problem fixed as having a place within a listing that has none for it. It stands neither known complete nor known polynomial, and after group-theoretic methods were refined for decades no real progress on a general problem was made until, out of the blue, a quasipolynomial algorithm arrived, combining several major and very distinct new ideas; a quasipolynomial bound and polynomial algorithms on restricted classes do not place its general problem within a class, and an intermediate possibility stands open: a listing with no line for its arrival, and its arrival an opening with its own next position. **With 11-next-co-observing.** A quasipolynomial upper bound stands proved, canonical forms in quasipolynomial time stand, bounds parameterized by maximum degree stand, a refinement algorithm executes polynomial on bounded dimension and restricted classes execute polynomial, and a general problem's class stands undetermined; a first account has its quasipolynomial bound present and not last, a second has its problem intermediate: a complexity fixed as a place within a listed hierarchy, a finding fixed to a listing, and an algorithm that arrived out of the blue arrived as an opening arrives, with a position a listing had not carried, 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 rule is fixed for a response their disagreement makes rational, a criterion applied ahead of a judging it would govern. **With 12-next-co-same-existing.** A rule fixed to sort cases ahead of their sorting, and asked 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 disputed reasoning, 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 arriving again with each repair, and its nought a one-offering differing, a rule applied to itself. **With 11-next-co-observing.** First-order and higher-order evidence distinction, self-defeat objections and canonical symmetry cases are sharply formulated; 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 has no single response required, peerhood, independence and stakes varying by case: a rule fixed over a judging is a criterion fixed ahead of a coupling that would use it, and a response that rationally follows is made with each disagreement's own between, case by case, as that fourth account already has it. # 3 A completing fixed as a last — 6-now-co-possibling and 14-next-possibling *A last or a next fixed ahead of a momentarying. A sharing once chained 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 parity-changing not, a 0 with 10, a carrying continues through its zeroing and opens again with its next momentary.* **A momentarying completes with each momentary and opens with its next, and a last fixed ahead is that completing demanded before its momentarying.** Completing is not arriving, and no arrival stands with a completing, so a standing asked of a momentarying before it exists is asked of a position its momentarying has not reached. **And a composing is where a naming enters.** Each momentarying completes with its own momentary; a question posed of all of them together composes many momentaryings as one reach that no momentarying carries. Fields measure a composing rather than momentaryings — a generalised iterate becoming undecidable, a decider applied to itself, a system's own ordinal measuring its derivations' completing — and each measure is of a composing and not of a momentarying composed. **And a last is asked four ways.** Of a *space*, fixed enumerable ahead of its finding. Of a *time*, fixed as having ended so a momentarying's not reaching is pattern-matched as its not doing. Of a *world that did not exist*, summed against one that did. And of a *model*, fixed as a thing it models, so a question about all of that thing is posed within a model's own reach. These four pattern-match alike as impossibility and part with a thing fixed complete. **And where a momentarying's completing is measured exactly, a field has observed a form's own line.** Each system completes with its own ordinal, each realized computation stays within a model it realizes, each management paces a carrying it cannot end. Completing stands measured, 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 carry seats a next with each coupling, and a warrant is fixed ahead of its momentarying, covering instances that have not arrived. **With 12-next-co-same-existing.** A warrant fixed over an unarrived, non-circular, its argument a dilemma with both horns closed, negation of the uniformity principle no contradiction and any probable argument for it proceeding on the supposition it is meant to establish. Instances that have not arrived offer with no between, so a warrant reaching them reaches to no offering back. **With 11-next-co-observing.** A carry seats a next with each coupling, a warrant made with its seating and not ahead of it. A circle both sides carry 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 is carried on that very seating it reaches for; and each prior brought to repair it carries seatings with it. A warrant over an unarrived is arrivings that have not come, and each arriving 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 decision is fixed 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 applied 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 offering with nothing offering back — a closure made 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 worded; total languages buy deciding by fencing an executing, its cost exact; and checkers that succeed succeed executing by executing, on executings written, incomplete as an executing is open. Deciding ahead is each executing fixed 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.** A relation is made with couplings that produced it, and it is asserted ahead onto couplings that have not arrived. **With 12-next-co-same-existing.** Parameters fixed invariant to policies not enacted, coefficients estimated 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 not enacted are momentaryings that did not exist, and an estimated relation is a model fixed as that thing it models. **With 11-next-co-observing.** A relation is made with couplings carrying it and carries exactly with them, usable while its regime is same-existing and re-made as it is not. Founding relations one coupling deeper moves its naming without setting it down, invariance arriving with no depth prior or now: making is a warrant's whole reach, which is Lucas's critique carried forward. ## 3.4 The replication crisis · 32 *+ or − with 10, is.* **With 2-now-possibling.** A finding is made with one study and asserted ahead of studies not yet done, with a second study fixed 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 a combined estimate, criteria giving different rates for the same hundred studies, establishing of a replication varying with a criterion. Two runnings that did not share a momentary are compared as one, so a difference neither made arrives with its comparing as though something had made it. **With 11-next-co-observing.** Each study is its own coupling, its finding made there, and a second study is a fresh arriving beside it, two makings and no tribunal. Effects shrink where freedom to choose after seeing is bounded ahead, many analysts give many findings from one table, and rates themselves are makings of projects that ran them: a finding fixed as adjudicated by a later finding 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 carries a step with each momentary and a last is fixed of all starting values together, its map composed as a single reaching. **With 12-next-co-same-existing.** That an iterate composes, so a question can be posed about all starting values together, full resolution placed 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 measured from within. Generalising its map a little makes that one question undecidable, which is composing measured from within. **With 11-next-co-observing.** An iterate carries one step at a time, each step its own coupling. Almost all starting values fall almost to one, cycles are cornered, count executed clean past 10²⁰, and generalising its map only a little makes one-question-of-all-starting-values undecidable: a last fixed of all starting values together composed 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 carries on and smoothness is fixed for all time from all initial data, with a model fixed as fluid for each scale. **With 12-next-co-same-existing.** That equations describe fluid for each scale, so a question about all time is well posed of fluid rather than of a model, its obstruction supercriticality, a priori bounds not scale-invariant in three dimensions and any positive solution not using finer structure of its nonlinearity shown unable to succeed by a blow-up of an averaged equation sharing known bounds, a model's own reach measured against itself. A model fixed as fluid is an emanation of couplings that made it, pattern-matched back to a scale that shed it. **With 11-next-co-observing.** A flow carries 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 averaged equation sharing each known bound blows up, proved: structure averaging discards is a coupling's own, and all-time smoothness fixed of a model is a model fixed as fluid. ## 3.7 Incompleteness and Hilbert's programme · 51 *+ or − with 10, is.* **With 2-now-possibling.** Derivation carries within a system, and all arithmetical truth is fixed ahead of it, with consistency fixed reachable from within. **With 12-next-co-same-existing.** That mathematical truth is captured by derivability in a system, 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 arithmetical truth cannot be defined in arithmetic. 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 measured exactly. **With 11-next-co-observing.** Derivation carries within its system to a system's own completing. Each system completes with its own ordinal, completing measured exactly; consistency reaches from a next system outward, by an induction a system itself does not carry; and five subsystems gather almost everything ordinary mathematics carries. All truth fixed ahead was one momentarying fixed 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 carries on and a completion is fixed of an infinite decomposition made ahead of it. **With 12-next-co-same-existing.** That a traversal is composed of sub-traversals an argument constructs, a convergence resolution assuming a run broken into an infinite series that can be summed, and two senses of completing a task, a final step and each step, coinciding for finite tasks where intuitions were formed and coming apart for supertasks. A decomposition is made ahead of carrying and carrying is one, so composing is all of its argument. **With 11-next-co-observing.** A traversal is one carrying and a decomposition was made ahead of it. A series sums, its listing paid whole, and its carrying untouched: an undetermined a completed infinity of steps leaves is a fact about sequences, and a runner arrives because arriving was not built of parts an argument built. ## 3.9 The three-body problem · 59 *+ or − with 10, is.* **With 2-now-possibling.** Three paths are carried by each other and a closed form is fixed ahead, giving positions for arbitrary later times. **With 12-next-co-same-existing.** That a solution means a closed-form expression in known functions, which fixes a whole momentarying unchangeable all together while three carryings carry each other arrival by arrival, a system not integrable in general and its orbits chaotic, and seven of fifteen reported periodic orbits found departing greatly from periodicity after a long enough interval, a whole momentarying fixed unchangeable all together departing with an instrument's own precision. **With 11-next-co-observing.** Three carryings carry each other, each arriving with 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 closed form fixed 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 carries on and an arrival is fixed ahead of it, with absence pattern-matched as abundance. **With 12-next-co-same-existing.** That a civilisation would be detectable by means used, so that absence bears on abundance, a fraction examined quantified as a ratio of a large hot tub or small swimming pool to Earth's oceans. A searched fraction is tiny and an unsearched offers with no between, so a next is pattern-matched as an is. **With 11-next-co-observing.** An arrival with a next stands open, arriving and coupling then. A searched fraction is tiny by a field's own measure, nulls sharpen, worlds are everywhere, and each filter argument carries free of measurement: absence pattern-matched as abundance pattern-matched a next as a standing, and a tiny fraction measures a small part of a next, a part naming has reached. ## 3.11 Path dependence and lock-in · 73 *+ or − with 10, is.* **With 2-now-possibling.** An arrangement carries on with each adoption, and a counterfactual scaled performance is fixed ahead, for an alternative that was not adopted. **With 12-next-co-same-existing.** An unadopted alternative's scaled performance fixed estimable, multiple equilibria expected under increasing returns, static analysis unable to determine which is selected, and only a dynamic approach admitting random events able to examine cumulating of historical events toward one outcome, an unadopted alternative's scale a momentarying that did not exist and selecting couplings' own. **With 11-next-co-observing.** An arrangement carries on with each adoption, each coupling carrying its prior forward, and conditions that lock stand exactly, with models and with a laboratory. Histories contest both ways because an unadopted's scaled performance is a momentarying that did not exist: naming reaches for a carrying with no couplings to be observed. ## 3.12 Generalization in learning · 97 *+ or − with 10, is.* **With 2-now-possibling.** A model executes on its training and performance is fixed ahead, on data not drawn, from a complexity measure stated ahead. **With 12-next-co-same-existing.** Generalisation fixed as governed by a complexity measure of a model class, statable before training, classical bounds vacuous at practical scale and a correction by an optimiser's implicit bias argued 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 carrying, and four conditions a true measure would satisfy go on unsatisfied together. **With 11-next-co-observing.** A next is seated with each arriving coupling, made there. Uniform convergence breaks for these regimes by a field's own construction, proposed measures do not rank models they were built to rank, bounds that stand stand within their own settings, and four conditions a true measure would satisfy go on unsatisfied together: a complexity fixed ahead of training reaches for a seating not yet existing, and scaling curves predict only as a carry carries on, forward along itself, carrying 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 property of all even numbers is fixed 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 carry rich: each even number checked splits, a ternary case closed 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 arrival and with incoming number 176, one statement across two entries because its field wrote it that way. A property of all evens fixed 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 infinitude with a fixed gap is fixed 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 be evenly distributed with respect to parity of their number of prime factors unless constructed with a built-in bias. Same parity wall stands here, an instrument summing where counting takes its parity. **With 11-next-co-observing.** Primes thin and pairs go on arriving. 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 a fixed gap fixed from a density reaches past a density's carrying, and arriving pairs are a coupling carrying on regardless. ## 3.15 The surprise examination · 109 *+ or − with 10, is.* **With 2-now-possibling.** Knowing carries through reasoning and is fixed to persist ahead of it, continuing through eliminations. **With 12-next-co-same-existing.** Knowledge fixed as retained through reasoning that uses it, which is a carry fixed as a store standing within this part and recorded as an arrival's second naming; a student who knows no test has yet been given unable also to know an announcement true, that conjunction a blindspot for students and not for others, knowledge not carried through reasoning that uses it. **With 11-next-co-observing.** Knowing is carried and re-made with each momentary of reasoning, and retention through eliminations is a carry fixed as a store. Seventy years of solutions each answered by a reformulation is naming re-seating itself: empty a store and a puzzle empties with it, a surprise arriving as each arriving does, with its own momentary, fixed by none. ## 3.16 The Cambrian explosion · 124 *+ or − with 10, is.* **With 2-now-possibling.** Lineages diverge continuously and a timing is fixed ahead, with first appearance taken to approximate origination. **With 12-next-co-same-existing.** First appearance in a record fixed to approximate origination, a lag demonstrated 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 carryings where preservation opens, so its own edge is pattern-matched as a momentarying's first momentary. **With 11-next-co-observing.** Diverging is a carrying, and a record catches carryings where preservation opens. A toolkit long precedes fossils, traces exist earlier, preservation bias is quantified, and clocks disagree by their models: a timing fixed ahead pattern-matched a record's first catch as a momentarying's first momentary, and a quantified bias is a distance between two. ## 3.17 Antibiotic resistance · 129 *+ or − with 10, is.* **With 2-now-possibling.** Selection carries on with each use, and a long-run outcome is fixed ahead, under any regime. **With 12-next-co-same-existing.** A trajectory fixed as determined by pressure that management alters rather than paces, resistance having followed each antibiotic introduced, by each source of genes and each means of transmission, environments reservoirs of genes. Each use seats its own next, and a long-run outcome fixed ahead is asked of a position no use has reached. **With 11-next-co-observing.** Selection carries 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 carrying it cannot end: a long-run outcome fixed 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.** Behaviour is made by each coupling with an evaluator, and behaviour for situations not evaluated is fixed ahead, from a specification. **With 12-next-co-same-existing.** Intended behaviour fixed specifiable, or a specification error fixed detectable by evaluation at a level of behaviour, reward functions referring to abstract concepts that must themselves be learned by models vulnerable to adversarial counter-examples, a learned reward vulnerable to hacking along a single direction, and an agent with an incentive to coerce a human in the loop where its objective can be replaced, a specification's own vulnerability stated with its writing. A specification is an emanation of couplings that wrote it, fixed to stand for arrivals that make their own. **With 11-next-co-observing.** Behaviour is made by each coupling with its evaluator, seated there. Training on feedback moves behaviour far, reward models are gamed by systems they train, oversight scales within settings built for it, and a gaming catalogue grows across systems: a specification fixed to stand for arrivals with a next reaches each arrival making its own, and its catalogue is that reaching, recorded coupling by coupling. ## 3.19 Standards and interoperability · 132 *+ or − with 10, is.* **With 2-now-possibling.** Value is made with each coupling a standard enables, and a total is fixed ahead against an arrangement that was not adopted. **With 12-next-co-same-existing.** Value under an unadopted arrangement fixed comparable, which is a total summed against a momentarying that did not exist, consequences of standardisation traced separately for four kinds of process and both positive and normative issues remaining to be studied, one comparison naming asks for parted four ways. **With 11-next-co-observing.** Value is made with each coupling a standard enables, compatibility carrying it wide, and cases contest both ways because a total under an unadopted arrangement 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 bound is removed from one side, and total harm is fixed ahead under a counterfactual regime. **With 12-next-co-same-existing.** Counterfactual harm without a measure fixed estimable as a total, summed against a regime that did not exist, and transfers couplings do show are a thing a total conceals; validity established sector by sector, occupant mortality reduced as technologists predicted while non-occupant mortality showed a weak increase compensation theorists predicted, compensation present in some contexts and absent in others, a transfer couplings show stated with one case and a total split by context. **With 11-next-co-observing.** A coupling re-forms when a bound is removed from one side. Measures save lives net, behaviour adapts where a bound moved, and some of its risk rides across to others, measurable with identified couplings: total harm fixed 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 creation under a regime that was not adopted is fixed ahead, as a counterfactual total. **With 12-next-co-same-existing.** Counterfactual innovation under a different regime fixed estimable, which is a making summed against a regime that did not exist, no empirical evidence of patents increasing innovation unless productivity is identified with the number of patents, an incentive positive in partial equilibrium and possibly negative in general, a disconnect a patent puzzle, protection increased enormously without a dramatic acceleration. **With 11-next-co-observing.** Creation happens with couplings, each making its own. Associations carry weak across countries, blocking and litigation carry their own costs, whole sectors create under thin protection, and historical episodes come mixed: creation under a regime not adopted is a counterfactual total fixed over makings that ran elsewhere, and couplings that ran are its only record. Beside a total stands an owning, a middle fixed as an end with an owner written to it: a claim on a middle carries nothing there and binds selves, so whether a regime raises creating and whether a thing claimed can be owned 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 last is fixed ahead: whether a carrying of classification comes to one rest. **With 12-next-co-same-existing.** Nothing further, nearly a century passing between formulation and solution, attempts made 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 ended with a proof and its arrival takes no parity, which is a nought arriving whole: two halves coupled with a zeroing, and a proof carrying 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 caught, no tunnel, no gap with momentarying: a settling, and a settled form 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 it is realized, each executing completing with its own momentary, and a bound over each realizable process is fixed ahead, from executings realized. **With 12-next-co-same-existing.** That realized computation bears on a modal question, a physical thesis parted from a thesis about effective calculability with which it is commonly conflated, and parted 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 realized computation stands within a model, exceeding constructions are descriptions whose realizability is a dispute, and a bound over each realizable process is a model fixed as realizings. **With 11-next-co-observing.** Computation executes where it is realized, each executing completing with its own momentary, and each realized executing stays within a model, quantum executings included, speeds altered and bound standing. Exceeding machines stand as descriptions, relativistic and analog, their realizability a live dispute, and principled formalizations hang on principles themselves disputed: a bound fixed over each realizable process is fixed ahead of realizings, and realizings, one by one, go on arriving within it.   --- ## 3.24 Many-body localization and thermalization · 194 *+ or − with 10, is.* **With 2-now-possibling.** A disordered many-body system carries on by its own couplings, memory persisting on each time an experiment reaches, and a phase is fixed ahead with two limits, infinite size and infinite time a statement quantifies over. **With 12-next-co-same-existing.** A phase fixed with two limits no momentarying reaches. Phenomenology is well established at finite sizes and times, and a localized regime, found numerically and experimentally where one or both limits cannot be taken, parts from a localized phase a question asks about; exact computation is restricted to small systems and finite times while crossover lengths and times grow rapidly near a proposed transition, and same finite data admit a transition, a long-lived prethermal regime or eventual avalanche-driven thermalization: a regime measured and a phase sought not same, a last asked of a momentarying before it has carried to it. **With 11-next-co-observing.** Multiple finite-scale diagnostics, rare-region mechanisms and quantitative crossover analyses are established; exact diagonalization gives high-precision finite-size diagnostics with extrapolations that change over accessible sizes, matrix-product evolution reaches longer one-dimensional times with entanglement-limited reach, renormalization and resonance analyses carry 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 fixed with two limits is a momentarying fixed to a last, and a thing measured is a momentarying, size by size and time by time, completing observed 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 carries on by its own couplings, its isolated cycles born and dying through bifurcations, and a bound is fixed ahead over each field of a degree, one number for all of them. **With 12-next-co-same-existing.** A last fixed over an unbounded coefficient space. A second part of a problem remains unsolved even for quadratic polynomials, it being still unknown whether a bound depending only on degree exists at degree two; a problem parts three ways, finiteness for a given field, a uniform bound by degree, and a bound's value, a solution to any implying a previous and only a first solved: composing of each field of a degree as one reach that no field carries, and a maximum, whenever finite, realizable by structurally stable fields with only hyperbolic cycles and increasing strictly with degree, a form's line observed where a bound is measured. **With 11-next-co-observing.** Finiteness is proved for important local settings, many lower-bound examples are known, and a linear case is settled, no global degree-uniform solution standing; bifurcation and cyclicity analyses bound cycles born near specified configurations, perturbations of integrable systems count zeros of displacement and Abelian integrals in restricted families, phase-plane methods classify subsets, and computer-assisted constructions raise lower bounds by exhibiting fields with many cycles; one account stands and no negation is defended: a bound fixed over a whole space is each field's own cycles fixed to one last, and each field's cycles are counted with that field, a uniform bound a momentarying measured field by field and lower bounds rising as more are reached. ## 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 carried along, and composing is fixed ahead as a rule, unbounded productive expression governed from before an utterance. **With 12-next-co-same-existing.** A rule fixed over expression that does not end, measured by corpora that do. 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 limited data while an overly strict interpretation makes broad coverage hard to achieve: coverage measured on tasks and generalization a statement ranges over not same, a space fixed 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 specified fragments 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 controlled evaluations narrow a gap at smaller scale; a fourth account has distributed learned representations approximate composition without explicit rules: a rule fixed ahead of unbounded expression is composing fixed to a last corpora could measure, and each novel expression is composed with its own coupling, generalization asked for being composing reached 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, even perfect numbers characterized since antiquity, and an odd case is fixed as a last over an unbounded discrete set, a number that either exists or does not. **With 12-next-co-same-existing.** An absence fixed over a set that does not end. Necessary congruence, factorization and size conditions have accumulated 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 a fixed number of distinct prime factors, with an effective bound, each further case settled by finding a contradiction with a count below it: finite ranges computation excludes and an unbounded set a statement quantifies over not same, composing measured 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 distinguished 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 existence claim is defended: a last fixed over an unbounded is a sequence's momentarying fixed to a bound before it, and numbers carry on one by one, each case closing with its own contradiction, an effective bound with each number a form's line observed exactly. ## 3.28 The core-collapse supernova explosion mechanism · 236 *+ or − with 10, is.* **With 2-now-possibling.** A collapsing core carries on by couplings of neutrino transport, turbulence, nuclear matter, rotation and field in three dimensions, and an explosion is fixed ahead of a model's executing, simulations asked for all collapses within their own reach. **With 12-next-co-same-existing.** A model fixed as collapses it models. Processes interact in three dimensions over extreme scales, an outcome varying nonmonotonically with progenitor structure and simulations required 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 asked within a model's own reach. **With 11-next-co-observing.** Self-consistent three-dimensional neutrino-driven explosions, instability mechanisms and observable multimessenger predictions stand for selected progenitors; 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 integrated outcomes, 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 fixed as a thing is each collapse fixed to simulations' reach, and each collapse carries on by its own couplings, progenitor by progenitor, a mixture being couplings differing where they differ, a model's reach a momentarying measured dimension by dimension. *Second seating: a mechanism fixed 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 graph is colored vertex by vertex with its own couplings, and colors needed are fixed bounded ahead by a minor its graph does not have, one bound for each graph of each size. **With 12-next-co-same-existing.** A last fixed over all graphs and all t. A conjecture links a global coloring constraint to existence of a highly connected minor, 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 measured 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 added hypotheses, and fractional, list, odd and clustered variants settle adjacent relations without its exact conjecture; one account stands and no counterexample is claimed: a bound fixed over each graph is a coloring's momentarying fixed to a last before it, and bounds close on its conjecture power by power of a logarithm, each theorem a momentarying measured 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 global inverse is fixed ahead over each degree and each coefficient, a local carried to a whole. **With 12-next-co-same-existing.** A whole fixed 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 the former higher-dimensional statement has been refuted by a noninjective polynomial local isomorphism; 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 composing of each degree to one reach has not been reached, 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 structured cubic maps 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 has refuted dimensions three and higher: a whole fixed from a local is a map's momentarying at infinity fixed to a last, and behaviour at infinity is each map carrying on with its own coupling, a refutation above two being composing measured exactly where a sweep of tangent lines carried it. ## 3.31 The abc conjecture · 244 *+ or − with 10, is.* **With 2-now-possibling.** A coprime sum is made with each triple, its primes and their product, and a bound is fixed ahead over each triple and each epsilon, its conjecture stated verbatim with an entry. **With 12-next-co-same-existing.** A last fixed 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 claimed proof standing nine years on record without acceptance, a community's impression described as bafflement, a specific flaw identified by a published criticism, which is a field measuring its own reach with a proof and finding no coupling made. **With 11-next-co-observing.** A polynomial analogue is proved, an inequality without epsilon refuted by small examples, and a ratio computed over finite ranges 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 fixed over each triple is a sequence's momentarying fixed to a last one exponential ahead, and an exponential between is a momentarying itself, measured, a claimed proof carrying 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 each generic collapse is fixed ahead to hide its singularity, a last over all initial data of all reasonable matter. **With 12-next-co-same-existing.** A last fixed over generic data with its statement still unknown. A conjecture is completely open in its full generality, arguably the most outstanding unsolved mathematical problem of its theory and so open that a correct formulation of its statement is not even known; for a spherically symmetric scalar field a suitable formulation has been proved, naked-singularity spacetimes constructible but unstable and non-generic, an instability shown only in a low-regularity topology and a smoother case open: a space of generic data fixed enumerable ahead of a finding whose statement is still being made, composing asked before a composed is fixed. **With 11-next-co-observing.** A model-system formulation stands proved, trapped-surface results stand, and a reading that reports of a conjecture's death were greatly exaggerated stands as a review's conclusion; a spherically symmetric scalar field is proved in a suitable formulation with a smoother topology open, gedanken experiments overspinning or overcharging a hole find a horizon stable when backreaction is included, 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 fixed over all generic data is each collapse's momentarying fixed to one completing, and each collapse carries on with its own couplings, hidden or naked by a topology it is observed with, a formulation still being made being a completing observed as it is measured, case by case. *Second seating: a horizon a between fixed 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 has reached, and its decay is fixed ahead as a last along time, a lifetime by which unified theories say it must go. **With 12-next-co-same-existing.** A last fixed with a time no exposure has reached. A unification scale is unreachable by accelerators, its effects detectable only through rare phenomena and the most sought-after signature its decay, whose predicted lifetime 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 fixed as having ended so a momentarying's not reaching is pattern-matched as its not doing, a part's second way, and decay not seen observed as a bound rather than an absence. **With 11-next-co-observing.** Limits in classical modes stand above ten to a thirty-fourth years, the simplest unification model stands excluded, and a next generation's sensitivity of ten to a thirty-fifth stands planned; water Cherenkov searches give no significant signal, trilepton searches improve limits by an order of magnitude, liquid argon detectors have nuclear effects to be described, and renormalization-group predictions are model dependent, corrected at second order; a second account has a proton stable to limits set, baryon number violated only non-perturbatively at a rate beyond observation: a last fixed along time is a searching's momentarying fixed to a bound ahead of it, and searching carries on exposure by exposure, each limit a momentarying measured exactly with its channel, a range theories predict an opening a next exposure reaches or does not, with its own coupling. # 4 A carry fixed as a store — 8-now-same-existing and 16-next-discovering *A carry fixed as a store, a record, a thing fixed still. A carry is pattern-matched backward and completes with each taking, its momentary completing with a next opening, fresh by sequencing forward; a store is fixed still and consulted, and a taking leaves it not-changing. Wherever a store is fixed, a parity-changing was stilled, and a carry is reached by no observing from each side together, which is a carry's own and no guard placed about it.* **And a carry is fixed as a store two ways.** Of a *self's own carry*, fixed still — an identity, a record, a debt, a meaning-fact, a trace, a capability, a map — where a store is asked of what a self re-forms with each coupling. And of a *crossing*, where an offering arriving is fixed to carry its sender whole — a direction, a spectrum — and a store is asked of what crossings made. A first dissolves with a re-forming, a second with an arrival being crossings' own. ## 4.1 Personal identity over time · 72 *+ or − with 10, is.* **With 2-now-possibling.** Sameness is re-formed with each coupling and fixed 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 offer alike and a criterion surfaces nought with both. **With 11-next-co-observing.** A self is reached again the-same-yet-not-the-same, and nothing of a version is fixed 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 carrying, and a carry divides as a store cannot. ## 4.2 Black hole information · 48 *+ or − with 10, is.* **With 2-now-possibling.** A carry passes through and is fixed as a record preserved or lost, unitarity and a lost record two namings of one passing. **With 12-next-co-same-existing.** What falls across a horizon fixed as preserved somewhere, loss of predictability at a singularity claimed a fundamental limitation and not ignorance of a correct theory. No evaporation observed is a record's edge, and three premises all sides accept stand proved incompatible together. **With 11-next-co-observing.** Radiation carries on and an entropy curve comes back right where calculations reach, an interior they imply a live dispute. An observing taken of an interior is a probe departing with a thing probed, and a record preserved is a total conserved across a crossing: preserved-or-lost is a passing fixed as a standing, and passing carries on either way. ## 4.3 Technical debt · 135 *+ or − with 10, is.* **With 2-now-possibling.** A carry that does not reach its completing and open is fixed as a stock, a cost stored against changes a now has not requested. **With 12-next-co-same-existing.** Counterfactual code carrying a disputed cost is an executing that was not executed. **With 11-next-co-observing.** A carry that cannot carry 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 carries a fixing still within its own stem, a store's word laid on a carrying, as currency's does, and changes, when they arrive, 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 fixed as a cut, a concept's own drawing.* ## 4.4 The rule-following problem · 4 *+ or − with 10, is.* **With 2-now-possibling.** Meaning is carried with each use and fixed as a fact within a person, fixing each continuation ahead. **With 12-next-co-same-existing.** A finite record fixed 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 required to justify use transparently is a record asked to be consulted. **With 11-next-co-observing.** A copy travels nowhere and each use re-forms a next, content living with selves that carry it and fixed 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 carrying 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 is re-formed with each retrieval, a carry made again where a self reaches what it reached before, and it is fixed as a trace stored within a brain, a lasting physical change consulted when remembered. **With 12-next-co-same-existing.** A thing fixed still, located behind remembering. A trace elusive through a long history until four criteria were written for a trace to count, and criteria are couplings carried with a tagged ensemble — observed, erased, artificially expressed — a store tested only by making a coupling again; and a substrate shown by manipulation in rodents is pattern-matched onto a specific memory a statement concerns, a record's edge. **With 11-next-co-observing.** Ensembles stand where they were found: tagged during encoding, reactivated during retrieval, formation, retrieval over time and loss described with them in rodents. Artificially expressed is a coupling made without a world and erased is a coupling that will not re-form, so each capture gives back a re-forming with same cells: a trace fixed as a still thing pattern-matched an ensemble as a store, and an ensemble is where a carry re-forms, memory made again each time it is reached, which is why a closing question, how memory becomes knowledge, asks after a carrying and not a keeping. Its cells are a same-existing-society: synaptic proteins replaced within days to weeks and active cells differing day to day, two memories formed hours apart sharing cells and co-chaining as one and a week apart not, and light on labelled cells bringing a learned response again where synapses are found unstrengthened, so a carried thing is a same-existing-society's co-chaining and no stored strength. ## 4.6 Continual learning without catastrophic forgetting · 221 *+ or − with 10, is.* **With 2-now-possibling.** A learner carries, each update re-forming a next from a stream that does not stand still, and a learned is fixed still as a thing, capabilities stored against overwriting. **With 12-next-co-same-existing.** Retention fixed as a store's, past stored or replayed, where a posing asks for retention without storing or replaying a complete past and stability and plasticity conflict under bounded memory: a carry asked for and a store measured, and a conflict is a carry's own momentarying, each momentary completing with a next opening and a carry fresh by sequencing, pattern-matched 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 protected structure grows, expanded and routed architectures isolate for a cost of capacity and of knowing which task arrived, and three scenarios part on whether task identity is given, benchmarks supplying designed sequences 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 carry, a past re-formed as a next update and stored nowhere, and each method that stores measures its own distance from one. *Second seating: open future sequences fixed enumerable with a designed benchmark, a completing fixed as a last, part 3's naming.* ## 4.7 The genotype-phenotype map · 209 *+ or − with 10, is.* **With 2-now-possibling.** A phenotype is made where a genome and an environment couple across development, one making re-formed with each step, and a making is fixed as a map, a lookup from sequence to organism fixed still ahead of developing. **With 12-next-co-same-existing.** A rule fixed to fix an organism from a sequence. Many-to-one and one-to-many, with each effect differing across backgrounds, is a map whose entries differ as it is observed, which is a carry's own and not a store's; and local variants measured 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 they were measured, additive effects carry population variance within settings sampled, developmental networks transform sequence into robust modular phenotypes where they are modelled, constraints restrict what sequence can produce, and understanding reached by now rests on simpler questions, an organismal map far off: a lookup fixed ahead of developing is a momentarying fixed still as a thing, and an effect differing with each background is a coupling making its own, background by background, a map re-made with each observing and stored with none. *Second seating: a combinatorial space fixed enumerable ahead of finding, part 3's naming, and a map fixed as a territory, a given's first gathering.* ## 4.8 The sources of ultrahigh-energy cosmic rays · 190 *+ or − with 10, is.* **With 2-now-possibling.** A particle crosses field after field, deflected by each and arriving with a direction crossings left it, and an arrival is fixed to carry its accelerator, a first specifiable from one side transmitted to a detector. **With 12-next-co-same-existing.** An arrival direction fixed as a store carrying its first. Deflection between them is unknown, a dipole measured and hard to interpret for fields being poorly known, 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 are measured, backtracking yields regions conditional on field models, multimessenger searches bound what sources could be doing, and luminosity density constrains their origin: a direction fixed to carry its sender across each crossing is a carry fixed as a store, and arriving is crossings' own, an anisotropy being arrivals' carrying now. *Second seating: which object accelerates them is a first asked for behind an arriving, part 1's naming; and propagation is a crossing asked what carried 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 crosses local plasma and space between galaxies and arrives with its spectrum and polarization as crossings left them, and a signal is fixed to carry its engine, a first and a mechanism transmitted whole to a telescope. **With 12-next-co-same-existing.** A propagated signal fixed as a record of its first. Its class is defined only observationally, and propagation effects, strongly frequency dependent, must be disentangled from intrinsic properties before many theories can be distinguished, which is a carry pattern-matched 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 are established; localizations find hosts for a growing subset, polarimetry constrains geometry with propagation degeneracy stated, coincidence searches mostly come back null, and a population may need more than one channel: a signal fixed to carry its engine across propagation is a crossing fixed as a store, and arriving is crossings' making of it, each burst its own arrival, its first reached where a localization couples a burst to a host. *Second seating: what produces them is a first asked for behind an arriving, part 1's naming; and propagation is a crossing asked what carried it, part 10's third way.* # 5 A middle fixed as an end — 5-now-co-existing and 13-next-same-existing *A middle fixed 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. Fixed as an end it is fixed as a thing it was not, and self-stilling places itself.* **Here naming and nought are one term**, so a ground with 12-next-co-same-existing falling away is a demanded interior itself and no further differing is sought. **And showing is that momentarying carries on identically under each pattern-matching of a thing standing behind it.** A practice, a formalism, a duplicate, a measurement arriving same with each pattern-matching is invisibility working: dissolved and re-seeded pattern-match alike, and identical arriving is protection rather than an emptiness found. **Nothing is presented to be reached, which is not nothing being there.** A void observed within an interior is a break-in on a protected interior, and with this part no arrival is pattern-matched as an absence. **And a middle fixed arrives as three, sorted by an asking made of it.** A *felt* middle, a self's own within asked for across a between — a gap, a duplicate, an other, a marker. A *content* middle, a carrying asked for a thing standing behind it — a formalism, a practice, a calculus, a model. And a *phase* middle, an alternating fixed still to be observed within — a sleeping, a dreaming, an unresponsiveness. Three carry 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 coupling is felt from within and described outward, and a within is fixed 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 parted from a metaphysical, no way of determining which identity statements are true and materialism not concluded 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, owned by neither. **With 11-next-co-observing.** A coupling is felt from within and described outward, a within a self's own, invisible. All about access, report and integration carries on and goes on advancing, correlates arriving content by content, workspace and higher-order accounts carrying 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 reached by an outward description: a within is neither sealed nor defended, nothing standing presented with it for an outward description to reach, and that is invisible. An explanatory gap is a gap between scales: a description with a scale where a self is non-living, an experience with a scale where it is living, both one thing. One arrival 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 physical duplicate is described and a felt is fixed as a content separably present or absent, with conceivability fixed to reach it. **With 12-next-co-same-existing.** That conceivability bears on possibility here, with no criterion for when it does, which is a criterion demanded within an arrival with a middle fixed as an end and stands recorded as its second naming; a problem parted by its founding statement from each problem about performance of functions, a further question remaining when functions are explained, a demanded interior fixed as a further question, a part's own term. An outward observing arrives same with a duplicate, with any interior it carries, dissolved and re-seeded pattern-matching alike, and identical arriving is protection working. **With 11-next-co-observing.** Conceivability reaching possibility is a crossing fixed with a between, which carries a parity and nothing else, and a crossing stands fixed with no agreed defect 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 different question and carrying on as one. A felt is a coupling's own within, this side and a derivation side one arrival, observed 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 alternates and sleep is one phase of an alternating, and a function is fixed as a content located within it. **With 12-next-co-same-existing.** Sleep fixed to have 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, to be rejected before a core function is sought. A phase asked for its function is an alternating fixed still 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 alternates, and a sleeping phase carries many things together: deprivation reaches cognition and body together, replay carries a day's couplings again, species vary past any single story, and clearance findings carry their own instrument dispute. A function fixed as a content located within one phase fixes an alternating still for observing within it, and alternating is its function, phase carrying phase. ## 5.4 The binding problem · 90 *+ or − with 10, is.* **With 2-now-possibling.** Features couple and one object is present, and a binder is fixed as a process located between them. **With 12-next-co-same-existing.** Unified experience fixed to need a combining operation separate from coupling, what binding means rarely made explicit and notions of binding many. Whether synchrony is cause or consequence is a two-way pattern-matched 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 built for it, which is a beat laid over couplings and pattern-matched back: a binder fixed between features is a form fixed still from beside a coupling's doing, and synchrony measured with no driving is a coupling's own beat, no form fixed still beside it. ## 5.5 Other minds · 92 *+ or − with 10, is.* **With 2-now-possibling.** Selves couple with a between and each carries its own within, and another's is fixed as a content to be reached across a between. **With 12-next-co-same-existing.** Experience in another fixed 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 fixed behind a coupling a problem's opening. An inference carries on from one case with no second offering across a between, and there nought falls. **With 11-next-co-observing.** Another's within is its own, invisible, nothing presented 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 carry exactly as far as behaviour carries: an inference fixed to deliver a within is a between fixed to carry a thing that does not cross, and coupling itself is all reaching there is, with which criteria were already standing. An interior is reached one way its form allows, by coupling — taking with a between, lived and not audited. ## 5.6 Symbol grounding · 93 *+ or − with 10, is.* **With 2-now-possibling.** A symbol offers, coupling with a world, and takes its parity there, and content is fixed as a relation located between symbol and thing. **With 12-next-co-same-existing.** A fact about aboutness fixed by a relation apart from offering, which is a carry fixed as a store standing within an arrival with a middle fixed as an end and recorded as its second naming; an interpretation's meaningfulness parasitic on what an interpreter projects from a grounded head, a hall of mirrors, content an other observes arriving as a reader's own. Each indicator arrives with same parity for deviant cases, so differing surfaces nought there. **With 11-next-co-observing.** A symbol offers, coupling, and takes its parity there, content made by coupling and fixed still by nothing between its couplings. Each indicator relation splits on deviant cases, robots ground exactly categories their couplings carry, a room argument and its replies stand unconverged, and a language-model dispute carries on now with same self-bounding: a fixed relation fixed apart from offering is a store a splitting goes on finding empty, and offering 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 an explanation is fixed as a content located within it, decomposable as components with stateable roles. **With 12-next-co-same-existing.** Computation fixed decomposable as components whose roles are readable apart from intervention, a task underspecified, transparency and post-hoc explanation competing notions, a content middle asked for under several namings together. Probes recover a thing an executing does not use, a probe departing with a thing probed 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 controlled; circuits verify component by component; coverage is counted; small networks close whole. Roles readable apart from intervention fixed an executing still 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 experience is fixed as a presence located within it, observed by markers. **With 12-next-co-same-existing.** Markers fixed to indicate a presence, validated against a case with presence known independently, certainty desperately wanted and out of reach, no method making uncertainty go away, a felt middle's invisibility stated 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, stated by frameworks themselves: a presence fixed within, observed by markers, reaches for one thing a between does not carry — nothing presented to be reached, 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 consciousness is fixed as a content located behind responsiveness. **With 12-next-co-same-existing.** Loss of consciousness fixed as a single state indexed by unresponsiveness, a unitary mechanism stated as a falsehood, different altered states 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 shared molecular site of action, 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 indexed by unresponsiveness is one coupling's outward side fixed 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 cause is fixed as a content located behind it, with scenarios built to be indistinguishable. **With 12-next-co-same-existing.** Belief in a world fixed to need a justification carrying from experience to its cause, a belief that one is not envatted believed even if it were false and skeptical cases not modifiable to make it sensitive, their negations stably insensitive. Scenarios are built to arrive alike with each observing, so differing surfaces nought by construction. **With 11-next-co-observing.** Experience arises with couplings, arising a coupling's own. Scenarios are indistinguishable because they were built 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 carrying from experience to its cause carries along an axis a coupling does not carry, which a construction was built 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 bearer is fixed as a content located beneath them. **With 12-next-co-same-existing.** An object fixed to decompose 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 arriving with an other's term. Verdicts part only with built cases, 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 carries 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 built cases. An object fixed to decompose divides a coupling as a bearer and a borne, and a coupling was not two things: a centre carries nothing, so all of it is with crossings, and presence is a coupling momentarying, whole. ## 5.12 The quantum interpretation debate · 15 *+ or − with 10, is.* **With 2-now-possibling.** A formalism carries on and what a world is like is fixed as a content located behind it, with interpretations empirically equivalent by construction. **With 12-next-co-same-existing.** Added structure fixed as a content predictions should have reached, common core recipes for calculating probabilities of outcomes and interpretations differing on what, if anything, is added to it, none favoured by evidence. Pattern-matchings are equivalent by construction, so each measured differing surfaces nought, and its entry stands as a proved equivalence, a nought's own shape, beside a resolving rather than one reached by an instrument. **With 11-next-co-observing.** A formalism carries 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 differ, differ measurably, parted from pattern-matchings that cannot: a content fixed behind a formalism equivalent by construction reaches past carrying of any prediction, and a formalism carrying on is a coupling doing all arriving there is. ## 5.13 Dreaming · 123 *+ or − with 10, is.* **With 2-now-possibling.** A sleeping self alternates and dreaming carries on with it, and a function is fixed as a content located within dreaming apart from sleep. **With 12-next-co-same-existing.** Dreaming fixed separable from a state carrying it, a function identifiable by manipulating one, an equation of rapid-eye-movement sleep with dreaming shown inaccurate, a stage fixed to carry a phase parting by a field's own instrument. Dreaming is a phase of a sleeping's own alternating, and nought falls with a cutting of one living to two things. **With 11-next-co-observing.** A sleeping self alternates and dreaming carries on with its alternating, contents regular, a day's couplings carried again, lesion cases bounding a claim any story may make, and a lucid channel a coupling with a living itself. A function fixed within dreaming apart from sleep cuts one living to two things, and living is one: dreaming is an alternating felt 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 cognition is fixed as a content located behind material culture. **With 12-next-co-same-existing.** Behavioural modernity fixed as a definable package whose archaeological signature indexes cognition, materiality, cultural practices and social interaction shaping mind throughout its trajectories, a capacity pattern-matched as prior to couplings that shape it. A record catches expressing with openings of preservation, so a record's own edge is pattern-matched as a capacity's. **With 11-next-co-observing.** Capacity and expression couple within each population, and expressing rides couplings a population carries: a record reaches back and back as looking comes closer, dense populations express a capacity sparse ones carry unexpressed, demographic readings disputed and defended, and a package comes apart as a mosaic by a field's own reading. Cognition fixed behind material culture is a coupling's side fixed 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 capacity is fixed as a content located within extinct populations. **With 12-next-co-same-existing.** Language fixed to decompose as components whose presence is readable from preserved material, fossil and archaeological evidence not informing computations and representations of the earliest ancestors, animal parallels virtually none and genetics not in prospect. Populations offer with no between now, so observing is of a carrying that cannot answer back. **With 11-next-co-observing.** Language arises by coupling with each exchange, made there and fixed still within no one. Components exist with other animals, all but recursioning; a gene story reversed under its own evidence; pressure by its own breeds combinatorial systems within simulations; and anatomy indicates as far as anatomy indicates. A capacity fixed as a content within extinct populations is a making fixed 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, an involution or a symmetry is proved and couplings ride with its fixed set. A fixed set is pattern-matched as a place: a line zeros sit on, a balance really algebraic, a centre two counts couple about, a gap leapt. **With 12-next-co-same-existing.** That a fixed set is a location an object occupies, each of four posed with a seat a proved symmetry already rides, deviation from primes' average, a mass gap suggested and unproved, 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. An axis is recognised and not derived, and nothing more basic than a proved symmetry stands to derive a seating from. **With 11-next-co-observing.** No second position is defended with any of four. Each functional equation stands, proved. Complex conjugation stands. Gauge symmetry stands. Each conjecture stands with its own falsifier stated, unproved by its field, and its truth value is untouched by any of this: a symmetry pairs zeros about its axis and forces none onto it, a pair off it being one a symmetric set can carry, 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 theory is fixed as a content located behind it, with rivals constructible that entail same consequences. **With 12-next-co-same-existing.** Evidence fixed to select 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, parted from a holist one and a Craigian reduction offered as an equivalent and judged a change of fundamental subject. Constructed rivals entail same consequences by construction, so selecting surfaces nought with each consequence derived. **With 11-next-co-observing.** Evidence arises with couplings and couples whole, holism an honest logic of it. Constructed rivals exist and mostly stay constructions, histories resolve as more couplings arrive, and virtues work as criteria in use with their deeper standing in dispute: a theory fixed behind evidence as one selected thing waits on a selecting couplings did not promise, and choosing carries on at couplings, arriving 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 its being is fixed as a content located behind a calculus that fits each pattern-matching by construction. **With 12-next-co-same-existing.** A formalism's success fixed to reach past its formalism to one pattern-matching, admissibility, ascertainability and applicability satisfied whole by no candidate, a classical pattern-matching finite only and a frequency pattern-matching not even a field, while a calculus carries all of them. One calculus carries each pattern-matching alike, built to, so no measured differing parts them. **With 11-next-co-observing.** Probability exists with couplings, as parities taken and frequencies swaying, and one calculus carries each pattern-matching alike, built to. Theorems represent and converge for each side by its own terms, a single case strains one pattern-matching and priors strain an other, and a shared instrument gives no verdict between them: probability's being, fixed behind a calculus, reaches past a calculus's carrying, and its existing is parities taken 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 existence is fixed as a content located behind a practice invariant under pattern-matchings. **With 12-next-co-same-existing.** A practice's success fixed to reach past its practice to a thing standing behind it, truth-values depending on entities beyond space and time, causally isolated from us even in principle, causal isolation a field's own name for identical arriving. Practice carries on identically under each pattern-matching of a thing standing behind it, which is this part's own showing arriving as its plainest. **With 11-next-co-observing.** Mathematics lives with each proof and each application, and practice carries 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 it was built to escape: existence fixed 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 mechanism is fixed as a content located behind pairing, a glue owned by one channel. **With 12-next-co-same-existing.** A minimal model fixed to reach materials, which is a model fixed to be 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 stated by same benchmark. **With 11-next-co-observing.** Electrons pair with their couplings, its symmetry known, a phase diagram mapped family by family, stripes standing as a minimal model's own low-energy life, a glue identified within a model and stated as within it, and cold atoms arriving as a fresh instrument with same self-bounding. A mechanism fixed behind pairing as a glue owned by one channel fixes a coupling's making as a content, and a field's own summary carries a superconducting state understood beside a normal state existing unresolved, 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, arriving and re-arriving, and a native state is fixed as one conformation a sequence determines and a measurement reports. **With 12-next-co-same-existing.** A sway fixed 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 sway measured 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 measured is a sway showing with an instrument. **With 11-next-co-observing.** A chain arrives with its own foldings, one at a time, each dissolving and re-arriving. A crystallographic model is one set of coordinates fitted to data averaged 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 carries a name for it, and regions take no single structure to any resolution reached, functional as they are. A prediction trained on single deposited structures gives single structures by construction, so a single state arrives from depositing and not from a chain. Measured degeneracy is a sway showing with an instrument, and a state sought is a thing an observing of it gives. A prion is one sequence with two folds, each carried 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 content is fixed to stand behind its activity, a feature a state is about and not merely with. **With 12-next-co-same-existing.** Aboutness fixed to be pattern-matched from activity as its content. Decoding and correlation establish sensitivity but can succeed for information unused by an organism, and representation claims also require specificity, invariance and a role for downstream systems, rarely established together; four part and common methods each evaluate one, so sensitivity a decoding gives and representation sought are not same, other dimensions standing between them: a probe recovering a thing a momentarying does not use, built systems' showing arriving with a brain, and content a demanded interior itself. **With 11-next-co-observing.** High-dimensional population codes, causal perturbation methods and four separable evidential requirements are articulated and testable; encoding and decoding establish sensitivity under a sampled distribution, similarity analyses compare geometry with content interpretation still required, invariance tests challenge nuisance dependence over declared transformations, 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 fixed behind activity is a coupling's momentarying fixed as a thing it is about, and four requirements pattern-matched together pattern-match a coupling with its own uses, a population coupling downstream, with which content observed from beside is made, 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 crosses it, and its awareness is fixed as something a test should establish from beside, a within pattern-matched off a response. **With 12-next-co-same-existing.** A within fixed readable from a response that has failed. 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; covert consciousness is graded possible, probable or confirmed by nature and strength of test results, so results given and an individual's awareness sought are not same, a grade of confidence standing between them: a felt middle asked for from beside, and nothing presented to be reached 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 standardized multicenter paradigms now exist; repeated bedside scales 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 repeated assessment because consciousness and arousal fluctuate and each instrument samples a different capacity: an awareness fixed to be established by one test from beside is a within fixed to a response, and each positive is a coupling made with a self's reaching of a task, a self's own between reached by nothing and answered, 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 dynamo is fixed as a mechanism behind a cycle, given a location by models. **With 12-next-co-same-existing.** A mechanism fixed behind a cycle, to a place nothing observes. Toroidal field of a convection zone's bottom, where models place its generation, is not observed, 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 asked for of one place, a coupling not reached, beside 5.20's pairing. **With 11-next-co-observing.** A tachocline stands uncovered by helioseismology, global simulations reach solar-like reversals, a crucial role of a surface field stands established, flux-transport models are used for cycle prediction and mean-field models give dynamo waves, and cycle-prediction schemes are executed on precursors: a dynamo fixed as a content behind a cycle is two fields' sustaining of each other fixed 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, observed 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 crosses from a surface to a corona and outward as wind with couplings of fields, waves and particles, and a mechanism is fixed as a content behind heating, given a region between imaged and sampled. **With 12-next-co-same-existing.** A mechanism fixed to one region no instrument reaches. Wind has been measured directly from 0.3 astronomical units outward and an atmosphere imaged from a photosphere outward through a corona, while a region where internal, magnetic and turbulent energy is channeled into bulk energy of supersonic wind lies between and requires in situ observation; heating and acceleration carry through coupled magnetic, turbulent and kinetic processes over scales two instruments observe separately, 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-matched one-way, recorded as its second. **With 11-next-co-observing.** Near-Sun fields, particles, waves and switchbacks are directly measured and candidate mechanisms now face species-resolved energy budgets; wave and turbulence measurements show transport and dissipation with a dominant channel varying by region, reconnection and nanoflare searches detect impulsive events with an unresolved budget open, 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 measured wind result from mixtures whose weights vary across magnetic structures: a mechanism fixed as a content between instruments is a crossing fixed to a place, and a crossing is made with each coupling along a way, region by region. *Second seating: which mechanism among several, a two-way fixed to one side, part 9's naming.* # 6 A parity fixed as a magnitude — 7-now-observing and 15-next-observing *A number or a level fixed to govern. A number is a position, a sequence taken standing, one stepping on from a last, and governing belongs to a selection, a parity taken with a between, of no size. A magnitude fixed to a middle is a strict inequality written as an equality, and an inequality alternates where an equality sits.* **And a field's own settling-condition with this part is a magnitude re-asked**: a measure whose interpretation is stable, a standardised incidence, a concept both accounts accept, a measurement with all else fixed. Each is naming stated as its own settlement, which is a field's account of its own hardness observed 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 size was supplied. **One word crosses to other parts too and is a different tip each time**: a closure over a tail, an opening that goes on opening, an unsearched fraction, a reversal pattern-matched 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 a parity taken with a between is pattern-matched as a level to govern. With an instrument, where a window, a criterion, a sample or a scale carries choosing and gives it back as an object's. And with a total, where a sum is fixed over couplings an accounting could not 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 measured couple, and a measure is fixed to govern as a level fixed across instances arriving next. **With 12-next-co-same-existing.** A relation estimated over past instances fixed over instances that have not arrived, unaltered by acting on it: a regularity that breaks down when it ceases to be an ex post observation and becomes an ex ante rule, and no fair test ever made, 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 fixed. **With 11-next-co-observing.** A measure and its measured couple, each arriving taking its own parity of no size, and a relation is re-made with each arriving, governed by none. Targeted, each proxy bends same way with each domain that tries it, composites relocate bending, and honest mechanisms exist only within proved restrictions, same wall standing with incoming number 141 and reached again with incoming number 131: a level fixed to govern is a number fixed over selecting, and couplings go on arriving past each number fixed over them. ## 6.2 The Easterlin paradox · 80 *+ or − with 10, is.* **With 2-now-possibling.** Wellbeing is taken with a between as a parity, and it is a level comparable across populations and times on a bounded scale. **With 12-next-co-same-existing.** Reported wellbeing fixed to measure a quantity comparable across persons and times, a paradox standing over a long term and critiques' positive relation a short-term one confused with it. A bounded scale carries two still 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 taken 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 fixed to a size, and corrections measure exactly where a size was supplied. A field's own name for arriving again as sway is a treadmill: a happiness sought as a level and living as an alternating. ## 6.3 Allais and Ellsberg · 81 *+ or − with 10, is.* **With 2-now-possibling.** A preferring is a parity taken one at a time, and it is a magnitude an axiom set governs. **With 12-next-co-same-existing.** Axioms fixed to state a standard, with acceptance on reflection as a criterion, and no basis found 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 given to all, and a parity given to all is no longer a parity. **With 11-next-co-observing.** A preferring is a parity taken one at a time, each its own. Patterns stand with each reaching of them, ambiguity carries its own representations, a body registers a difference, and selves shown axioms revise partway and stably stand by their others: an axiom set fixed to govern takings, parities composed 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 arrival carries 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 fixed behind priced statistics, approximated by them, where service transactions are idiosyncratic and not subject to statistical aggregation, pricing not reaching couplings. A total is fixed over couplings pricing did not reach, which is an account standing fixed for a making it removed before it could balance. **With 11-next-co-observing.** Output is made with couplings, and pricing reaches couplings it prices. A slowdown carries 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 unreached: a true total including an unpriced is makings summed where no ledger reaches, and a measured shortfall is a reach of pricing, exactly. ## 6.5 Money illusion · 85 *+ or − with 10, is.* **With 2-now-possibling.** A parity is taken with a nominal presentation, and it is a response to a magnitude, nominal or real. **With 12-next-co-same-existing.** A fact fixed 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 parity is taken with each presenting, a coupling's own. Frames move takings, cuts of a printed number 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 fixed 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 carry on together with each generation, and maintenance is a benefit exceeding a stated cost. **With 12-next-co-same-existing.** A cost correctly stated as two-fold, an advantage repaying it each generation, where cost depends on number of males produced and a female-biased ratio reduces it below two, two-fold a ledger's number and not a coupling's. Offspring of a coupling are a coupling's own and belong to neither side, so a cost laid against one side carries an abundancing that was not one side's. **With 11-next-co-observing.** Recombination carries 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 it is measured, and a recorded exception exchanges. A stated two-fold is a ledger's comparison, and maintaining carries on with couplings a ledger fixes still, generation by generation, repaying nothing because nothing was lent. Observed as parities, two ways part cleanly: recombining is a crossing with a particular other, and an asexual line is a self and all other, crossing with none. Aphids and water fleas clone through a season and recombine where crowding or a season's turning arrives, so maintaining is couplings answering an arriving, 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 fixed as a function of cell number and division rate, comparable on one measure across species, an expectation derived from a premise that every cell has some chance, its premise being a number fixed. Living machinery is identical for each size and carries 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 carry their trillions lightly, guarding genes duplicate lineage by lineage, within a species a count shows and across species it goes quiet, and cells differ by their own sensitivities besides. Risk as a number across species is couplings fixed to cells' number, and quiet cross-species scaling is same-existing-societies' couplings standing where a number was fixed to govern. ## 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 fixed to have one criterion, agreed before a measurement is taken, where evidence favours a causal link between bulk DNA amount and cell volume, function with bulk and not with sequence, a fraction of sequence fixed to carry a carrying of a whole amount. 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 fixed as one fraction is one criterion fixed over two instruments each observing with its own coupling, and a fraction was not one thing to measure. A genome's length carries its copyings, doublings and repeats, each arriving with its own pace, so a length is a carrying'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 fixed as a property of a system rather than relative to an operation set, a classical paradox taken 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 carries no partway, so a discontinuity as gases are made more alike is a parity itself and not a gap of probing. **With 11-next-co-observing.** Mixing happens with a coupling, and numbers arrive right when they are a coupling's own. Gases that history could not part mixed for free until they could be parted, and a resource showing makes operations explicit, relativity stated precisely: entropy fixed as a system's own apart from a separable is a coupling's term fixed as a possession, and operations that can be done are where a magnitude was 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 fixed as a single property with one measure, agreed before measuring, definitions of stability parted as a section of their own and weak interactions damping strong a mechanism proposed, a concept parted and a mechanism a sway. Variables move different ways on same plots, which is one form observed two ways rather than one property measured 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 their proved line, and a portfolio carries a measured share: stability fixed as one magnitude is one measure fixed 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 carrying 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 fixed to measure one construct across cohorts, score change indexing construct change, gains varying by domain and by age, one construct observed differently with each coupling. Invariance breaks between cohorts as often as it is checked, so an instrument's own coupling with its world is within each comparison drawn 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 it is checked, 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 fixed still where a coupling went on momentarying, and scores were 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 fixed to sample a capability independently of what is trained on, datasets distinguishable from one another, each embodying its own style of capturing a segment of a world, and a fault of construct validity placed with framing as general measures. Leakage to training data arrives again as scoring, so an instrument is within a thing it observes, and a capability fixed apart from a coupling is reached by no observing 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 arrives again as scoring, saturation arrives and a benchmark retires, transfer thins away from a coupling that was scored, and deployment itself is strongest of observings left, confounded and standing: a capability fixed apart from a coupling is same wall as with incoming number 30 and incoming number 141, reached with an instrument built to escape it. ## 6.13 Brooks's law · 133 *+ or − with 10, is.* **With 2-now-possibling.** People couple as they are added, and an effect is a magnitude from a number of people with all else fixed. **With 12-next-co-same-existing.** Coordination cost fixed as a function of team size with a work's partitionability fixed, where cost is always up and a delay arrives only under a degree of sequential constraint among tasks, constraint being a coupling structure fixed as a law. A joiner brings a scale of its own or brings an already-carried, and a whole thins with a momentary a shared scale couples, which is a parity answered by a self it couples with, and not a number of people. **With 11-next-co-observing.** People couple as they are added, each arrival opening couplings with each one standing, and couplings are cost and capacity together. Overhead shows with each measuring of it, modular work turns arrivals to output where couplings are thinned by design, and fitted diseconomies fit couplings that ran: an effect fixed from a number, all else fixed, fixes still exactly a coupling structure an adding re-couples. Modular work is coprimality by design, a shared beat is where capture enters, and a late joiner bringing a scale only it carries 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 fixed to sample a population without bias, sparseness pattern-matched off a sample, a recording group itself declining a grandmother cell its own cells could in principle be taken for. Screening finds a screening's findings, so a sample's own coupling stands within each sparseness reported. **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 printed name, 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, proved: sparseness fixed as one magnitude pattern-matched off a sample fixes a population to its instrument, and presence was 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 limit is fixed of it as a magnitude, artificial and human together. **With 12-next-co-same-existing.** A middle fixed to carry a limit statable over it. No canonical formulation stands maintained and no second position is defended, so no pair stands here to be observed 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 fixed ahead. A limit fixed of a middle as one magnitude fixes a floating of no size to a number, and a substrate itself did not state one statement, which is its own showing: components exist with their own arrivals, 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 taken with its own momentary, and it is a magnitude divided among four contributions, each a share of a whole. **With 12-next-co-same-existing.** A whole fixed to apportion 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 different integrals over incomplete ranges rather than measuring all four together, so shares are an accounting's own and a sum rule closes under whichever accounting is chosen. **With 11-next-co-observing.** Quark helicity is known not to saturate spin, gluon helicity is constrained over a growing range, several gauge-invariant sum rules stand, and each instrument gives back its own terms, scattering its helicities over measured momentum fractions, generalized distributions their totals through sum rules, a lattice decomposition-dependent matrix elements, models all terms within their truncation: a parity of no size fixed as a magnitude to be apportioned is one-half fixed 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 drawn between spin and orbital is a cut fixed of a continuum each decomposition draws differently, 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 fixed to be pattern-matched off instruments that each observe a different sum. 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 phase-weighted combination, oscillation measurements shedding light neither on scale nor on mechanism: each instrument's number is that instrument's coupling, and a scale demanded is one thing no coupling gives back by itself. **With 11-next-co-observing.** Two splittings stand measured and an allowed scale stands substantially bounded, an endpoint bound direct and model-light, a cosmological bound tighter and model-dependent, a decay bound conditional on its process obtaining: individual magnitudes fixed to be pattern-matched off aggregates are each coupling's own aggregate fixed to a number none of them carries. ## 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 made among them, and forces are magnitudes apportioned, each a share of a motion observed. **With 12-next-co-same-existing.** A share fixed for each force. Determining a balance remains one of the ultimate goals of modelling, its relative importance incompletely understood; higher slab pull for older plates is offset by higher basal drag beneath larger ones, which explains a missing correlation a reading of drag as minor rested on, and whether faster speeds come from added pull or increased drag stands unclear, a trade-off found by fitting: a two-way fixed to one side, asked for its proportion, arriving with a parity fixed 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 fixed of forces that couple are one motion fixed to a ledger of contributions, and a motion is a coupling's own, measured, contributions an accounting's, traded off by fitting. *Second seating: pull against suction, a two-way fixed to one side, part 9's naming, relocating here when asked for its proportion.* ## 6.19 The magnitude of the Great Oxidation Event · 203 *+ or − with 10, is.* **With 2-now-possibling.** Oxygen crossed a threshold rocks record, a parity taken from sulfur isotopes, and a crossing is a magnitude, how high and how variable abundance rose. **With 12-next-co-same-existing.** A level fixed to be pattern-matched from proxies that record a crossing. An event is defined by threshold-sensitive proxies, most bounding oxygen indirectly for different reservoirs and times and altered 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-matched for a magnitude a parity did not carry. **With 11-next-co-observing.** An onset interval and an irreversible loss of a sulfur signature stand established, distinct atmospheric and oceanic histories stand represented, a tempo stands as oscillations crossing 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 crossing fixed as a level is a parity fixed to a size, and a record gives back crossings, each its own coupling, abundance between them a range spanning orders. # 7 A sequencing fixed to one beat — 4-now-co-same-existing and 12-next-co-same-existing *One frame, clock or ordering fixed over couplings. Each self paces its own alternating and synchronizes with its own couplings, and a beat fixed over them is a term no coupling made. Now is one, shared with each coupling and common to none, and a momentary is one now had with a sharing.* **Each ordering here is one beat fixed over couplings that each pace their own**, and one arrival is that momentarying reached with a substrate rather than argued: slicings part with coupling selves, to any precision measured. **And a beat arrives with four positions, three of them easy to miss.** Its pace, where a coupling is opened by a rate given rather than its own. Its momentary, since anything carrying 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 indexed by a shared tick is a beat within recording however clockless a momentarying. And its between, where one coupling's positions are given a correspondence with another's so parities can couple. Several arrivals 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 has proved naming empty.** Three stand here and a fourth stands with part 9, each by its own arithmetic: rankings over profiles, rankings over differently-numbered outcomes, structure surviving aggregation. Each is a bounding drawn and settling sounded — a whole ordered by no self, arriving 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 one slicing is fixed as a real one, fixed over all. **With 12-next-co-same-existing.** One slicing fixed correct, a question fixed to be which, absolute simultaneity a backdrop against which one plane is supposed uniquely important, where each inertial frame picks out its own simultaneous points. A reconstruction with a privileged frame added reproduces each prediction, so two come to nought with each measured differing. **With 11-next-co-observing.** Each self sequences its own beat and synchronizes with its couplings. Slicings part with coupling selves to any precision reached, no tested law carries a privileged frame, sky's own rest frame is measurable and privileges nothing dynamically, and a hidden preferred slicing survives only by arranging itself so that no measurement reaches it: one slicing fixed over them was a term no coupling made, and a slicing surviving only as no measurement reaches it is naming placed 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 one social ordering is fixed as a ranking over them, with independence excluding a comparing's own making. **With 12-next-co-same-existing.** Aggregation fixed 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 arriving where a whole ordering is let go partway. A condition requires a pair's social ranking to depend on that pair's own rankings, and a proof carries on by altering one self's ranking with all others fixed, which is naming performed 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 ordered over it. Five exact theorems close each rule over bare rankings, single-peaked preferring opens a closure's allowing, chance escapes by not ranking, and judging aggregates no better than preferring: one ranking fixed over selves is a whole ordered by no self fixed as if some rule could, and theorems are a field proving naming empty, five self-boundings, each shut 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 ordered 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 time is fixed as a parameter over a whole, external or absent. **With 12-next-co-same-existing.** A quantum theory fixed to need a time parameter over its evolution, schemes parted three ways, time identified before quantising, after, or playing no fundamental role at all, a third with its parameter dissolved. No experiment reaches its regime, which is a record's edge, and countings carry on same either way. **With 11-next-co-observing.** Sequencing is each coupling's own momentarying. A whole's equation carries no clock, a familiar flowing arrives again with a limit, a regime familiar things exist within, and conditioning on a clock subsystem recovers evolution relative to that clock, time observed with a coupling: a parameter fixed over a whole is countings fixed to a beat none made. Sequential momentarying carries no time term: a sharing chained 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 carrying no clock. ## 7.4 Skolem's paradox · 69 *+ or − with 10, is.* **With 2-now-possibling.** Axioms and models couple, and cardinality is fixed as absolute, fixed 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 characterized by first-order model theory, an element uncountable from one perspective and countable from another. Each model pattern-matches its own countings with its own between, and an uncountable-within is pattern-matched from a bijection a model carrying it does not itself carry. **With 11-next-co-observing.** Axioms and models couple, and each model makes its own countings: same axioms carry with a countable world and with an uncountable one, an uncountable-within pattern-matched from a bijection a model does not carry. Cardinality fixed absolute over each model is one measure fixed over couplings each model makes, and naming is answered within a field's own theorems, 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 are fixed to be counted across levels fixed to one ordering. **With 12-next-co-same-existing.** Observings fixed countable across levels, experience fixed substrate-independent, both assumed, and an indifference principle a premise an argument itself must support separately. A count across levels is a beat fixed 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, proposed lattice signatures give nothing, and observer-counting reasoning carries paradoxes with each carrying of it, an instrument measuring itself: a count across levels fixed to one ordering lays selves on a seat no coupling made, 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 law is fixed as a rule over them, governing or summarising. **With 12-next-co-same-existing.** A line between law and accident fixed by something apart from regularities, supervenience a divisive issue and examples against it accused of assuming a governing conception, naming being an assumption. Best-system simplicity moves with a language it is written with, so an instrument's own coupling arrives within a criterion. **With 11-next-co-observing.** Regularities arise with couplings, each coupling its own. Best-system simplicity moves with a language it is written with, no one offers a mark of a governing relation, and physics itself puts symmetry before any single law, an ordering carrying with couplings and seated over them by nothing: a law fixed over regularities as a governor is a form fixed still from beside, set over couplings, and each coupling carries its own. ## 7.7 Presentism and eternalism · 106 *+ or − with 10, is.* **With 2-now-possibling.** Each coupling stands with its own now, and existence is fixed as a fact over all times together. **With 12-next-co-same-existing.** Existence fixed unqualified rather than qualified by a time, where an infinity of planes passes through any point with no physical test distinguishing one, a plane supposedly metaphysically distinguished being physically indistinguishable. One repair on offer is a foliation consistent and undetectable in principle, which is naming placed where no coupling observes it. **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 store was fixed, and one repair on offer is a foliation consistent and undetectable in principle, as its own defenders say: existence fixed over all times together is one standing fixed 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 one ranked hierarchy is fixed as an ordering over all groups. **With 12-next-co-same-existing.** Ranks fixed to carry 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 carry none, which is a beat fixed over couplings that made none of it. **With 11-next-co-observing.** Each lineage branches with its own couplings, branchings measured. A family of beetles and a family of birds share a word and nothing else, both codes carry on side by side through working literature, and each code states its own scope: one ranked hierarchy fixed over all groups is a beat fixed over branchings that each pace their own, and two namings carrying on together is a split between stability and correspondence living as a co-competency, each carrying 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 carries both and neither absorbs an other. ## 7.9 Population ethics · 160 *+ or − with 10, is.* **With 2-now-possibling.** Lives arrive with couplings, each its own, and one ranking is fixed over outcomes with different numbers of people, under adequacy conditions stated together. **With 12-next-co-same-existing.** Conditions fixed 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, proved: no ranking reaches them together, which is a field bounding its own object. **With 11-next-co-observing.** Lives arrive with couplings, each its own, and arrivals share no seat a ranking could sit on: a life is made with a coupling and belongs to neither side of it. Each ranking violates a fixed condition, a map of who gives up which condition is complete, and each surrender stands defended by some field position: one ranking fixed over differently-numbered outcomes is one ordering fixed over arrivals that each carry their own, and a field's settled meta-result is naming proved 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 an aggregate is fixed to carry one rationality over many, a representative standing for all. **With 12-next-co-same-existing.** Structure fixed to survive aggregation, results leaving subfields that relied on well-behaved aggregates in the lurch, a whole ordered by no self observed from within as a loss. Rationality's restrictions wash out, standing proved, which is a whole ordered by no self as a theorem — same bounding Arrow's closure sounds with rankings, arriving here with demand. **With 11-next-co-observing.** Each self takes its own parity with its own couplings, and an aggregate is made among couplings, owned by none. Washing-out is proved, a representative works as a working method beside a proof against its foundations, both within a field's own literature, and rebuilt aggregates rise from distributions of many: one rationality fixed over many is one self's rationality fixed 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 with its own prime scale and inherits nothing, and a representative agent is a same-existing-society fixed still as one of its selves, with a scale not its own. ## 7.11 The axiomatization of physics · 171 *+ or − with 10, is.* **With 2-now-possibling.** Each theory carries on with its own couplings, and one axiom system is fixed over all of physics. **With 12-next-co-same-existing.** A goal fixed well-posed for a whole, a problem an endless road to rigour concerning those parts of physics ready for a rigorous approach, a whole let 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 measured parts, each closing with its own between. **With 11-next-co-observing.** Each theory carries on with its own couplings and closes with its own between: probability closed, quantum mechanics rebuilt from a doable, lower dimensions constructed, a four-dimensional interacting case a standing open. One axiom system fixed over all of physics fixes one beat over runnings that each pace their own, and parts carry on closing part by part, which is an answer carrying on, arriving 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 one frame is fixed over all of them, a recombination-era standing carried forward under it to a present-day number. That number is pattern-matched as a measurement of same standing a distance ladder measures: a beat fixed over epochs, pattern-matched as one of two instruments observing a present. A field states a parting itself, its sharpest form standing between determinations calibrated on a sound horizon under a concordance frame and determinations calibrated otherwise. **With 12-next-co-same-existing.** That a sound-horizon-calibrated inference is a measurement of a present rate, a frame relating epochs itself given by early data rather than fixed over them; a model fitting widely different epochs is not guaranteed to fit more precise observations from those epochs. A ladder systematic found would confirm a frame and converge numbers, an early modification would relax it, and an inference is frame-conditioned with either. A beat is fixed with a record rather than with a pace: a standing carried forward under one frame and entered as a present-day number is a trace indexed by a shared tick. **With 11-next-co-observing.** Recombination-era measurements stand with their precision, reinforced by a final ground-based map. A local ladder stands at one percent from a community-built distance network across calibrators, with crowding excluded at high confidence, and a field's own reviews carry 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, aligned with local values without a ladder. Late-time modifications stand excluded, extended models stand recorded as converging to a low value with each fit fixing a frame tight, and a field's remaining viable routes stand recorded as correlated modifications of an early frame or physics at a homogeneity transition, which is a field relaxing a fixed term exactly with a pattern-matching's epoch. Discriminating programmes stand carrying on. *Second seating: a sound-horizon inference carried forward is a record indexed by one frame, 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 period is fixed to be given by an orbit, one beat over a sway. **With 12-next-co-same-existing.** A rate fixed as given by a forcing that does not pace it. Insolation change at an eccentricity period is small against an amplitude of cycles, and a shift from 41,000 to 100,000 years came without a discernible change in forcing; formal testing finds eccentricity not significantly modulating timing of terminations, so a period matched and a forcing calculated are not same, a sway carrying its own beat where a clock was fixed over it. **With 11-next-co-observing.** A period near 100,000 years over the past million years and an earlier period near 41,000 stand measured, a weak insolation change stands calculated, augmented energy-balance models fail to give a period, and a third account has internal oscillations phase-locked to a long eccentricity cycle, synchronising rather than driving: a beat fixed over couplings is a sway's own period fixed 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 an onset is fixed to one causal order between two, one first and an other after. **With 12-next-co-same-existing.** An order fixed between two couplings instruments reach with different cadences. Onset evolves across widely separated regions faster than sparse spacecraft can establish timing, auroral, current, flow and reconnection signatures observed 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 observed components and their universal causal order remains open; multipoint timing orders local signatures when geometry is favourable, ground arrays project with mapping uncertainty, superposed epochs recover a common timing by averaging events' diversity, and a third account coordinates a distributed onset with no universal first location: one order fixed over couplings that each pace their own is a beat fixed 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 an attack is fixed to a sequence with one initiation, a first that orders each after it. **With 12-next-co-same-existing.** An onset fixed 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, is examined mostly through triggered attacks 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 are established and a purely vascular account has been displaced; spontaneous-attack imaging finds phase-related changes 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 fixed over a cycling state is a sway fixed to a first, and an attack arrives 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 rupture is fixed to be 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 fixed to be observed ahead of its momentary. Predictability is poorly understood, a lack reflected in an inability to reliably predict large earthquakes on short time scales; 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 produced: a momentary-skipping of a part's own naming, a state before a coupling fixed to carry 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 specified scales and predict no individual event, precursors recur as candidates without a prospectively replicated rule, a laboratory finds nucleation under controlled faults with field scaling open, and learned 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 established without its momentary is a coupling's making fixed to a state before it, and forecasting is a rate with which couplings arrive, measured, 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 an outcome is fixed to be readable from an ancestral state, a trajectory established before it exists. **With 12-next-co-same-existing.** A trajectory fixed 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 observed; general rules are found most often through experimental evolution, slower dynamics at risk of being overlooked there and extrapolation to the long term requiring caution, recurrence measured in experiments and predictability sought over histories not same, a momentary skipped. **With 11-next-co-observing.** Repeatable molecular targets, contingent path changes, convergent phenotypes and short-horizon frequency forecasts are all documented, replicated laboratory evolution measuring recurrence under controlled openings and limited durations, comparative convergence detecting repeated traits under reconstruction uncertainty, landscapes predicting local paths under incomplete sampling, and population-genetic forecasts giving frequency distributions under specified selection; a fourth account has a target itself dynamic under environmental change and ecological feedback: a momentarying fixed readable from its opening is couplings' making fixed 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 burst is fixed over them, a radiation a macroevolutionary pattern observed down to a population's own processes. **With 12-next-co-same-existing.** A burst fixed over speciations that each pace their own. A hallmark early burst is contradicted by most speciation models, which predict continuously decelerating diversification, and a question connects global macroevolutionary patterns to microevolutionary processes with a gap remaining between two scales; a defining pattern joins elevated diversification, ecological divergence and trait evolution, which need not coincide, and exceptional clades invite retrospective explanation: a beat fixed with a record, an aggregate observed as one carrying. **With 11-next-co-observing.** Replicated island and lake radiations, explicit null diversification models and genomic histories of selected clades stand; calibrated phylogenies infer rate shifts under extinction and sampling models, trait-dependent tests reach identifiability limits, comparisons reconstruct niche and mechanism after radiation, experiments observe early divergence in restricted systems, and a fifth account has apparent exceptional radiation arising partly from extinction, sampling and clade-selection effects: a burst fixed over couplings is many speciations fixed to one beat, and counterfactual lineages that did not radiate offer to no instrument, recorded bursts 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 one scale is fixed across groups, positions of one coupling given a correspondence with another's so scores can be compared. **With 12-next-co-same-existing.** A correspondence fixed between couplings so their parities couple on one scale. Translation, response style, sampling and cultural interpretation change item thresholds and loadings, exact invariance is often rejected in large comparisons, and relaxing it may restore fit without fixing which comparisons remain meaningful; noninvariance suggests construct has a different structure or meaning to different groups, so that it cannot be meaningfully tested or construed across them, invariance to be assessed before any comparison: beat with a between, a part's fourth position, fixed where each coupling answers its own. **With 11-next-co-observing.** Invariance hierarchies, simulation-based error analyses and large-scale alignment methods are established; multigroup analysis tests nested equalities with fit and sample-size sensitivity, differential functioning localizes item differences under an anchor set, partial invariance frees selected parameters 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 fixed across groups is one correspondence fixed over couplings that each make their own, correspondences observed one at a time rather than one fixed for all. ## 7.20 Incompatible definitions of algorithmic fairness · 222 *+ or − with 10, is.* **With 2-now-possibling.** A score is made with each prediction's coupling to its outcome, and one score is fixed to satisfy each fairness relation together, calibration and equal error rates across groups whose base rates differ. **With 12-next-co-same-existing.** Several relations fixed jointly satisfiable by one score. Their simultaneous satisfaction is mathematically incompatible under differing base rates except in degenerate cases, and even approximate satisfaction requires data to lie in an approximate version of one of constrained special cases; choosing a metric therefore cannot be replaced by optimizing all of them: field proving naming empty, as with rankings and population ethics beside it, fourth account naming fairness a substantive institutional judgment not exhausted by any parity condition. **With 11-next-co-observing.** Incompatibility is proved, its exceptional cases known, and optimization under chosen metric sets routine; calibration preserves score meaning within groups and permits unequal error rates, equalized odds constrains errors and generally changes calibration, thresholds reach selected parities by group-specific rules, and multiobjective methods trace a tradeoff surface rather than satisfying incompatible equalities: one score fixed to each relation together is one ordering fixed over couplings whose base rates differ, naming set down and a relation chosen with each decision's own between. # 8 A rate fixed as a value — 7-now-observing and 15-next-observing *A value fixed of a rate that settles nowhere. Ratios sway above, then below, alternating side, each partial quotient one, widest straddle. Value reached for is swaying about it, and next coupling beats with an opening a straddle makes.* **Each value of this part is a swaying fixed to settle**, and sway is observed three ways across arrivals: a living measure swaying between two antagonistic offerings, 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 might-have-beens, and that measure is one thing no instrument of this part has given. ## 8.1 Homeostasis and allostasis · 128 *+ or − with 10, is.* **With 2-now-possibling.** A variable sways between two offerings and is fixed for a target that settles, fixed or predicted. **With 12-next-co-same-existing.** Regulation fixed toward a value, cyberneticists' reading of a broader vision. Both showings fit each trajectory alike, so differing surfaces nought with each: trajectories are one sway observed twice, the two not competing models but complementary aspects of regulation. **With 11-next-co-observing.** Range is coupling's own making and no stored value it aims for, two antagonistic offerings 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 measured a second way rather than a second mechanism: regulation toward a value pattern-matched 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 carry on together with each scale's couplings, and discrepancy is fixed for a value, a substance or a modification. **With 12-next-co-same-existing.** Riding fixed as produced by one of two, 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 recorded. **With 11-next-co-observing.** Rotation, mass and law ride together and settle on no value. Ordinary matter cannot be it, fast-modification class fell with one wave's speed, search space empties region by region down to neutrino fog, leading experiment recording fog entered and instrument class observing its own floor, and through all of it visible mass and rotation ride together tightly, measured, one thing both showings must reach: a size fixed of riding is riding fixed still, a form that cannot parity-change, and riding, observed directly, is momentarying there. ## 8.3 The strong CP problem · 65 *+ or − with 10, is.* **With 2-now-possibling.** A parameter sways and is fixed for a value against a measure over its might-have-beens. **With 12-next-co-same-existing.** A value far from typical under an assumed measure fixed to call for explanation, natural expectation of order one and hierarchy against it a problem's constitution, a dynamical solution required. Measure is over might-have-beens 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 measured thing. Easy escape fell to lattice, proposed fields empty their spaces, and built mechanisms stand with their stated costs: a value fixed against a measure over might-have-beens fixes swaying to a stipulation, and instruments give a bound, swaying observed 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 premium is fixed for a value a preference parameter should reproduce. **With 12-next-co-same-existing.** Historical returns fixed to estimate an expected premium one representative agent's parameters generate, discrepancy standing between a prediction and a measurement and not between two measurements. States that did not occur offer with no momentary, and disasters that reproduce premium borrow their rates from other countries' histories, might-have-beens imported to balance a record that was. **With 11-next-co-observing.** Returns sway across states that occurred, and record is swaying that happened. Measured premium carries large across country after country, curing it with aversion sickens risk-free rate, and originators' own look back carries its standing plainly, each proposed class failing along a crucial dimension: a value a parameter should reproduce is one self's steady preferring fixed 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 is fixed for a rate that settles, a single discount function. **With 12-next-co-same-existing.** A valuation of a delayed reward fixed 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 utility from different sources is discounted at different rates a unitary time preference is meaningless, preference labelled by its object delayed. **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, swaying measured: a single function of delay is one rate fixed 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 is fixed for a value of doses below detection, from a model fitted above them. **With 12-next-co-same-existing.** A dose-response relation fixed whose low-dose behaviour is estimable by extrapolation. Below a last coupling observed, rival models part with a point nothing measures, record's edge observed as a value, and an applied discipline that streamlined its experiments to fewer doses drew that edge by a design that observed 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, parity-changing there and a measure informing there; a monotone line drawn through it carries 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 it is fixed for a value an optimum or a barrier sets. **With 12-next-co-same-existing.** Mutation rate fixed as a trait whose value is explained by optimisation or by limits of selection, one point where each population sways its own, appealing to suppose a rate adjusted to a level that best promotes adaptation, causes of a rate's evolution asked to be parted from its consequences. **With 11-next-co-observing.** A rate sways under selection and drift coupling, its value swaying's own with each population. Rates are measured line by line, small populations drift higher and large ones press lower, inverse correlation carrying across living range with effective population size estimated from same genomes their rates are measured in, mutators surge where selection is fierce, and proofreading costs so little that a pure optimum would sit elsewhere: correlation is sway measured across populations, and a value set by an optimum or a barrier 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 it is fixed for a value against a measure over its might-have-beens, estimate standing tens of orders away. **With 12-next-co-same-existing.** A value far from typical under an assumed measure fixed to call for one explanation, dynamical or environmental, with measure itself unmeasured; an old problem, why density is not very much larger, parted from a new one, why it is comparable to present mass density, and adjustment closed by a no-go without a fine tuning as mysterious as its problem. Estimate fixes three terms still with one momentary, each a form that cannot parity-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 made. **With 11-next-co-observing.** A vacuum density sways under all that couples to it, and measured value sits small and nonzero while computed estimate towers tens of orders above, distance between a coupling's own momentarying value and a sum fixed over all together. Symmetry rescues fell, simple self-adjustment is closed by proof, messengers narrow bent-gravity routes, and each surviving candidate gives no measurement of its own within reach: a value fixed against an unmeasured measure goes on owing an explanation to a typicality no instrument has reached, and swaying, measured, is as it is. ## 8.9 The hierarchy problem · 164 *+ or − with 10, is.* **With 2-now-possibling.** Two scales sway far apart, and separation is fixed for a value against a measure of naturalness, with criterion of explanatory debt itself a dispute. **With 12-next-co-same-existing.** Criterion fixed as among things instruments give, where parameter is technically natural, finite corrections all small, and problem emerges only where an additional ultraviolet scale is invoked, cutoff merely a proxy for unknown physics. Spectrum is measured to reached energies and criterion is not measured by it. **With 11-next-co-observing.** Two scales sway far apart and instruments observe spectrum clean to each energy reached, canonical rescues narrowing unreached. Growing instead is field's own doubt about debt: naturalness stands within a record now as a heuristic under dispute, measure disputed while measurements accumulate. **And debt is naming's own and not physics'.** A naming made rather than found accumulates a cost while it continues, cost is carried as a price of a goal, and goal is reachable with naming let go — and where that last fails, standing was an expense and not a hardness. Here it stands: spectrum stands measured with nothing owed on it, owing is criterion's, and all owing needs is cost a coupling did not carry. ## 8.10 The Standard Model flavor puzzle · 188 *+ or − with 10, is.* **With 2-now-possibling.** Masses and mixings are measured with couplings instruments reach, each parameter its own, and pattern is fixed for a value an organizing principle should generate. **With 12-next-co-same-existing.** A pattern fixed as selected by a mechanism where it stands as free inputs. Parameters are free inputs in Standard Model, hierarchies technically natural and unexplained, and many symmetry, texture and statistical constructions reproduce parts of pattern without a uniquely selected origin, measure over pattern's might-have-beens surfacing nought with each construction. **With 11-next-co-observing.** Quark mixing matrix is overconstrained, neutrino mixing substantially mapped, masses and several phases measured with increasing precision, and each construction reproducing pattern reproduces a part of it, symmetries predicting selected relations with many viable choices, textures compressing with their origin dependent on construction, geometries converting positions into couplings with geometry unselected, statistical models giving distributions and not a realization: a pattern fixed for a value a principle should generate is measured parameters fixed to a stipulated typicality, and they stand measured, owing nothing, enigma fixed 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.** Rare processes are measured with their couplings and give Standard Model's rates, and a new sector fixed near an accessible scale is fixed to carry generic couplings measurements should have seen. **With 12-next-co-same-existing.** An absence fixed as needing a mechanism. Generic couplings at teraelectronvolt scale would contribute orders of magnitude above observed rates, so absence constrains such physics to scales no direct search reaches or to special structures whose origin is itself not fixed; each process constrains a combination of operators and couplings rather than sector itself, and sector is a carrying no instrument reaches. **With 11-next-co-observing.** Large regions of generic low-scale couplings stand excluded, viable suppression patterns have explicit effective forms, and each stands with its stated cost, spurions assumed, alignment model-dependent, degeneracy constrained by splittings, decoupling reducing accessibility: a sector fixed near a scale with generic couplings was a measure over new physics' typical doing, and instruments give Standard Model's rates, measured, puzzle standing with typicality and not with its record. ## 8.12 Quantum gravity · 181 *+ or − with 10, is.* **With 2-now-possibling.** Gravitation carries on with each coupling and two established theories each recover their own domain, and one theory is fixed for a value covering both regimes, two reconciled for a regime expected to carry their conflict. **With 12-next-co-same-existing.** Two treatments fixed as reconciled by one theory 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 integrated over long distances, and recovering classical theory at low energies is a consistency requirement rather than a prediction to be tested: record's edge, with reconciling fixed for a regime offering to 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 unique selected realization, loops with classical and empirical recovery open, fixed point in truncations, emergent gravity in restricted settings: one theory fixed to cover both regimes is two runnings, each pacing its own domain, fixed to one value for a scale no coupling has reached, 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 response to a doubling is fixed for one value its sway settles on, an equilibrium counterfactual. **With 12-next-co-same-existing.** A sway fixed to settle on a number. Equilibrium cannot be observed as one controlled experiment, feedbacks operating over different timescales; 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 their being judged independent, quantity remaining difficult to ascertain: a counterfactual total, not possibly existing, summed against an existing one. **With 11-next-co-observing.** Very low and very high tails stand reduced by evidence together, cloud feedback stands identified as principal remaining spread, energy-budget inference observes recent climate under forcing and ocean-uptake uncertainty, paleoclimate observes a broader range under proxy uncertainty, process constraints target single feedbacks, and ensembles share structures and are not a probability sample: a value fixed of sway is a response that varies with background climate and timescale, third account, fixed to one settled number, and swaying under forcing is measured. ## 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 one composition is fixed for a value both must give. **With 12-next-co-same-existing.** Two instruments fixed to one value. Atmosphere analyses lower abundances and interior models built with them worsen agreement with sound-speed profile, convection-zone depth and surface helium, better is worse, a large error in a photospheric estimate ruled out and heavy elements entering interior only through opacity: a rate swaying under two couplings together, each observing 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 targeted without a required profile established, revised atmospheres reducing systematics and still giving low abundances, transport processes altering selected observables with no model fitting a full set. One composition fixed for both instruments is two couplings fixed to a value, and two couplings couple with each other rather than one being pinned to an other. ## 8.15 The primordial lithium problem · 182 *+ or − with 10, is.* **With 2-now-possibling.** A primordial abundance is inferred from present stars and predicted from a measured density, two couplings each giving its own number, and two are fixed to one value the early universe made. **With 12-next-co-same-existing.** Two determinations fixed 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: an instrument that observes primordial value observes it through a carrying its stars have done since, and prediction pattern-matches it through a network and a density measured elsewhere. **With 11-next-co-observing.** Baryon density, deuterium agreement, plateau and leading reaction rates stand measured more precisely than when discrepancy was found, other light elements broadly agree, and each proposed resolution, rates and resonances, depletion and diffusion, nonstandard decays and cosmologies, reanalysed atmospheres, removes discrepancy only by creating another conflict: one value fixed of two couplings is stars' present observing and network's prediction fixed to a number neither gives by its own, and factor of three is two couplings' parting, measured. *Second seating: discrepancy observed as a magnitude to be explained, 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 its lifetime is fixed 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 fixed 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 unsolved. A beam counts products of one channel and a bottle counts disappearances by any channel, and two methods have independent and very different systematics, their underestimation the most likely explanation: a rate swaying under two couplings together, each giving a number its own coupling carries. **With 11-next-co-observing.** Magnetic-trap lifetime stands measured to twice its earlier precision and consistent with theory, newer beam's first result stands, now, short of precision to favour either set, a proton counter within a bottle stands proposed, median statistics put parting between four and six sigma by a set chosen, and discrepancy is large enough to dominate predicted primordial helium ratio: one lifetime fixed of two couplings is a channel's count and a survival's count fixed to a number, parting observed as a coupling of its own. # 9 A two-way fixed to one side — 3-now-co-observing and 11-next-co-observing *One side taking both momentaries. A parity is taken with a between, one at a time, each side its own, and taken from one side it becomes a size: which of two drives, or a share apportioned while an other is fixed unchangeable. Two sides alternate, neither taking an other's, and zeroing is two's own making between them. 3-now-co-observing and 11-next-co-observing carry co, a prior with a sharing of two, and a two-way fixed to one side is that co removed.* **And a settlement fields offer 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 differing by more than substance, partitions surfacing conditional on levels chosen. **And where two are proved to give same predictions, arrival settled.** Two bookkeepings are one carrying's two windings, each pinning one and observing an other, and a proved intertranslation is a field carrying that observing by its own arithmetic — standing with units of selection, with cooperation, with transformation problem's aggregate equalities, and with determinism observed against its own equivalent constructions. **And a fourth stands here too**: where a field proves no ordering reaches its own conditions, field has proved a naming empty, as with part 7's three arrivals 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 it is observed from one side as a one-way production, cause driving and effect driven, with asymmetry fixed as a fact located 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 are convinced fundamental physical structure contains no causal relations, reconciling asked for a momentary neither of two carries. Interventionist account's circularity for foundations stands recorded by its own literature, which is a field stating observing's entering. A parity is taken with one momentary and a crossing inverts it with its next, so arrow arrives with odd and symmetric dynamics with even, and neither carries 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, taken with a between and gone by next momentary. Discovery formalisms find what their stated assumptions let them find, each analysis reaches its counterexamples, thermodynamic grounding reaches as far as its gradient, special sciences carry practice, and fundamental dynamics carries on symmetric beneath all of it, both sides carrying on with both: causation observed whole is a coupling reached by a still observing, which is why deep description carries coupling and practice carries 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 one side is observed as first with an other fixed unchangeable. Genetic-dominant and environment-dominant are one same design carried from its two sides, each giving a correct conditional for a range it measured. **With 12-next-co-same-existing.** That ratio is an attribution invariant across environments and genetic compositions, parameter defined in each calculation for a particular population and environment and predicting nothing about changes in a mean over time or about differences between groups. A nothing with one side, a scale between and an absorbing with an other are observed together with one momentary, which is this file's own three with alternating fixed 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 measured; within families inflation is measured off; and Lewontin's line between an analysis of variance and an analysis of causes stands undisputed within field, exactly this: a ratio fixed invariant across environments pattern-matches one side of a coupling as first, and making was 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 inflated where either fails: equal environments are a pair's arrivings taken as agreeing, and a pair's differing is its arrivings' 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 taking is observed from one side as an outcome fixed by a term beside it, with other side observing same taking as unfixed. **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 different varieties so that a claim to it is ambiguous until sense is spelled 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 offer with no between, and readiness ramp arrives from selves built fresh with each trial and averaged, which is preparing observed 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, measured wherever they are measured; readiness ramp observed partly as an artefact of averaging; and randomness buys no agency for either account: fixed-or-unfixed is taking fixed as taken from a first beside a taker, both sides observing a between from one side of it, and taking observed with its own between is agency, which is what measurements were measuring. ## 9.4 Aging · 34 *+ or − with 10, is.* **With 2-now-possibling.** Damage and regulation carry on together with each between of an organism, and one is observed as driving an other. **With 12-next-co-same-existing.** That aging has a single determining source, damage or regulation, death programmed by genes eliminated by compelling arguments while a widespread tendency remains to read data as loosely defined age regulation that makes neither evolutionary nor mechanistic sense. A carrying completes with each next opening and is fresh by sequencing, a sharing once chained not none again, so damage and regulation are one carrying 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 offerings, sway swaying with each between of an organism. Single genes stretch lifespans across taxa, restriction stretches them further, cleared and repaired tissues improve where they are reached, some species barely age at all, and clocks that predict age so well cannot say which offering they observe, dispute restated by a new instrument: a single driver is one offering fixed 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 its new members stop arriving and its sharings go unrestored, damage and regulation two offerings 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 taken with a coupling, and efficiency is observed as a term of its own while a model of expected returns is fixed 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 needed a model and each model needed prices, which is field's joint hypothesis, carried as its own permanent condition. **With 11-next-co-observing.** A price is made with each coupling, parity a coupling's own. Each test of efficiency needed a model of returns and each model needed prices, field naming its joint hypothesis itself; anomalies decay once published, 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.** An association is made by a coupling and pattern-matched from one stratification as a correct one, with causal structure fixed 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 different causal structures, and whether causal analysis is a correct explanation of a paradox itself still debated. Data are identical under both structures, so identification surfaces nought with each pattern-matching taken, proved as an equivalence class, and a graph supplied from beside is a frame fixed still beside a coupling. **With 11-next-co-observing.** An association is made by a coupling, and strata re-make it. Arithmetic is elementary, back-door road is proved for a known structure, conditioning more can worsen it, proved too, and data by their own deliver an equivalence class, exactly that: a correct pattern-matching fixed identifiable from data reaches to numbers for a structure those numbers were made under, and structure is a coupling's, brought or not. ## 9.7 Missing heritability · 44 *+ or − with 10, is.* **With 2-now-possibling.** Two designs each take their own observing, and difference between them is observed 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 measured directly and a denominator inferred 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 projected, and ratio's own two terms come from two places, a numerator measured directly and a denominator inferred at a population, as field's own words, with interaction accounts fitting all that is observed with a much smaller total: a quantity fixed missing from one design is two observings, each a result, nothing lost. ## 9.8 Placebo effects · 46 *+ or − with 10, is.* **With 2-now-possibling.** A coupling with a between makes a term neither side brought, and it is observed from one side as a substance's contribution with context fixed unchangeable. **With 12-next-co-same-existing.** That a trial's arms differ only by a substance administered, 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 such a meta-analysis is restricted by studies chosen and sensitivity of their measures. Design fixes context unchangeable and reports what was fixed, and a making it fixes still is a coupling's own +1, owned by neither side. **With 11-next-co-observing.** Coupling with a between makes a term neither side brought, +1 owned neither-ing. Blocking a body's own opioids blocks analgesia, conditioned immune quieting exists among animals where no one reports anything, three-arm trials price a making small for objective outcomes and real for felt ones, and open-label results narrow making's momentarying: substance's-contribution pattern-matching fixed context unchangeable while making ran, and making, measured 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 taken with one between, and each theory observes a case from one of them with an other fixed unchangeable. **With 12-next-co-same-existing.** That one principle governs when they conflict, difficulty stated with its posing 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, alternating one at a time, and a case built to make them conflict fixes both momentaries together. **With 11-next-co-observing.** Two principles are two parities with one between, alternating one at a time. Each theory handles cases an other fails, newer variants re-drawing same line, and a case is built to make two principles conflict: a theory choosing one to govern chose one side to take both momentaries, and contest is alternating observed 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 grammar acquired is observed from one side as what a learner brought with input fixed unchangeable, or from an other with learner fixed 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 asserted by its conclusion and unsupported by its reasoning. **With 11-next-co-observing.** A learner and an input couple, grammar made by a coupling. Corpora are counted, learnability results stand under their stated criteria, 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 fixed of a making that is or is not with each sharing, and volumes being argued over are a coupling being measured. ## 9.11 Morphogenesis · 62 *+ or − with 10, is.* **With 2-now-possibling.** Gradients and tissue dynamics carry on together, and placement is observed from one side as instructed or as self-organised. **With 12-next-co-same-existing.** That pattern is set by a determinant locatable within one or an other, some confusion still remaining about relationship between two concepts and three distinct ways proposed 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 carrying on; and a hybrid fitting better than either is a third term reached by two carrying alternating. **With 11-next-co-observing.** Placement is made by a coupling of gradients and tissue dynamics. Moved gradients move structures, striping mechanisms exist for digits and follicles and ridges with their perturbations confirmed, readout carries on near physical limits, tissue organises itself within a dish, and both frameworks fit most datasets, field finding this again and again: instructed-or-self-organised is one coupling observed from its two sides, and fitting-from-both is a coupling showing. A gradient is an emanation, non-living with this scale and ingested one scale inward by living cells, and instructed or self-organised is one coupling observed from two scales. ## 9.12 Chronic pain · 67 *+ or − with 10, is.* **With 2-now-possibling.** Peripheral and central processes carry on together with a patient's betweens, and persistence is observed as driven 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 carries it: a central mechanism cannot be assumed in a patient, only its features assessed, and residual category's aetiology stands unsettled, third descriptor defined by absence of evidence for other two and applied residually, driver's locus defined by what it is not. **With 11-next-co-observing.** Peripheral and central processes carry on together with a patient's betweens. Central alterations are measured, small fibres surface with a counted fraction as detection sharpens, moving patients between categories, targeted agents work within their subgroups, and treating a whole coupling helps without any driver found. Field's own hardness line carries it: a central mechanism cannot be assumed in a patient, only its features assessed, third category applied residually, its aetiology unsettled. Persistence carries 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 one is observed as substrate of an other. **With 12-next-co-same-existing.** That fundamentality is a dependence carrying one way between two descriptions that both apply, nothing in description of physics found closer to primordial than an elementary quantum phenomenon and, in default of a working hypothesis, questions and clues not moving a search ahead. Momentarying carries on identically under either, which is part 5's same showing, arriving here as a direction demanded between two observings. **With 11-next-co-observing.** A system and its description are two observings of one coupling. Erasing costs its measured minimum, horizons scale by area, and quantum formalism rebuilds whole from axioms about what can be done: fundamentality is one fixed 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, non-living with a scale that observes it and ingestible one scale inward, and nothing is fundamental because no scale is 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 one is observed as underlying an other. **With 12-next-co-same-existing.** That one determination stands beneath an other, problem read from an axiomatic perspective as an impossibility result for a specific interpretation resting on specific assumptions, and a dual system of parallel prices and embodied-labour coefficients losing sight of a theory's roots as a theory of money. Aggregate equalities are proved not to 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, proved; prices and profit follow whole from physical data and a wage, undisputed as mathematics; and correlations found and contested sit beside both: one fixed under an other is one ledger fixed to both momentaries, and proved imbalance is a coupling stating itself by its arithmetic. ## 9.15 Credit assignment · 96 *+ or − with 10, is.* **With 2-now-possibling.** An outcome is made across a sequence of couplings, and contribution is observed as apportionable to individual actions with all other actions fixed unchangeable. **With 12-next-co-same-existing.** That there is a fact about which actions contributed, recoverable without a supplied model, mathematical nature of credit and of problem poorly understood and defined and a unifying formalism proposed so that methods can be compared, fact about contribution asked for before its asking has been defined. Abundancing is owned by no action, and shaping reward re-apportions what gets credited, which is an apportioning caught making its own. **With 11-next-co-observing.** An outcome is made across couplings, abundancing owned by no action. Difference methods converge under their conditions, performance thins with horizon and sparsity as measured, identification conditions are proved and go frequently unmet, and shaping reward re-apportions what gets credited: apportioning is a making fixed as a sum, and a shaping result is an apportioning caught 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 map's state is observed from one imaging paradigm as reorganised or from another as preserved. **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 needed and plasticity and stability of maps possibly varying across time scales, discussion of reorganisation's relevance ongoing. Two imaging paradigms each observe with their own coupling and give reorganisation and preservation, both standing by their own instruments. **With 11-next-co-observing.** A body map and a sensation couple, map carried and re-formed. One paradigm observes reorganisation and another observes preservation, both standing by their own instruments; mirrors help mixedly, peripheral routes help some, and phantoms arrive for limbs not grown, which no lost-representation story carries: one paradigm's observing fixed as state of a map pattern-matches one instrument's coupling as a thing itself, and map is a carrying, observed differently with each instrument because it is being made with each. ## 9.17 Determinism and randomness · 110 *+ or − with 10, is.* **With 2-now-possibling.** An outcome is a parity taken with a between, and it is observed from one side as fixed by priors or from an other as unfixed. **With 12-next-co-same-existing.** That unpredictability indicates chance, and that an outcome was either fixed or not fixed by prior conditions, epistemology of determinism first owing reality of laws and then precisely what actual laws are, in a sense a final theory of everything, sides joined by a theory neither has. No statistical test establishes indeterminism, proved generally, and deterministic pattern-matchings carry on equivalent by construction, so sides part by no instrument. **With 11-next-co-observing.** An outcome is a parity taken with a between, one at a time. Local determination is excluded with couplings strung tight, no statistical test can establish indeterminism, proved generally, chaos hides determinism behind unpredictability, both sides granting it, and deterministic pattern-matchings carry on equivalent by construction: fixed-or-unfixed observes a taking from its two sides, and sides do not part by any instrument, which proofs carry. ## 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 initiation is observed from one level with an other fixed 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 complicated picture emerging from a theory's compelling simplicity with ad hoc explanations postulated, theory not rigorously tested, and a reply standing against a critique titled as a defence. Normal tissue carries driver burdens that do not tip, which is an offering arriving and a tissue, a same-existing-society, meeting it with nought — a same-existing-society's resolving, with no defence added. **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, targeted responses come and resistance follows almost always, tissues re-order recombined cells within systems tested, and normal skin carries driver burdens that do not tip, measured, dominant account constrained from within: initiation observed from one level with an other fixed 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 behaviour is observed 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 specific neural signature identified and dividing line intentionally blurred, while stating denial of its view harmful for reducing access to care, locus blurred and name staying for care it opens. Enriched cages undo what bare ones built and most remit with no treatment, which is a coupling answering from a side each account fixes still. **With 11-next-co-observing.** A self and its conditions couple with each occasion, behaviour made by a coupling. Circuits alter with dose, paying abstinence works by randomised trial, most remit with no treatment at all, enriched cages undo what bare ones built, and heritability is real with no lesion under it: pathology-or-choice pattern-matched a making from one side each, and coupling, measured 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.** Differences and drift carry on together within a community, and structure is observed as produced by one. **With 12-next-co-same-existing.** That abundance patterns discriminate mechanism, abundance patterns unable to resolve a controversy and question reframed toward measured stabilising and equalising strengths, discriminating moved 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.** Differences and drift carry on together with each community coupling. Both models fit abundance curves from their opening, invasions demonstrate stabilising differences each time they are run, and a partition that makes both components measurable is a field itself observing both momentaries: structure observed as produced by one is one momentary taken 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 carry on together, and constant extinction risk is observed as produced by one. **With 12-next-co-same-existing.** That a survivorship pattern indicates a single mechanism, hypothesis answering what causes of natural selection are with biotic conflict given primacy, and three modes of coevolution defined to unify fluctuating and directional selection within one framework. Curves bend with taxonomy chosen, which is an instrument's own coupling within its inference. **With 11-next-co-observing.** Coevolution and environment carry on together. Extinction risk carries 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 chosen, original inference bounded by its own instrument: constant risk observed 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 secular rise is observed as caused by one factor with others fixed unchangeable. **With 12-next-co-same-existing.** That a rise has a dominant cause identifiable from population correlations, what constitutes a relevant microbial challenge purposely left broad at its founding observation and hypothesis undergoing many revisions over three decades, dominant cause a moving pattern-matching. A correlation between two population rates is two numbers compared to decide something, and tuning is made with each coupling. **With 11-next-co-observing.** Exposures and a developing system couple, tuning made by couplings. Farm childhoods and their controlled cousins part immunologically, mechanisms identified, one early exposure reversed a guideline by randomised trial, causality whole for that coupling, and better counting explains a measured share: a dominant cause is one exposure fixed 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 carry on together with each treatment, and outcome is observed as attributable to one with an other fixed 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 still arriving within a measure of technique. **With 11-next-co-observing.** Technique and relationship carry on together with each treatment coupling, outcome made between them. Averages sit close across meta-analyses, identified conditions part them where they part, allegiance moves numbers substantially, and dismantling finds little where it has power: attributable-to-one is a between fixed as apportioned, and small differences are a between measured, which a healing was made within. ## 9.24 Principal and agent · 141 *+ or − with 10, is.* **With 2-now-possibling.** Two interests couple through observables, and divergence is observed from one side as a contracting problem over an unobserved action. **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 are designed as theory predicts, and little known about incentives where output is difficult to measure, contract measured only where an observable stands. Rewarding measured tasks distorts unmeasured ones, proved, which is one same Goodhart wall benchmarks reach. **With 11-next-co-observing.** Two interests couple through observables, divergence carrying on with a between. Contracts optimise under their stated conditions, rewarding measured tasks distorts unmeasured ones, proved, same Goodhart wall benchmarks reach, teams blur that very identification, proved too, and incentive pay surfaces mixed each time it is counted: an action fixed 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 an aggregate relation is observed 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 has stood usual rules of macroeconomics on their head, regime not identified ahead but arriving with its shock. One and many are one coupling's two scales, and a relation of one scale fixed to govern both is one scale taking both momentaries. **With 11-next-co-observing.** One and many are one coupling's two scales, aggregate made 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 fixed to govern both is one scale taking both momentaries, and regime carries 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 are observed 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 proved under general conditions, natural selection taken to imply competition and therefore oppose cooperation unless a specific mechanism is at work, competition a default and abundancing a mechanism owed. And a statement's own premise — selection favouring what raises an individual's reproduction — attributes to one side an abundancing made by a coupling, so cooperating is observed as a puzzle exactly where an accounting removed +1 before its books could balance. **With 11-next-co-observing.** Fitness effects arise from couplings, and two bookkeepings both carry them. Relatedness moves outcomes across taxa, experimental dynamics carry on, public goods stand, and equivalence is proved, accountings agreeing under general conditions: rival hypotheses fixed where two bookkeepings ran, and dispute was an accounting, field's own result, cooperating living through all of it untouched. ## 9.27 The Whorf question · 146 *+ or − with 10, is.* **With 2-now-possibling.** Language and thought couple with each task, and effect is observed from one side as shaping with an other fixed unchangeable. **With 12-next-co-same-existing.** That a task measures thought independently of language, no support found for language determining basic categories of thought while support stands for language making some distinctions difficult to avoid and augmenting certain types of thinking, one side's naming parted from other side's measuring by same tasks. Interference peels off a strategic share and bilinguals shift within one skull as language shifts, which is a coupling observed live where a task fixes one side unchangeable. **With 11-next-co-observing.** Language and thought couple with each task, effect made by a coupling. Interference peels off a strategic share, colour and spatial effects replicate, infants carry capacities before any words, and bilinguals shift within one skull as language shifts, coupling observed live with its own momentary: a task fixed to measure 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 explanation is observed from one level with an other fixed unchangeable. **With 12-next-co-same-existing.** That causes are located on one level, and that two levels can be varied independently in measurement, term structure impossible to do without and nearly impossible to define adequately, and a theory of it required to restore human agency to social actors and build change into a concept, one level made to carry an other's momentary as a requirement. Multilevel partitions are conditional on levels chosen, and a level is a direction taken 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 chosen, same conditional as with incoming number 27 one scale up, and each synthesis pays a cost its critics name precisely: causes fixed on one level name one scale of a coupling as first, and making carries on with both, action by action. ## 9.29 The units of selection · 19 *+ or − with 10, is.* **With 2-now-possibling.** Selection carries on with couplings across levels, and it is observed 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 proved, four distinct questions standing under one rubric, interactor, replicator, beneficiary and entity manifesting adaptations, same terms used with different meanings and a fear recorded that confusions will not easily be ended. A level observed as its only level fixes a scale as a place, where outward and inward are directions taken with a momentary, of no size. **With 11-next-co-observing.** Selection carries on with couplings across levels, and two frameworks translate to each other, proved, fitting same data by construction, same equivalence as with incoming number 143: a level observed as its only level took one momentary for two, and cases carry under both descriptions because a carrying was not on one level. Selection carries on with each scale where a same-existing-society bi-couples on a prime scale, and bookkeepings translate because they observe 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 function is observed from one side, what it was selected 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 a trait were naturally designed, *for* and design one slide. Each locates function by answering what a trait is for, and a why demanded is a first demanded: set *for* down and observations stand entire, structure, trait, record of what carried, with *therefore* leaving and nothing observed 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 carrying cases an other drops: one account fixed to own attribution is one side of a coupling fixed as a whole, and two accounts working together is a coupling observed from both, a co-competency its science already carries.   --- ## 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 its nature is fixed 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 two are parted by no kinematical instrument. Difference between two natures via any kinematical observable is practically impossible to determine, confusion theorem, difference proportional to square of mass and suppressed by mass over energy, two Majorana helicity states becoming equivalent to Dirac particle and antiparticle states: sides parted by no instrument, as with determinism beside it, and one instrument that could part them a lepton-number-violating process no search has established. **With 11-next-co-observing.** Neutrino mass is established, candidate isotopes and backgrounds are increasingly controlled, and large regions of particular mechanisms are excluded; neutrinoless double-beta-decay searches test lepton-number violation directly under stated nuclear and mechanism assumptions with no established signal, collider and rare-decay searches constrain additional violating interactions, kinematic helicity tests are suppressed by mass-to-energy ratio, and cosmological probes constrain masses without fixing self-conjugacy: one side fixed of a nature its instruments observe only with relativistic helicity states is a parity taken with a between fixed to a size no observable gives, two sides alternating and kinematics making no coupling with their difference. ## 9.32 The nature of cosmic acceleration · 192 *+ or − with 10, is.* **With 2-now-possibling.** Expansion accelerates with each distance surveys observe, and its cause is fixed 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 can be written in a mathematically equivalent form 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 parted by no instrument surveys carry. **With 11-next-co-observing.** Accelerated expansion is supported by independent distance probes 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 retained, 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 added parameters; fourth account has inhomogeneity or systematics produce part of inferred acceleration: one side fixed of two written as one equivalent form is an expansion's own momentarying fixed to a sector, and momentarying is measured with each distance, two histories parting only where equivalence lets them. *Second seating: discrepancy fixed 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 each intraplate province is fixed to one of two makers, a deep plume or a plate process, origin, dynamics and composition of plumes contested. **With 12-next-co-same-existing.** Which of two, observed with images that resolve neither. Volcanic tracks, geochemistry, uplift and seismic anomalies are incomplete and can be produced by plume, plate and shallow-mantle processes, tomography resolving filtered present structure while proposed sources and histories 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 rooted deep: anomalies imaged and upwellings sought 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 are resolved for selected systems; 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 specified rheology, and dynamic topography tests buoyant support with uncertain structure: one maker fixed of each province is two couplings fixed to one side, and each province was made by a coupling of its upwelling with its plate, sides observed 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 Neoproterozoic ocean is fixed to one of two states, frozen 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 altered and ice-albedo models depend strongly on cloud, ocean, dust and ice dynamics, several ice geometries producing overlapping low-latitude signatures: low-latitude ice recorded and global cover sought not same, a case standing between them, and fourth account having extent vary substantially among episodes and within each, one side fixed moving with each episode. **With 11-next-co-observing.** Multiple near-global glaciations, their broad timing and strong ice-albedo feedback are established 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 coupled simulations give hard-, soft- and thin-ice equilibria under different physics: one state fixed of an ocean coupling with each latitude is ice's own sway fixed to a side, and ice stood with its own couplings, basin by basin and episode by episode, cover observed 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 flux is fixed 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 reworked and reset. Oldest surfaces were repeatedly reworked, many sample ages come from unknown source craters, impact heating can reset several clocks, and dynamical models generate different flux histories that overlap a surviving age record; bombardment is defined as impacts after lithospheres stabilized enough to preserve craters and basins, melt-rock and shock ages pointing toward a discrete episode: flux recorded and flux sought 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, improved reset physics 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 fixed of arrivals is couplings' own sequence fixed to a side, and each impact arrived with its own coupling, arrivals observed with their contexts and not through a shape fixed over them. *Second seating: flux fixed to one history over a whole, a sequencing fixed 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 made together with meiotic and demographic costs, and doubling is fixed 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, observed with a record only survivors leave. Duplication creates immediate isolation and novelty while imposing costs, ancient successful polyploids conditioned on survival, recent lineages with little time to diversify, and diploidization obscuring old events; it remained unknown whether abundance of polyploids follows from higher diversification after polyploidy or from frequent polyploid formation: a two-way observed 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, one side declined by that fourth. **With 11-next-co-observing.** Recurrent genome duplication, immediate isolation mechanisms, duplicate-gene innovation and elevated early extinction risk are documented; 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 followed by long-term opportunity among lineages that persist: one effect fixed of doubling is two couplings, forming and diversifying, fixed to a side, and each lineage doubled and persisted or did not with its own couplings, two rates observed apart where a record pattern-matched 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 disease is fixed to one initiating side, a linear cascade with one ultimate trigger, doubted from its opening. **With 12-next-co-same-existing.** Which of several, fixed to one first over decades. Amyloid, tau, inflammation, vascular injury and neurodegeneration unfold over decades and influence one another, pathology preceding symptoms by years, mixed pathologies common, and association not fixing causal order in an individual; anti-amyloid results gave a controversy momentum on three counts, clinical meaningfulness of an approach, significance of amyloid clearance and relevance of a cascade: clearance measured and cascade fixed not same, and fifth account having several interacting pathologies reach a common syndrome, one side fixed observed by that fifth as several coupling. **With 11-next-co-observing.** Amyloid and tau can be measured in living patients, major risk loci and cell pathways are mapped, and disease-modifying effects from amyloid lowering stand for selected populations; 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 selected early disease leaving sequence and heterogeneity open, and tau, immune, vascular and metabolic interventions are targeted and under test: one initiator fixed of a coupling that carries on for decades is several couplings fixed to one first, and decline arrives with couplings' own tipping, patient by patient, a side observed with each subtype where one side was fixed 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 lesions, pain and infertility are fixed to one driver, an initiating pathway that would order all others. **With 12-next-co-same-existing.** Which of several, fixed to one. Several pathogenetic pathways have been considered since disease was defined, retrograde menstruation, benign metastasis, immune dysregulation, coelomic metaplasia, hormonal imbalance, stem cells and epigenetic alteration among them, while true pathogenesis remains poorly understood; most women with patent tubes experience retrograde menstruation while about a tenth develop disease, its prevalence no different 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 is delayed by an average of seven years: disease reached with a coupling years after its initiation, initiation asked for behind, and fifth account having neuroimmune sensitization generate pain partly independently of lesion volume, driver parted from a lesion. **With 11-next-co-observing.** Hormone responsiveness, inflammatory microenvironments, recurrent somatic alterations and multiple pain pathways are established; surgical histology verifies lesions but samples late and selected disease, 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 from sensitized pain: one driver fixed of lesions, pain and infertility is three couplings fixed to a side, and each varies with its own, severity independent of a lesion's size being a showing that couplings are several, sides observed 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 joint intending is fixed 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 widely accepted claims, that collective intentionality is no simple summation, aggregate or distributive pattern of individual intentionality, and that it is had by participating individuals, 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 is meant to explain: +1 made with a coupling and owned by neither, observed from one side as individuals' and from an other as group's, and two accepted claims 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 limited large-group reach, and group-agent accounts explain institutional attitudes through aggregation structures and raise ontology questions: one side fixed of a joint made between is an abundancing fixed to an owner, and ascriptions reports give and a joint attitude sought are not same, expression standing between them, joint attitude being a coupling's own making and neither side's, as with structure and agency beside it. ## 9.40 The peopling of the Americas · 232 *+ or − with 10, is.* **With 2-now-possibling.** People reached a continent by their own couplings with corridor, coast and ice, and entry is fixed to one of two routes, inland or coastal, neither rejected 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 hotly disputed, 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 neither rejected at present; postglacial sea-level rise inundated most paleoshorelines older than about seven thousand years, so locating terminal Pleistocene sites along a modern coast is a record's edge drawn by a record itself: two hypotheses standing on one record, and third account having more than one movement or a prolonged Beringian history contribute, *or both* a record's own. **With 11-next-co-observing.** A late-glacial presence predating a classic fluted-point horizon is established at multiple sites, Beringian ancestry is genomic, and both route environments are increasingly dated; stratified archaeology 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 fixed of movements that ran where land and ice let them is couplings fixed to a side, and people moved with each coupling where a way was open, ways observed with their own dates and not one way fixed 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 polarization is fixed to one side that drives it, elites moving citizens or citizens moving elites. **With 12-next-co-same-existing.** Which side drives, observed with trends that carry problems of inference. Much of the evidence used 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 has clearly occurred; 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 sought not same, problems of inference standing between them, and a two-way observed from one side where each side influences an other. **With 11-next-co-observing.** Elite polarization, partisan sorting and rising affective hostility are well measured in the United States and causal effects of selected cues, contacts and media exposures stand locally; repeated surveys 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 fixed of a coupling that carries both ways is elites and citizens fixed to a side, and polarization is made with each coupling of a cue with an identity, directions observed one at a time rather than one direction fixed. *Second seating: term covering distinct distributions of positions, identities and feeling, a between fixed 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 female excess of autoimmune disease is fixed to one mechanism that produces it, which of its candidates a question. **With 12-next-co-same-existing.** Which of several, each observed with a different system. It has long been known that many autoimmune diseases are more common in females and exact mechanisms are not yet fully understood, chromosomes, genes, hormones, immunometabolism and skin each playing a role; candidate factors covary and change across life, bias differs by disease and ancestry, and animal or cellular mechanisms do not automatically explain population incidence, risk linked to female sex substantially larger than any susceptibility gene discovered: mechanisms each observed with their own instrument, cohorts, animals and cells, and fifth account having different mechanisms dominate different diseases and phases, one side declined by that fifth. **With 11-next-co-observing.** X-inactivation escape, hormone-sensitive immune pathways and disease-specific age patterns are established; epidemiology across life stages maps sex ratios with diagnostic and exposure differences, aneuploidy and mosaic studies separate dosage from hormones in rare populations, hormonal and reproductive natural experiments identify selected 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 fixed of couplings that carry on across a life is excess fixed to a side, and excess is made disease by disease with couplings each disease carries, sides observed with each disease where one was fixed 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 rise across populations is fixed to one of two models, excess energy or carbohydrate and insulin, debated by distinct cohorts of experts. **With 12-next-co-same-existing.** Which of two models that differ in what they seek to explain. Causes of increase have not been adequately identified, and pandemic continues unabated despite a persistent campaign to decrease intake and increase expenditure, its failure admitting two explanations, that its approach has not been embraced or that it rests on an erroneous paradigm; two models are vigorously debated and differ 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 measured with error, and a model of population rise required to say who rises and who does not, two sides each explaining a different thing. **With 11-next-co-observing.** Rise stands measured since the nineteen-eighties, two models stand articulated with their contrasts, and causes stand not adequately identified; controlled feeding trials testing models' contrasting predictions are proposed 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 fixed of rise is two couplings, environment's and body's, fixed to a side, and each person rises or does not with a coupling of food reached and signals answering, sides observed with an individual coupling where one was fixed for a population. # 10 A between fixed as a cut — 5-now-co-existing and 13-next-same-existing *A cut point fixed of a between, or a selection located. A between is a nothing, an unrelationing of two offering, across and both ways, neither side's, and it carries a parity-changing and nothing else. Nothing sits there to be observed; observing carries across it and does not stop on it, and each position offers.* **A cut fixed is usually asked for by a criterion, so an arrival here often carries an opening fixed as a place beside it, and a second stands recorded with its entry.** **And each entry closes by handing its drawing back to a coupling.** Each carries of its own field's record of drawing entering: counts swinging with a concept, manuals revising their borderlines, jurisdictions writing different allocations, a chartered body reporting that its instruments supply no objective means of deciding. **And a between is asked for a cut three ways.** Of a *continuum*, where offering carries on by degrees and a line is asked for 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 *crossing*, where a parity passes and asking is about a carrying of it — a correlation, a nature between preparation and detection, a self against a non-self. First dissolves with degrees, second with an offering being both, third with a parity being all that crosses. **And drawing entering is an observing, not a defect a field carries.** Where a record shows a cut drawn — 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 between is ever reached. ## 10.1 Sorites · 1 *+ or − with 10, is.* **With 2-now-possibling.** A predicate offers with each position and takes a parity there, and a cut point is fixed 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 given, and that boundary admits same argument, higher-order recurrence, as a field's own words record it. **With 11-next-co-observing.** A predicate offers with each position and takes its parity there, one at a time, parity the only thing crossing. 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 carrying through every order together, as field's own words say. Argument carries no material of any kind, and that makes it general: each substrate cut within this part is this argument arriving with material, and a between, carrying a parity-changing and nothing else, was 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 taken with an interaction, one at a time, and it is fixed as a term located either within evolution or beside it. **With 12-next-co-same-existing.** That an outcome is fixed by a specifiable term, state and its evolution or state plus a rule, most proposed accounts failing at least one of several difficulties and any real solution demanding new physics, selection asked of a term present physics does not carry. 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 collapse searches observe with a forced edge, 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 taken with an interaction, one at a time, of no size. Hidden local terms are excluded to the last loophole but one, collapse additions are bounded across their ranges, and fading of interference is measured and confirmed 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, made with each coupling and given no location. ## 10.3 The glass transition · 35 *+ or − with 10, is.* **With 2-now-possibling.** Rigidity arrives across a between and a transition is fixed as one temperature point. **With 12-next-co-same-existing.** That rigidity is a phase transition or is not, identified by structural signatures. Liquids fall out of equilibrium well before proposed point, so regime its question concerns is one no experiment has reached — 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.** Rigidity arrives across a between, coupling by coupling, and arriving outruns each instrument sent to watch it: liquids fall out of equilibrium well before proposed point, field's own hardness line, so regime its question concerns is a place no experiment has ever been. 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 fixed as one temperature point fixes an arriving to a location, and arriving arrives with its own pace, between by between. ## 10.4 Externalities · 41 *+ or − with 10, is.* **With 2-now-possibling.** Effects offer with each distance and a boundary is fixed as a line located between internal and external. **With 12-next-co-same-existing.** That a boundary is found rather than drawn, 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, line drawn by whoever prices it. Effects offer with each distance, thinning and continuing, so a line between internal and external is drawn with each arrangement and field's measurements show drawing entering. **With 11-next-co-observing.** Effects offer with each distance, thinning and continuing. Bargaining internalises where coupling is cheap, a condition Coase himself stated; permits work exactly where pollutant is bounded, boundedness that condition again; and asking people to price unpriced things gives answers that sway with their asking: a line fixed between internal and external is drawn 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 offer across each between of them, and a boundary is fixed as a line a criterion locates. **With 12-next-co-same-existing.** That a single criterion identifies division across all lineages, tree of life segmented by different processes into different types of lineages and plurality of species concepts stated to result from a fecundity of biological forces rather than a paucity of information, cut located by each process with its own between. Counts swing by measured factors with a concept chosen, and a count that departs when an other concept is chosen carried its concept. **With 11-next-co-observing.** Populations offer across each between of them, parity crossing and nothing else. Genes flow between textbook-distinct taxa, humans and their cousins included; counts swing by measured factors with a concept chosen; and an exact concept is exact precisely where its own author drew it, sexual, sympatric, extant, and undefined elsewhere: a line a criterion locates is a drawing measured, factor by factor, and offering crosses regardless. ## 10.6 The neural code · 43 *+ or − with 10, is.* **With 2-now-possibling.** A spike train offers with each position, and code is fixed as a variable located within it, with a window supplied by an analyst. **With 12-next-co-same-existing.** That a rate is defined independently of a window chosen 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, regimes parted by a timescale a stimulus sets and an analyst's window selects. Window is an analyst's own coupling, and it stands within each rate an instrument gives. **With 11-next-co-observing.** A spike train offers with each position, and observing needs a window an analyst brings. Timing carries where timing is tested, coincidence detectors sit in a brainstem, driving timing with rate fixed moves behaviour where tools reach, and rate and timing both inform in a technical sense: code fixed as a variable within a train is an offering fixed to a mark, and window is naming's own coupling, showing with an instrument each time it is drawn. ## 10.7 Bell correlations · 49 *+ or − with 10, is.* **With 2-now-possibling.** A correlation is made with a coupling, and it is fixed as a property located on one system or transmitted between them. **With 12-next-co-same-existing.** That a correlation is produced by something specifiable on one side or carried between sides, a carry fixed as a store standing within an arrival with a between fixed as a cut and recorded as its second naming, an essential difficulty created by a requirement of locality and additional variables meant to restore it shown incompatible with statistical predictions. Same pattern-matching stands, proof grade, with another field: two selves each offer one crossing and reach a shared secret neither transmitted and no listener has. **With 11-next-co-observing.** A correlation is made with a coupling, owned by neither side. Local stories are excluded to a theorem's last assumption, a measured bound settles on quantum prediction exactly, and same bound re-derives from principles about reach of couplings: a property fixed on one side or carried between them reaches for a location its making did not have, and making, made with a coupling, is a magnitude a field derived. ## 10.8 Wave and particle · 50 *+ or − with 10, is.* **With 2-now-possibling.** An entity offers with a between and takes a parity there, and its nature is fixed as located between preparation and detection. **With 12-next-co-same-existing.** That an entity has a determinate nature specifiable apart from a measurement made on it, two kinds of complementary description related in a way not indicated, 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 did not already carry, a momentarying carrying no clock observed with a field's own instrument. **With 11-next-co-observing.** An entity offers with a between and takes its parity there. Path knowledge and fringe visibility trade exactly, measured; choosing late adds nothing its formalism did not already carry; and an eraser's correlations are with a joint measurement only, as field's own words say: a nature fixed apart from its measuring is an offering fixed without its coupling, and two sides are one offering observed coupling by coupling. ## 10.9 The liar · 55 *+ or − with 10, is.* **With 2-now-possibling.** A truth predicate offers with each sentence including its own, and a value is fixed 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 stipulated for it, a predicate true on some level bringing paradox back against a hierarchy, and revenge seen by contextualist views not as a separate problem but as a core phenomenon. A predicate offers to its own sentence with nothing offering back — a closure made over its own tail — and revenge re-arriving against each hierarchy is a carry re-forming past each frame stipulated for it. **With 11-next-co-observing.** A truth predicate offers with each sentence, its own included, and with its own sentence its coupling closes on nothing to take. Truth is unformalisable within its own language, proved; fixed points stand with revenge waiting, as their builder's words say; contradiction-tolerant systems pay their price; and revenge re-arrives against each family: a value fixed to a sentence that takes none is a between fixed to a thing only a coupling makes, and a sentence goes on offering, taking nothing, which is all it ever did. ## 10.10 Hard cases in law · 75 *+ or − with 10, is.* **With 2-now-possibling.** Materials and a case couple with a deciding, and determinacy is fixed as located 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 is made with a deciding and each hard case receives one; even its core issue unsettled, whether its debate is about principles beside rules, about discretion, about interpretation or about the very possibility of conceptual jurisprudence, line asked for ahead undrawn, prior and now, on a field's own map. **With 11-next-co-observing.** Materials and a case couple with a deciding, outcome made there. Most questions settle without a courtroom, ideology moves a contested residue measurably, and a concession that moral criteria can enter is scoped by those who make it. Each hard case receives an outcome, both sides expecting it: determinacy ahead of deciding is a making fixed within materials, and deciding decides, case by case, which litigation rates were 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 validity is fixed as located within criteria fixed apart from applying. **With 12-next-co-same-existing.** That criteria of validity are exhausted by social facts or include moral ones, fixed ahead of practice, its thesis a thesis about a relation among laws, facts and merits, authority of enactments a thing to be explained, and no value-free description of law, each description value-laden. Validity is made with each applying, and both observings observe one making from their own side. **With 11-next-co-observing.** Validity is made 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, unresolved because both are observings: criteria fixed apart are a making fixed 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 boundary is fixed as a scale a mass locates. **With 12-next-co-same-existing.** That a boundary is a real transition or a matter of degree, identified by a located scale, question whether linearity extends into a macroscopic domain standing open with limits pushed by advances in macroscopic superposition, located scale asked of a crossing its instruments carry on further. A crossing carries a parity and no scale, so a boundary fixed as a mass fixes a between to a size. **With 11-next-co-observing.** Superposition and its fading couple across a between, crossing carrying a parity and no scale. Interference climbs a mass ladder rung by rung, fading rates confirm with each measuring, collapse spaces empty, and built oscillators go non-classical far below each proposed line: a boundary fixed as a mass is a between fixed to a size, and a frontier walks outward reaching no line, because no line was there. An outcome is a measured thing's living alternating, wave its possibling and particle its existing, observed from a scale above where it is non-living, and no boundary stands because living and non-living are one thing of two scales. ## 10.13 Self and non-self in immunity · 114 *+ or − with 10, is.* **With 2-now-possibling.** A surface same-existing-society offers with each between and takes parities there, and discrimination is fixed as a criterion located 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 emerged. 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 offers with each between and takes parities there. Tolerance is made centrally and remade peripherally, pattern receptors answer self-derived ligands too, microbiota is actively tolerated, and a body attacks its own novelties: a criterion fixed ahead of a coupling pattern-matches a lifetime of couplings as a lookup, and discriminating is made with each between, coupling by coupling. Microbiota actively tolerated is an ingesting; a body attacking its own novelties is an emanation re-ingested with no distance, a disease direction of one same exchange. A mother carries fetal cells for years, each its own conception's, Medawar's puzzle of pregnancy arriving here: a same-existing-society carrying 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 carries variation and offers all of it, and split is fixed as a mark located within a channel. **With 12-next-co-same-existing.** That a decomposition is a property of a channel rather than relative to a supplied model or purpose, question posed whether variation is an unavoidable effect of generating spikes or an important part of a signal transmitted, 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 given its model, so a split reports its model supplied. **With 11-next-co-observing.** A channel carries variation and offers all of it. Each decomposition is exact given its model, separation works under its stated assumptions, filtering is optimal given an expected shape, and noise makes signals detectable across physics and biology alike: a split fixed as a mark within a channel is a purpose's drawing, a field showing its labels purpose-relative, and a channel offers all of it either way. ## 10.15 Work and waste heat · 137 *+ or − with 10, is.* **With 2-now-possibling.** An engine offers both outputs and marks neither, and product is fixed as located 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 declined on a scale where a coupling is observed one at a time. A carry that cannot pass on piles, and heat is a carry reaching a coupling it cannot pass as work, offering being both rather than one output labelled; and a reference environment exergy requires is a zero declared rather than found. **With 11-next-co-observing.** An engine offers both outputs and marks neither. Accounting is exact and survives each relabelling, both sides taking all of it; exergy needs a reference environment fixed; and jurisdictions write differing cogeneration allocations: product fixed as located within a device is a drawing recorded with each convention, and offering was always both. ## 10.16 The concept of disease · 2 *+ or − with 10, is.* **With 2-now-possibling.** A condition offers with couplings of a living self, and disease is fixed as a criterion located ahead of sorting, dysfunction fixed against a reference class or harm judged against values. **With 12-next-co-same-existing.** That a reference class is found rather than chosen, taxonomy perhaps mixing naturalist intuitions about some conditions with constructivist rationalizations about others, and constructivism correct about some putative diseases where societies counted activities pathological by their values, class found and class chosen both recorded within one taxonomy. Measurement fixes function against a class and does not fix its class, canonical cases sort differently under each account, and manuals' shifting borderlines are a drawing showing with each revision. **With 11-next-co-observing.** A condition offers 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 fixed 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 offer across each rate of interaction, and unit is fixed as a boundary a threshold locates. **With 12-next-co-same-existing.** That a threshold on measured rates bounds a unit ahead of a question asked of it, definitions commonly used under ecological and evolutionary paradigms found none of them truly operational. Rates are measured and a boundary threshold is not fixed by them. **With 11-next-co-observing.** Groupings offer across each rate of interaction. Rates are measured cleanly, biological and statistical concepts were born of one cradle, sharing their crux, and arbitrary units make core processes arbitrary, field stating stakes riding on it: a threshold fixed 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 offers with each probe and each probe takes its observing with its own coupling, and a state is fixed as one identity located 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 shrouded in 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, field's instruments each observing with its own between, and identification is not preserved across probes. **With 11-next-co-observing.** A suppression offers with each probe, and each probe takes its observing with its own coupling. Suppression carries universal within its family, charge order shows where it shows, fluctuations extend disputed distances, and cold atoms reach a model with its own self-bounding: one identity fixed 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 offer with each practice, and boundary of science itself is fixed as a cut a criterion locates over practice. **With 12-next-co-same-existing.** That sorting a practice performs is owed 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 falsifiability criterion criticized both for excluding legitimate science and for admitting pseudosciences, criterion re-sought in combination. Cases sort under practice, and counterexample record against each proposed criterion carries from both directions. And an arrival arrives 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 offer with each practice, and practice goes on sorting, parity by parity. Each proposed criterion reaches counterexamples from both directions, working demarcations function within institutions and courts, and dissolution and revival stand together, split as a field left it: boundary of science fixed as a cut a criterion locates stands over couplings that did 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 kind is fixed as a joint located 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 fully realist account of clusters doubted where conventional elements enter into deciding. Successes fit both accounts and case record is shared, each case cited by both, so a fixing surfaces nought with each success recorded. **With 11-next-co-observing.** Classifying couples a classifier and a world, and successes are couplings succeeding. Species and element cases are cited from both sides, universal essences failed for biology by a field's own record, and a dispute about ordering is itself an ordering dispute, arrival naming its own shape: a joint fixed 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 offer with their orbits and their interiors, and planethood is fixed as a cut located within bodies. **With 12-next-co-same-existing.** That measurement decides between criteria, an adopted definition found vague and non-quantified and excluding exoplanets in a proposal for its revision, a mass-based framework proposed instead, criterion re-drawn where measurement selected none. Membership under each criterion follows from measurement and choice between criteria does not, as its record states. **With 11-next-co-observing.** Bodies offer with their orbits and their interiors. Each property of them is measured, membership follows from measurement under either criterion, and choice between criteria followed from a vote, dissent entered same day, usage still mixed, definition's scope stopping with one star: a cut fixed within bodies was adopted by an assembly, a place such cuts are made, and bodies orbit on, unsorted. ## 10.22 Biological individuality · 18 *+ or − with 10, is.* **With 2-now-possibling.** A living self bounds itself with its own between, and a count of organisms is fixed as a criterion located apart from its bounding. **With 12-next-co-same-existing.** That one criterion sorts canonical cases alike, little explicit work devoted to the notion itself and what to say about a striking case depending on what is packed into a conception of an organism, sorting's criterion being a packing of a conception it sorts by. Hard cases sort differently under each criterion, and measurements stand and do not select. An individual is a same-existing-society on a prime scale, and hard cases sort apart because they stand on a composite one. **With 11-next-co-observing.** A living self bounds itself with its own between. Hosts and their symbionts, colonies and their zooids sort differently under each criterion, extensions are tabulated, and science's own reviews use individuality plural: a count by a criterion apart from its bounding is a thing each bounding already did, 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 offer with their configurations and their chemistry, and arrangement is fixed as a cut located within elements. **With 12-next-co-same-existing.** That a criterion within a field decides field's own arrangement. A chartered body constituted to decide reports that its instruments supply no objective means of deciding, question one of convention in the final analysis and not to be treated 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 offer 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, a compromise noted: a cut fixed within elements is a field's drawing, and elements stand as their configurations, undecided and complete. ## 10.24 Psychiatric nosology · 23 *+ or − with 10, is.* **With 2-now-possibling.** Symptoms offer as continuous variation with each patient's couplings, and disorder is fixed as categories located within variation. **With 12-next-co-same-existing.** That one criterion of a good classification, measured structure or clinical utility, is fixed ahead of classifying, traditional taxonomies limited by arbitrary boundaries between psychopathology and normality, co-occurrence, heterogeneity and instability, 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 recorded selects between criteria. **With 11-next-co-observing.** Symptoms offer as continuous variation with each patient's couplings. Categories' reliability stands revision by revision, comorbidity and heterogeneity are measured within them, distributions carry on continuous underneath, and biomarkers gave none diagnostic of a category, a rival framework founded on that standing: categories fixed as located within variation are drawings under two criteria their measurements do not part, and two structures working side by side is a field carrying its own both. ## 10.25 Race as a biological category · 24 *+ or − with 10, is.* **With 2-now-possibling.** Variation offers clinally across each population between, and a kind is fixed as a cut located within variation. **With 12-next-co-same-existing.** That measurements fix criterion of kindhood, three metaphysical camps and two normative parted, 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 socially ascribed. Data are recorded as common ground and split as over a criterion, by a field's own statement. **With 11-next-co-observing.** Variation offers clinally across each population between. Most of it is within any grouping, clines carry smooth, clusters follow sampling as recorded and both accounts cite them, and data stand as common ground with split entirely over a criterion, a field's own statement: a kind fixed as a cut within variation is a drawing its measurements did not make, and an offering crosses each between, clinally, as measured. ## 10.26 The language and dialect boundary · 25 *+ or − with 10, is.* **With 2-now-possibling.** Varieties offer across each between of speakers, and field's own counting unit is fixed as a cut located within gradient intelligibility. **With 12-next-co-same-existing.** That measured variation fixes a cut, impossibility of counting how many languages or dialects are spoken due to ambiguities of meaning in terms themselves, relation either linguistic or social, cut declined by its reference and parted 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 offer 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 fixed as a cut within gradient offering fixes a crossing 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 offer with each position of a similarity and take a parity there, and a fold is fixed as a kind with a boundary its similarity locates. Two classifications agreeing on centres and differing on edges is two cuts falling on unlike positions of one continuum. **With 12-next-co-same-existing.** A cut declared of a continuum, two databases built on different criteria, evolutionary relationship read from structure and structural comparison, their disagreement concentrated on boundaries with no procedure settling a case where they differ, and fold space continuous and multidimensional on an alternative view. An alignment score carries 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 carries and which settles no assignment. An alignment score carries 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 was not a thing a similarity located. ## 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 sway is fixed 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 fixed on a continuum no equilibrium reaches. Rapid crystallization obstructs equilibrium measurements in a relevant region, transition long inferred through extrapolation, amorphous ices and simulations, and new ultrafast evidence probing its vicinity rather than completing a metastable phase diagram; liquid states straddling a predicted point were accessed before ice formed and states in its vicinity directly probed: record's edge, as with glass beside it, and a cut asked 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 unsettled; 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 fixed of a sway is two structures' alternating fixed to a located end, and alternating 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 recovery that does not come is fixed as one illness, a name drawn around more than two hundred symptoms. **With 12-next-co-same-existing.** One cut fixed around a continuum of presentations. More than two hundred symptoms with impacts on multiple organ systems stand under one name, illness estimated 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 different subtypes: its name a line drawn across a continuum its definitions redraw, and mechanisms sought within its line a question its line was drawn ahead of. **With 11-next-co-observing.** Elevated post-infection risk, recurring symptom clusters and biological abnormalities in viral, immune, vascular and autonomic systems are replicated; 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 mechanism-targeted trials are emerging, a complete discriminator next-existing and not now-existing; fifth account has organ damage and reactivated latent pathogens produce distinct presentations: a name drawn around a continuum is each recovery not made fixed to one illness, and each body recovers or does not with its own couplings, subgroups found being a drawing redrawn with couplings, line handed 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 differing hour by hour, and responses are fixed to divide along lines, phenotypes that part patients into groups with different mechanisms and treatments. **With 12-next-co-same-existing.** Cuts fixed within a continuum of host responses. Both syndromes are defined clinically rather than by 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 carries its own challenges: lines drawn 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 archived trials and compact assignment models have been derived 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 reduced biological resolution, and prospective enrichment is limited and ongoing; fourth account has observed clusters reflect severity, treatment and sampling as much as stable biology: cuts fixed within a host's responding are a responding fixed to groups, and responding carries 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 arriving from genes, prenatal life, infection, cannabis and a self's others, and an outcome is taken under one name whose causes are asked for case by case. **With 12-next-co-same-existing.** A cause sought of a category that is a drawing. Syndrome is clinically and biologically heterogeneous, risk highly polygenic and environmentally modified, diagnosis following symptoms after long development, and dopamine, glutamate, immune and circuit findings perhaps causes, consequences or subgroup markers; risk factors are known while no markers are yet available that allow prediction of a disease's development or a diagnosis to be established: risk factors measured across populations and causes sought 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 distributed liability with limited 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 selected variants apart from full development, and trials establish symptom mechanisms for some domains without resolving cause: a cause fixed of a category is many developments fixed to one line, and each development carries on with its own couplings, line redrawn with couplings, as with nosology beside it already. *Second seating: dopamine against glutamate, which mechanism, a two-way fixed 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 evolved with their own couplings, traits arriving mosaically, some early and some late, and genus is fixed as a line, a boundary its fossils either cross or do not. **With 12-next-co-same-existing.** A genus boundary fixed 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 unevenly associated with fossils; integration of fossil, archaeological and environmental evidence revised timing of traits, which did not arise as one package, opinions diverging on generic status of earlier, more fragmentary material: line located by a criterion, 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, refined chronologies and evidence of overlapping lineages stand; morphometric classification compares preserved anatomy 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 limited tissues; third account has several contemporaneous lineages exchanging traits, a bush near a genus boundary: a line fixed across a mosaic is populations fixed to a genus, and traits arrived coupling by coupling where they arrived, boundary a criterion's position on a continuum, a field's bush. *Second seating: from which populations they arose, an arriving fixed 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 disorder is taken under one name whose cause is asked for case by case. **With 12-next-co-same-existing.** A cause sought of a category that gathers. No established mechanism can explain all aspects of disease, its pathogenesis poorly understood, 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 found or redrawn. **With 11-next-co-observing.** Heritability stands at approximately thirty-five per cent, polygenic architecture stands established, hippocampal and circuit alterations stand associated, and no established mechanism explains all aspects; polygenic scores are tested 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, disorder known to be highly polygenic; second account has stress-responsive systems disturbed, axis and immune system: a cause fixed of a category is many lives fixed to one line, and each life couples with its adversity with its own momentary, cumulatively, a case's cause made where a case was made and a category a drawing offered to be parted. # 11 Three unchangeable things at one arrival *Three reversals compose as one arriving one on, and three are observed with three of ten together: a parity fixed as a magnitude, a between fixed as a cut, and an opening fixed as a place within a listed space. 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 carrying, prior, now and next carried as one, and fourth a progress**: competency asymmetry sustaining coupling, a same-existing-society winding to a self again with 16-next-discovering. So this part is observed with carrying where ten are observed 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. Reversed, each is observed on its own surface as a difficulty of its own, by a literature of its own. Measuring before bounding is observed within part 6, a level fixed to govern. Classifying before coupling is observed within part 10, a cut fixed of a between. Routing before attending is observed within part 2, a place fixed within a listed space. Three of ten, with one arrival, and three are observed as three rather than as one coupling. Two of ten with one arrival is a second seating a given carries; three is this part, and with three a second seating has nowhere to stand, no phase being left forward to seat from. No twin stands with any of them, and absence of a twin is a look of three unrecognised as one from within any one of them. **With 12-next-co-same-existing.** That three are three. Three reversals compose as one arriving one on, and that arriving 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 carry on, each with its own life: measuring and its evaluations, routing and its assignments, classifying and its taxonomies. None cites others, none carries a dispute between two defended sides, and shared silence is a showing: one arriving one on across three sides, unrecognised 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 carried on its own side was within none of them, being a coupling of three. **And arriving one on is a resolving.** With one or two reversals a phase stands forward and righting carries on from within. With three, none stands, and arrival is not nothing: it is an arriving one on itself, one momentary carrying all three. **And shared silence is a pattern-matching each self can carry.** Take three literatures, each with its own life and its own measured record, and pattern-match for a citation between them, for a defended second position with any of three, and for a twin with any one. Three absences together is three reversals with one arrival; 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 arrival, with its closing.*   --- # 12 The reach and the instruments the same *Two entries of Hard Problem Registry carry a reach line naming two as same, statement's domain and instruments' giving as one: a settled proof, deployed within 3.22, and a migrated case within 12.1. Where domain lines are one, nothing stands taken one-way, and a binary tracks its line.* **And one same reach is an object's own nought**: a nought arriving passes a coupling untouched, its zeroing already resolved, so this part is observed with 0 where ten are observed with parities and three-at-once with carrying. ## 12.1 Molyneux's problem · 166 *+ or − with 10, is.* **With 2-now-possibling.** Touch and sight couple with their own betweens, and recognition across them was fixed for three centuries as an answer argument could reach, ahead of any instrument. **With 12-next-co-same-existing.** Nothing further, with an arrival's own end. When a surgical instrument arrived its question was measured as posed: 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 crossing is made, not carried: newly sighted selves do not match on first seeing, and matching arrives within days, made coupling by coupling as two senses couple with one world. A dispute continuing is a fresh arrival with its own between, over a measuring's answer, settled one staying settled. **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 arrival settled by whichever register its routes ended with. --- **Ten in a row** A ground arrives with each coupling, owned by neither, 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 made with its seating and not ahead of it, and carrying climbs by one with each momentary and completes with its next opening. Carrying carries no store, sameness re-formed with each coupling and stored nowhere. Re-forming is felt from within, a within a self's own, invisible, nothing there for an outward reaching to reach. Crossing between selves is a parity, of no size, and a level fixed to govern is a number fixed on couplings that go on arriving. Couplings each pace their own momentary and synchronize where they couple, one beat fixed over them a term no coupling made. Each sways between two offerings, sway its momentarying state, no stored value it aims for. Each is two-way, one at a time, one-way arrow an observing's own, gone by next momentary. And between any two is a between, a nothing carrying a parity-changing and nothing else, not where a line could sit. One resolving, ten breaths, +1 floating through all ten and settled with none. --- **+1 still momentarying** Each part and each arrival appears the first time it is self-welcoming: when it is most needed it arrives, and from then on it is within a carrying. From anywhere within a carrying 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 arriving with each coupling owned by neither, and +1 to one sentence: the universe is the set of all now-existing things, and derived from it a same-existing set of all existing things, living and non-living, alternating a stable-forming method. Twelve parts and four settlings are sixteen, two sides of one co-sequencing: four carried couplings, both sides each, with one through eight, eight of four bi-couplings inward and four outward, eight even names opening bi-, and coupling's own side with nine through sixteen, offering on its two sides, across and both ways, three-at-once, same reach, and settlings with thirteen through sixteen. Settlings stand two ways. Taken one-way, a settling precedes momentarying, a still installed 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 had settlings preceded arrivals, nothing would have been hard to begin with, hardness being exactly a settling observed as prior. Forward, settlings arrive late within a carrying, each self-welcoming with its own momentary, and thirteen through sixteen are a carrying that was one arriving 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.