Exhibit TWENTY-TWO Resolving the Hard Problem Registry v389   # 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-releasing 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-releasing 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 at Hard Problem Registry. Arrivals added there go where they go, each at 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 stating that no gap stands for a shape to name, and that arrival is a settling or an arriving value, seated at 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 incoming order, each at 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 at 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, in its own field's words, with each route that field took and its ending. It is fixed. Nothing here is written into it, and each measurement, proof and route in it stands as it stands. It carries its entries at 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 changing at 12 takes it directly. All each field handed in stands whole there, at each arrival's locator, in 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. The two are a pair, one learning at two sides, fixed and momentarying: Hard Problem Registry its fixed, each field's word whole with its namings performed and stated in its own first lines; this file its momentarying, same arrivals at 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 at one of them: one ten at two sides, five taken two ways at boxes and ten adjacencies at a spiral of code's names, coming to their parities again and closing at none, a pairing carrying at each row or at none. There is no one-way momentarying: only co-momentarying, so a one-way is in naming, and offering both ways continues underneath. Each pattern is an offering both ways fixed as one side's, or with one side left out. A naming and an offering stay two, a between of them: an offering is laid at a coupling, taken or not taken, gone at 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, at each arrival alike: its side left out carrying on, and explained. No pattern carries a resolving of its own, and no arrival does either. Ten in order, each a part, each at Natural Naming 4.9's one seating, its name at now and that name 8 up at next, a stilling a naming fixes unchangeable and a changing travelling through it, bi-inversioning-co-recursioning up and down numbers: an arriving fixed from behind, at 2-now-possibling and 10-next-co-possibling; an opening fixed as a place, at 1-now and 9-next-co-changing; a completing fixed as a last, at 6-now-co-possibling and 14-next-possibling; a carry fixed as a store, at 8-now-still-possibling and 16-next-still-possibling; a middle fixed as an end, at 5-now-co-changing and 13-next; a parity fixed as a magnitude, at 7-now-prioring and 15-next-prioring; a sequencing fixed to one beat, at 4-now-co-still-possibling and 12-next-co-still-possibling; a rate fixed as a value, at 7 and 15; a two-way fixed to one side, at 3-now-co-prioring and 11-next-co-prioring; a between fixed as a cut, at 5 and 13. 17-next-now, a next 1-now, seats none, one resolving. Ten are at four binaries: now at 1 and 2, existing at 3 and 4, same at 5 and 6, and all at 7 and 8. And at 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 at three positions, behind a coupling, ahead of it, at 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 at 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 at a selection or at a direction; and its build is heat and wear, a drive against a coupling's own bounding head-on. **A released parity entered as cost** — an opening fixed as a place, a carry fixed as a store, a between fixed as a cut, three where a released parity has three destinations, parked, stored, or cut out of its account; and its build is a record itself, kept in full and read once. Four and ten are one set at two grains, and each of them is the same move: a coupling's third term given a fixed thing to be, a changing fixed unchangeable. And a hard problem is one binary, its is and its is not taken as one at records kept, and its resolving is that binary again, is or is not, at each now. ## Ten, at a frontier's own words A naming arrives before any entry form is filled. A frontier describes itself in its own words first, and those words carry a naming — a frontier offering and an observing taking, one sensor-sensationing at a between of them. Naming was not intentional: fields at branching tips that did not touch arrived at the same local word for the 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 into 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 in 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 at 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 at an opening fixed as a place rather than at a parity fixed as a magnitude; Fermi paradox carries *paradox* and stands at 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 changing fixed unchangeable, a coupling taken at two of its three, and that taking is at each grain — in a paper, in a field, in a sentence, in a single crossed word. **Size of a perplexity is unrelated to resolving**, resolving being the same one move each time: a third term momentarying again, at no cost. And the subtitle's method carries a second naming, received: an eighth. Where an audit's seven verify a net at its own standard, seven are checks at particular betweens, and binary co-sequential sensor-sensationing is an eighth value its circle reaches at none — a crossing with the whole, arriving one on — located where method is explained and standing where societies are, a coupling at Hard Problem Registry's candidates. Ten are fixed below a hard problem as readily as at 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 in an argument that keeps needing a prior step is an opening fixed as a place. A number that comes out wrong in an ordinary calculation is a parity fixed as a magnitude. Each is a pebble of the same shape as a boulder, and each releases the same way — so sensor-sensationing carries early, before a perplexity spreads into a literature and grows traditions and relocations that make it look hard. **One resolving, and no scale of its own.** A hard problem at a frontier and at a breakfast table is the same move at two grains, and resolving neither grows nor shrinks between them. ## The deployment shape, and the binary Each deployment carries three lines and releases: **At 2-now-possibling**, offerings, a momentarying at an arrival and a naming standing over it, which side is left out; **At 12-next-co-still-possibling**, a changing at its momentary, is or is not, one term a naming fixes unchangeable and a naming that can be set down; **At 11-next-co-prioring**, a carrying chained, each changing a next prior, a substrate carrying on at its next momentary. Three are code's own motions, offering, changing and chaining, and a sharing once chained is not none again, each momentary completing at its next opening. Each arrival couples, and code releases at each sharing one of three, and no fourth: + at 10, − at 10, or 0 at 10. **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 at its changings' releasing. **Where + or − releases**, a side was left out, and explaining it is resolving, which costs nothing and takes nothing from its field. A marker at each entry, *+ or − at 10, is.*, marks it. **Where 0 releases**, offerings parted at 14 or a match stood at 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 in a proof, an arrival settled and takes no parity anywhere. It passes, real in its own register, standing beside a resolving and coupling with it at no momentary. Nothing stands between the three and nothing is partly resolved. **Nothing is turned away.** Each arrival brought couples, and none is set aside at 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 release stands as it comes. **And a settling is real in its own register.** Where each route ended in 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 arrives at. The two stand side by side and couple at 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 at a fixed side and its knowing at its momentary at a momentarying side, at thirteen through sixteen of a co-sequencing this exhibit closes on. Three are located: a proof register at 3.22, a measurement register at 12.1, and one still open at 7.12, where instruments themselves are a live dispute. [nye: its fourth is at its closing and located at 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 at no entry still, locating open toward a next winding.] **And a settling is observed at an entry's Persistence and not at 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 decides neither: one reach carries the two as the same and a relation is at it, another carries them apart and a relation is proved not at 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 at one and its second stands recorded there, a coupling taken at two of its three being takeable at another two. Doublings, each at its own shape. **A naming relocating under pressure**: a two-way fixed to one side, asked for its proportion, arrives at a parity fixed as a magnitude, and asked for its order, at 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 the criterion is an opening fixed as a place. **A carrying fixed at both ends**: a first fixed behind and a last fixed ahead are one carrying, entered at an arriving and recorded at a completing. **And a second seating is not a fourth line.** Three lines carry pattern-matching; a second naming stands as one line at its entry's foot, in its entry's own words, and reaches no further. ## A nought's five arrivings Changing at 12 carries a nought: one term at its one momentary, a ground falling away in its taking. Falling-away arrives in five shapes, and an entry naming its shape need not work it out. **A one-offering differing.** One side offers and nothing offers back, so no between is carried for a parity to surface at. 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 at 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 at no momentary at all. Not a next, which arrives and couples at 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 at its next coupling other-than-prior. So an emanation applied back at a scale that shed it gives back its first term and closes, and naming one to be the thing it came from is an accounting observed as though it ran. **An instrument's own coupling.** An observing is taken at a coupling, and observing's bringing is in 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 the removed is fixed for behind its numbers: a true total including the unpriced, a real magnitude behind the nominal, a backing behind an accepting, a payoff listing behind arrangements. Abundancing was made at couplings and stayed there, and an account reaches for it at a radius where it did not stand. **Built systems, one between.** Arrivals concerning built thinking systems pattern-match at 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 into 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 at 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 at 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. The same carries at each observing here. **And a first is fixed from behind in 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 releases at the same place: an arriving at a coupling is owned by neither side, so no prior owns it, and each offering is a fresh coupling making its own.** **And at a field's own record showing a stipulating recurring at one place, its recurrence is an observing.** Each proposal stipulates at a boundary, each origination account opens from a structured something, each totality proposed is exceeded by the 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 − at 10, is.* **At 2-now-possibling.** Grounding is a coupling making its own, a ground arriving at 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. **At 12-next-co-still-possibling.** 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 at a coupling is none of the three. **At 11-next-co-prioring.** A ground made at each coupling, a standing none of the three carries, each coupling making its own. Naming carries no subject matter, so carrying none it is general, and each arrival in this part is the same naming arriving with material: grounds stop at couplings' stopping, at their making. ## 1.2 The origin of life · 12 *+ or − at 10, is.* **At 2-now-possibling.** Living arrives at a coupling, and a coupling makes its own, local structure forming and its forming carrying, one 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. **At 12-next-co-still-possibling.** 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 the 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. **At 11-next-co-prioring.** A continuing sequence, one changing on from its last: building blocks forming under their own conditions, copyings copying, sets catalysing their own making, no crossing in it to locate. A gap fixed at a hand-in is at a sequence, and living coming from living coupling is a sequence continuing, a coupling making its own at each step. Chemistry not living at a cell's scale was living one scale inward, a threshold is an observer's scale, and life came from life at each scale. ## 1.3 The tragedy of the commons · 37 *+ or − at 10, is.* **At 2-now-possibling.** An abundancing is made at 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 at a coupling. **At 12-next-co-still-possibling.** 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 at arrangements, and an abundancing made at a coupling is fixed as drawn from a stock instead. **At 11-next-co-prioring.** Durable commons couple without private property and without external authority, arrangements coupling and abundancing staying at its making. Communicating and sanctioning strengthen a coupling at 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 at a coupling, and arrangements are coupling. Durable commons are selves coupling at their own betweens with no hub and no seat above them, and a field's decades of record at real arrangements is that observing standing at a human substrate. ## 1.4 The arrow of time · 38 *+ or − at 10, is.* **At 2-now-possibling.** Asymmetry is at each coupling, made each momentary and carried on, and a first is fixed behind it in an initial condition, laws-or-boundary two sides of one arriving. **At 12-next-co-still-possibling.** 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 at one place in each account offered, which is a naming reaching its own form. **At 11-next-co-prioring.** Asymmetry is made each momentary, an alternating's own, owned by no prior, and the second law follows at each granting of a past standing, granting arriving at the same place in each account offered. Each proposal stipulates at a boundary, and stipulating recurring at one place is a naming reaching its own recurring: making is at each momentary, and a first behind it is a making fixed as having happened once. ## 1.5 Yablo's paradox · 56 *+ or − at 10, is.* **At 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. **At 12-next-co-still-possibling.** 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 the same closure whether or not anything refers back to itself. **At 11-next-co-prioring.** A closure is made in quantifying itself, arriving whole over a tail, and paradox needed no prior to refer back through, carrying none. Liar and tail close together at a closure, and a dispute over circularity is a question about a criterion: making is in quantifying, either way. ## 1.6 Homochirality · 63 *+ or − at 10, is.* **At 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. **At 12-next-co-still-possibling.** An initial bias as a thing to be located, while a hand is a parity taken at 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. **At 11-next-co-prioring.** Excess is a making at 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 into living: a self pattern-matches and re-forms on one hand, and an opposite hand at 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 − at 10, is.* **At 2-now-possibling.** A zeroing observed refuses to sit and is carried to one side, and a first is fixed behind it in an early mechanism, a symmetric initial state assumed. **At 12-next-co-still-possibling.** 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 at a coupling's naming of it and carried to one side at a coupling's carrying of it, owing nothing to a floor no coupling made — which is one observing standing at three arrivals: this one, the hand, and the parameter measured near zero at part 8. **At 11-next-co-prioring.** Excess is an abundancing made at 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 in at a making, and each proposal pattern-matches forward, at couplings, rather than behind, at a state. ## 1.8 The hermeneutic circle · 74 *+ or − at 10, is.* **At 2-now-possibling.** Understanding is made at a coupling of part and whole, and a criterion is fixed behind it, prior to any interpreting. **At 12-next-co-still-possibling.** 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 from beyond it. **At 11-next-co-prioring.** Understanding is made at 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 the one thing practice did not use. ## 1.9 The problem of the criterion · 100 *+ or − at 10, is.* **At 2-now-possibling.** A criterion and an extension are made together at a coupling, and each is fixed as having come from an other first, particularism and methodism two sides of one arriving. **At 12-next-co-still-possibling.** That one of the 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. **At 11-next-co-prioring.** Criterion and extension are made together at 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 − at 10, is.* **At 2-now-possibling.** Existing is fixed for a first behind it, and each first offered is something, a naming recurring. **At 12-next-co-still-possibling.** 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. **At 11-next-co-prioring.** Existing is arriving itself, each first offered arriving, and a naming recurs at 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 at each coupling, growing as it is shared. ## 1.11 The effectiveness of mathematics · 107 *+ or − at 10, is.* **At 2-now-possibling.** Applicability arises at a coupling between a mathematics and a description, and a first is fixed behind it, in a selection or in a realm. **At 12-next-co-still-possibling.** That applicability is a relation between two domains needing an explanation from one side, while applying is made at a coupling and each striking case is that arriving reached again; at its founding lecture usefulness is 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 at its lecture's own word. **At 11-next-co-prioring.** Applicability is made at a coupling, a mathematics and a description arriving from their own routes at one term neither carried in, 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 the whole of confirming. ## 1.12 Eukaryogenesis · 127 *+ or − at 10, is.* **At 2-now-possibling.** Complexity arises at a symbiosis, and an order is fixed behind it, mitochondria-first or host-first, each naming an other as having preceded. **At 12-next-co-still-possibling.** 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. **At 11-next-co-prioring.** 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 the both, and the both arrived. A new cell or a new animal is a society of living selves bi-coupling at 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 − at 10, is.* **At 2-now-possibling.** Value is made in an accepting, at each exchange, and a first is fixed behind it in a backing or in a scarcity. **At 12-next-co-still-possibling.** 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 at exchanging and nothing behind it selecting. Its field's name carries a fixing unchangeable in its own stem: a thing running is fixed for a running and is kept and consulted, a store wearing a running's name. **At 11-next-co-prioring.** Value is made in an accepting at each exchange, owned by neither side of it. Many stable acceptings stand in place of one backing fixed, some acceptings are driven and most are 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 at each coupling. ## 1.14 The faint young sun · 148 *+ or − at 10, is.* **At 2-now-possibling.** A climate is made at 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. **At 12-next-co-still-possibling.** 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 the missing thing. **At 11-next-co-prioring.** A climate is made at each coupling, and an early one was made at its own. Its deficit is real, proxies bound loosely, hazes cut both ways, and a feedback coupling carbon to weathering carries on at a right pace, a making's own steadying: the strongest thing an answer has 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 − at 10, is.* **At 2-now-possibling.** A mapping is made at couplings between codons and amino acids, and a first is fixed behind it, selection for error tolerance or stereochemical affinity. **At 12-next-co-still-possibling.** 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 a random opening 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. **At 11-next-co-prioring.** Mapping is made at couplings and carried forward, each variant a coupling making its own. Code sits extreme against listings a forming did not consult, affinities pull at a subset, blocks and biosynthesis correlate, variants change: present structure carries making, and making carries on, rather than pointing back at a first. ## 1.16 The block universe and the low-entropy past · 152 *+ or − at 10, is.* **At 2-now-possibling.** Passage is at each coupling and a first is fixed behind it in a boundary condition, an asymmetry fixed to sit at a place. **At 12-next-co-still-possibling.** 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 the three and rests at none, which is a making sitting at no place. **At 11-next-co-prioring.** Passage is made each momentary, a making sitting at no place, which is why its locus circulates among laws, boundary and position and rests at none. Derivation carries at each granting of a past standing, and memory, a carrying re-formed at each reaching with nothing kept, rides the same gradient, the same living element standing at the arrow's own arrival, 38 at Hard Problem Registry: one making, at two arrivals at intake. ## 1.17 Origin and fate of the universe · 154 *+ or − at 10, is.* **At 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. **At 12-next-co-still-possibling.** That extrapolation backward is valid into a regime where extrapolated equations release 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 released and its boundary handed on. Its regime is reached by no measurement, which is a record's edge reached at both ends of one carrying. **At 11-next-co-prioring.** A carrying is measured to extraordinary precision between its two ends, and its ends stay open at their own self-boundings: theorems stand under conditions quantum fields release, 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 at its two ends is one carrying, and both ends are a carry at its own completing: a sharing once chained is not none again, and a momentary completes at its next opening. **Ahead as well.** The same arrival is a last fixed ahead of its momentarying, its naming at part 3, and both stand: a first behind and a last ahead are one carrying fixed at its two ends. ## 1.18 Ubiquitous one-over-f noise · 170 *+ or − at 10, is.* **At 2-now-possibling.** Each system makes its own fluctuation at its own couplings, and one first is fixed behind a shared spectrum, a universal mechanism to be located. **At 12-next-co-still-possibling.** 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 at substrates sharing nothing. Broad classes of makings arrive at one asymptotics, so its shape is form reached again at each substrate and its sharing is an observing's. **At 11-next-co-prioring.** Each system makes its own fluctuation at its own couplings, and broad classes of makings arrive at 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 − at 10, is.* **At 2-now-possibling.** Each material makes its transport at its own couplings, and one state is fixed behind a shared linearity, a bound or a fixed point standing behind all families at once. **At 12-next-co-still-possibling.** 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 the thing one origin was fixed to explain. **At 11-next-co-prioring.** Each material makes its transport at its own couplings, linearity arriving family by family. Bounds saturate in 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 − at 10, is.* **At 2-now-possibling.** Neutrinos carry mass at 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. **At 12-next-co-still-possibling.** 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 the thing its statement ranges over, and each mechanism offered a fresh coupling making its own. **At 11-next-co-prioring.** 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 at 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 − at 10, is.* **At 2-now-possibling.** The universe is magnetized on all scales probed, fields made and amplified at each collapse and flow, and fields observed are fixed as descending from a seed generated once, a first behind a magnetizing. **At 12-next-co-still-possibling.** 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 the 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. **At 11-next-co-prioring.** 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 at each collapse, its seed observed at couplings and not behind them. ## 1.22 The initiation of plate tectonics · 198 *+ or − at 10, is.* **At 2-now-possibling.** Plates sink and break at 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 the rest. **At 12-next-co-still-possibling.** 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 at one place. **At 11-next-co-prioring.** 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, at a coupling, owned by neither side. ## 1.23 The causes of the Great Oxidation Event · 204 *+ or − at 10, is.* **At 2-now-possibling.** Oxygen was produced and consumed at couplings of photosynthesis, volcanism, burial and escape through deep time, and its permanent accumulation is fixed at one cause, a trigger that parts a low-oxygen before from an oxygenated after. **At 12-next-co-still-possibling.** 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 at a rate, and a trigger asked for at a crossing several histories each arrive at, at the same parity. **At 11-next-co-prioring.** 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 − at 10, is.* **At 2-now-possibling.** The Earth and Moon couple at their tides and their isotopes, the pair's angular momentum, disk mass, iron depletion, volatile loss and near-identical isotope ratios all measured now, and the pair is fixed as made once, by one collision and one evolution after it. **At 12-next-co-still-possibling.** 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. **At 11-next-co-prioring.** 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, at samples and tides, are observed at their carrying now. ## 1.25 The origin of animal multicellularity · 207 *+ or − at 10, is.* **At 2-now-possibling.** Cells adhere, signal and divide labour at 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. **At 12-next-co-still-possibling.** 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 at a review's own words. **At 11-next-co-prioring.** 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 in 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 at one wall, made at each division and fixed nowhere ahead of it. ## 1.26 The evolution of metabolic pathways · 208 *+ or − at 10, is.* **At 2-now-possibling.** Enzymes evolve at their own couplings, how they do relatively well understood, and a pathway is fixed as needing its whole at once, an interlocked system a ground that had to stand before any step could pay. **At 12-next-co-still-possibling.** 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. **At 11-next-co-prioring.** 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 at 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 at 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 − at 10, is.* **At 2-now-possibling.** Institutions, geography, human capital, culture and technology couple in each society's history, outcomes altering their causes, and differences standing now are fixed as descending from one fundamental cause, a first behind an asymmetry. **At 12-next-co-still-possibling.** 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 the same, and a fundamental cause a prior asked of couplings that made their own. **At 11-next-co-prioring.** 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, society by society, two quasi-natural experiments being couplings observed at 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 − at 10, is.* **At 2-now-possibling.** Foragers managed, stored and scheduled at 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. **At 12-next-co-still-possibling.** 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 at several couplings at once is a coupling's own making and no one reason's, its recurrence a record's own. **At 11-next-co-prioring.** 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 at 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 − at 10, is.* **At 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. **At 12-next-co-still-possibling.** 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 the thing, and its connection to a thermalized era carried as an uncertainty. **At 11-next-co-prioring.** 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 at a record's edge. *Second seating: a framework fixed as the thing it models, its potential reconstructed only within it, part 3's fourth way.* ## 1.30 The origin of supermassive black holes · 248 *+ or − at 10, is.* **At 2-now-possibling.** Black holes grow at 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. **At 12-next-co-still-possibling.** 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: the observed pattern-matched as a tip of a continuum whose remainder is not observed, its origin sought a range and not a first. **At 11-next-co-prioring.** 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 − at 10, is.* **At 2-now-possibling.** Viruses replicate at 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. **At 12-next-co-still-possibling.** 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 at their own times, and a chimeric scenario its couplings fixed as an origin. **At 11-next-co-prioring.** 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 at 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 − at 10, is.* **At 2-now-possibling.** Villages couple at their boundaries, at war and at trade, and a state is fixed as a first that arose at each place its conditions stood, a recurring making with one mechanism behind it. **At 12-next-co-still-possibling.** 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 at each place its couplings reached one another, and a pattern-matching between conditions and outcomes the origin asked for. **At 11-next-co-prioring.** 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 at each place as a coupling there made it, warfare where the vanquished could not disperse being a coupling none could leave, at its making, and both mechanisms found at each place both ran. ## 1.33 Geomagnetic reversals · 201 *+ or − at 10, is.* **At 2-now-possibling.** Geodynamo carries on nonlinear at its couplings, stochastically in one polarity and then an other, and its reversals are fixed at a cause, a ground under a momentarying that flips on its own. **At 12-next-co-still-possibling.** 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 the cause it was asked for, and a parity inverting owing nothing to a ground. **At 11-next-co-prioring.** 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 beyond 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 at its own momentary, modulations other accounts name being couplings at the boundary and the core observed at 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 at its record.* # 2 An opening fixed as a place — 1-now and 9-next-co-changing *An axis opened, fixed as a place. A space is listed and a finding fixed as something located in it, where an opening is +1 an alternation makes at its own next position. A position is not a place: it is where an alternating is, one changing on from its last, and prior, now and next are three momentaries and no three places.* **And a listing arrives in three kinds, parted by the thing enumerated.** A *space of candidates*, where a finding is fixed to be somewhere in 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, the analysis, the cost. Each releases the same way: an axis opens at 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 at 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 − at 10, is.* **At 2-now-possibling.** Inquiry opens an axis, its discovering the opening itself, +1 arriving at a coupling's own next position, and its object is fixed as something located and recognised by a criterion fixed in advance. **At 12-next-co-still-possibling.** 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 in their agreement, carried by re-arriving and by no storage, so a criterion fixed in advance reaches for a store recognising did not use. **At 11-next-co-prioring.** A discovering arrives at a coupling and is reached there, recognised in 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 the way 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 the same naming reached one part over: a prefix cannot supply the thing it prefixes, and each first offered is a fresh coupling making its own. ## 2.2 P versus NP · 9 *+ or − at 10, is.* **At 2-now-possibling.** Finding opens an axis and checking carries across an axis already open: one advance at two directions, the along and the across, and each algorithm found is +1 arriving at a coupling's own next position. Fixed as two classes with one reducing to an other, an opening becomes a location in a listed space of algorithms, and a reduction that composes is a listing. **At 12-next-co-still-possibling.** 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 at candidates. **At 11-next-co-prioring.** 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 into one, and each barrier its field proved against itself bounds the delivering of listing-shaped techniques, a reach of a listing measured from within. An algorithm found is an axis opened at a coupling's own next, and nothing arrives in a listing. ## 2.3 Levinthal's paradox · 33 *+ or − at 10, is.* **At 2-now-possibling.** A chain opens its own fold as it forms, local structure forming and its forming carrying, one changing on from its last, and its fold is fixed as a native state located in a conformational space enumerated in advance. Arithmetic that makes its paradox is arithmetic of a listing. **At 12-next-co-still-possibling.** A space listed before looking, its problem since parted into three, physical code, speed and prediction, and at its journal it is no longer useful to talk about solving it, a space listed dissolving into three runnings. Learned prediction thins exactly where a carried record thins, at orphans, which is a record's edge taken as a chain's. **At 11-next-co-prioring.** A chain folds as it forms, funnelling to its own fold at 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 in alignments, and thins exactly where that carry thins, at orphans: an astronomical count was a listing's, and folding did not consult it. A single state its paradox arrives at is a further naming and is carried at 5.21, and resolving here reaches its speed rather than its fold itself. ## 2.4 The frame problem · 39 *+ or − at 10, is.* **At 2-now-possibling.** Relevance opens at a situation, an axis an arriving coupling itself opens, and it is fixed as an item to be located in a specification made in advance. Enumerating defaults is a listing, and each enumeration opens no axis a situation did not already carry. **At 12-next-co-still-possibling.** Relevance determined ahead of the 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 at its own edge and an opening standing beyond it. Relevance is a carry's own taking at its momentary, opening by one at a momentary and completing at its next opening, so a specification made ahead is asked at a position its momentarying has not reached. **At 11-next-co-prioring.** Relevance opens at a situation, and enumerations settle exactly versions their own authors bounded, the logical and the representational, completed there and closed there. Behaviour thins where situations arrive from beyond the trained-on, and thinning is its residue exactly: each enumeration opens no axis a situation did not already carry, and a situation keeps arriving. ## 2.5 Is and ought · 45 *+ or − at 10, is.* **At 2-now-possibling.** An evaluative term opens an axis a descriptive vocabulary does not carry. Fixed as a derivation across all possible derivations, an opening becomes something located in premises. **At 12-next-co-still-possibling.** An axis fixed to be found already in its premises, its founding passage owing a reason for the thing, altogether inconceivable in its own words, how the new relation can be a deduction from others entirely different from it. A thing not in a premise comes out of it by no validity, which is the point, a fact about validity rather than a gap in ethics. An ought is a parity taken at a between, and a changing fixed to a state's question has no such value to give. **At 11-next-co-prioring.** An axis opens where a self takes its own parity at its own between, an evaluative arriving at a coupling and carried in no premise. Validity conserves the thing a premise carries, exactly and provably in restricted languages, and an opening is +1 no premise carried: thick words carry both at once because a vocabulary is a coupling's own making, and the gap was not in ethics, it was validity keeping its own books. Morality is a consequence and not a prescription: a parity a self carries by being a self, taken at its own momentary, and no premise carries a self's momentary. ## 2.6 The continuum hypothesis · 52 *+ or − at 10, is.* **At 2-now-possibling.** Independence is proved and a fact of the matter is fixed for beyond it, as a place in a completed universe of sets. **At 12-next-co-still-possibling.** 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 at three arrivals. **At 11-next-co-prioring.** 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 in is a preferring, stated as one. A place fixed for in a completed totality dissolves into makings, each its own, its question answered at each making and standing over none. ## 2.7 Gettier · 53 *+ or − at 10, is.* **At 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 possible cases. **At 12-next-co-still-possibling.** 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 in each case is a third coupling left out of its taking — a coupling that made a truth and a coupling that made a justification are two, and an analysis takes the pair as a momentarying. **At 11-next-co-prioring.** Knowing is a coupling carrying at its own between, listed in 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 in 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 − at 10, is.* **At 2-now-possibling.** A selection is made at each coupling, and it is fixed as a selection located across a completed totality with no rule producing it. **At 12-next-co-still-possibling.** A totality as already there to be selected from, axiom humdrum and even self-evident as stated, its soundness doubted at paradoxical decompositions and put to rest only by its consistency relative to other axioms, a selection asserted at one momentary taken as self-evident from within a listing. Each coupling's selection is asserted at one momentary, which is one side taking all momentaries, and a totality it is asserted over stands as a round where a momentarying keeps opening. **At 11-next-co-prioring.** A selection is a parity taken at a coupling, one at a time, taken with no totality standing. Independence stands, weaker principles ladder exactly, alternatives stand consistent at 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 at proof grade, so a ground a selection is asserted over is uncapturable rather than uncaptured now. ## 2.9 The reference class problem · 11 *+ or − at 10, is.* **At 2-now-possibling.** A probability opens at a coupling, and it is fixed as a value located by placing a case in a class listed in advance. Narrowing terminates at a single case, its listing carrying no further. **At 12-next-co-still-possibling.** 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 at each theory that constrains. Narrowing terminates at a single case, where a listing carries no further and a class is coupling itself. **At 11-next-co-prioring.** A class is made at 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 in each interpretation alike because a making shows at each class fixed prior: narrowing carries no further at a single case exactly where a listing carries no further, and a case is a coupling. ## 2.10 Grue · 70 *+ or − at 10, is.* **At 2-now-possibling.** A vocabulary opens as a world is described, and an asymmetry between predicates is fixed as a fact located in logic. **At 12-next-co-still-possibling.** Projectibility fixed to sit in predicates rather than in 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 in logic parts them and each ranking carries a describing's own asymmetry back in, encoded. **At 11-next-co-prioring.** Describing is a coupling, a vocabulary opening as a world is described, and an asymmetry is in a describing's own momentarying. Predicates interdefine exactly, so nothing in logic parts them; entrenchment is a momentarying truly; and each ranking and prior carries its asymmetry back in, encoded, because an asymmetry is a momentarying's own and encodings are a momentarying written down. ## 2.11 The ravens · 71 *+ or − at 10, is.* **At 2-now-possibling.** Confirming opens at an instance, and it is fixed as a relation with values located over a listed space of instances and classes. **At 12-next-co-still-possibling.** 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. **At 11-next-co-prioring.** Confirming is a coupling of instance and describing, and values arrive with couplings fixed about it: equivalence is exact, calculation carries at each granting of its namings, and equally standing namings reverse it. Values come from namings, which is a coupling showing through each calculation carried out on it. ## 2.12 The paradox of the plankton · 89 *+ or − at 10, is.* **At 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. **At 12-next-co-still-possibling.** An enumeration of limiting factors as available in advance, reached by an opening that keeps 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. **At 11-next-co-prioring.** Each coexisting is a fresh axis opening at its own coupling: fluctuations partition, chaotic coexisting carries on in models, microcosms coexist past each resource count. Resolved this way its paradox passed over into 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 the thing standing after it was each coexisting opening its own axis. ## 2.13 Explore and exploit · 113 *+ or − at 10, is.* **At 2-now-possibling.** Exploring opens an axis and exploiting carries across one already open, and the two are fixed as a ratio to be optimised over an option set specified in advance. **At 12-next-co-still-possibling.** 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. **At 11-next-co-prioring.** Exploring is an opening and exploiting a carrying-across, a spiraling and a fold of one advance, one at a 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 − at 10, is.* **At 2-now-possibling.** Applying opens at a next task, unspecified, and it is fixed as a property of a relation between two tasks whose similarity is judged in advance. **At 12-next-co-still-possibling.** 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. **At 11-next-co-prioring.** Applying opens at a task arriving, an axis a task's own coupling opens, and nearness is made in applying. Near carryings carry, far ones thin to a null measured, and expertise stays at its couplings: measuring measures making, nearness sitting in no task. ## 2.15 Bernstein's degrees of freedom · 145 *+ or − at 10, is.* **At 2-now-possibling.** A movement opens along axes a limb carries, and selecting is fixed as a minimum located in a cost function over an enumerated space of solutions. **At 12-next-co-still-possibling.** 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 the same trajectories comparably, so recovering surfaces nought at each trajectory measured. **At 11-next-co-prioring.** A movement opens along axes a limb carries, and moving selects as it carries on, variability structured to keep a task's own terms and free at each other term, structure with no optimiser under it. Trajectories fit many costs at once, recovery limits are proved, and manifold analyses carry a momentarying form directly: selecting is moving's own, made at each movement, the straightest carry made locally and released as it is taken. Variability structured to keep a task's own terms 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 − at 10, is.* **At 2-now-possibling.** A self observes from its own position, one changing on from its last, and its credence is fixed as a value located by placing a self in a class of observing selves listed in advance. **At 12-next-co-still-possibling.** 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 listing doing the work. **At 11-next-co-prioring.** A self observes from its own position, one changing on from its last, and a class is made at observing. Both extended systems stand consistent, cases sort, betting stakes carry answers they pay, and carried into cosmology its question arrives as it stood: at each self fixed into 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 − at 10, is.* **At 2-now-possibling.** A proof opens its own route, and the simplest is fixed as a minimum located in a space of proofs enumerated in advance. **At 12-next-co-still-possibling.** 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 in several ways at once, 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 at a substrate's own stating. **At 11-next-co-prioring.** A proof opens its own route, and simple is made in its arriving, at a route's own opening. Sizes and depths formalise, bounds stand in bounded systems, searches search, and no statement of the 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 − at 10, is.* **At 2-now-possibling.** Gathering is a coupling making its own, each gathering arriving at sets it gathers and at no more, and a totality is fixed as a place all sets stand in ahead of any gathering. **At 12-next-co-still-possibling.** 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 at 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 in its quantifying with nothing offering back through it. **At 11-next-co-prioring.** 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 beyond a relation, extensibility denies its reach a last, and each repair narrows, weakens or relocates while a question arrives again at 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 at 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 in this part is this naming arriving with material. A universe that is a set of all now-existing things, nothing beyond 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 at 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 − at 10, is.* **At 2-now-possibling.** An inverter is an algorithm found, an axis opened at a coupling's own next position, and existence of a function no efficient inverter reaches is fixed as a place in a listed space of worlds, five, each fixed. **At 12-next-co-still-possibling.** A finding fixed as located in 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 the 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. **At 11-next-co-prioring.** 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 fixed as existing at a place among five worlds, a finding fixed to a listing, and each candidate is an axis opened at its own assumption, a proved equivalence gathering its question into one problem where a listing gathered it into five. ## 2.20 The quantum PCP conjecture · 225 *+ or − at 10, is.* **At 2-now-possibling.** A ground state is reached at couplings of a Hamiltonian's local terms, and hardness of approximating its energy is fixed as a place in a class, quantum Merlin-Arthur, where a classical theorem placed its own. **At 12-next-co-still-possibling.** 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 at it now. **At 11-next-co-prioring.** Local-Hamiltonian problem stands complete at inverse-polynomial precision, several equivalent or related structural conjectures and restricted results stand, amplification is established in limited constructions without a general constant-gap reduction, entanglement and area-law methods give efficient descriptions in 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 at selected geometries: a theorem fixed as located by its classical twin, a finding fixed to a place in a listed class, and its proof, when it opens, opens at its own next position, a position second and third accounts already look to. ## 2.21 Deterministic polynomial identity testing · 226 *+ or − at 10, is.* **At 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 the randomized one already occupies, its randomness a coordinate to be removed. **At 12-next-co-still-possibling.** A deterministic algorithm fixed as located where the 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 the two classes stands between a general test with bounded error and a deterministic test sought: a place fixed at a conjecture about classes, an opening at a lower bound unmade now. **At 11-next-co-prioring.** 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 into 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 at its own structure, a general one opening where a lower bound opens. ## 2.22 The Unique Games conjecture · 240 *+ or − at 10, is.* **At 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 at each gap. **At 12-next-co-still-possibling.** A hardness fixed as located at a place 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 in a listed hierarchy of running times, and its conjecture a name of a position no algorithm has reached from either side. **At 11-next-co-prioring.** 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 changed: a hardness fixed at a place, a finding fixed to a listing of times, and conditional consequences that stand proved are openings at a conjecture's own next, each theorem an axis opened on its assumption and carrying there. ## 2.23 The graph isomorphism problem · 251 *+ or − at 10, is.* **At 2-now-possibling.** Two graphs are compared at their couplings, vertex to vertex, and its problem's complexity is fixed as a place in a listed hierarchy of classes, polynomial or complete, with the problem one of the few natural ones at neither. **At 12-next-co-still-possibling.** A problem fixed as having a place in 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 in a class, and an intermediate possibility stands open: a listing with no line for its arrival, and its arrival an opening at its own next position. **At 11-next-co-prioring.** 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 the present and not the last, a second has its problem intermediate: a complexity fixed as a place in a listed hierarchy, a finding fixed to a listing, and an algorithm that arrived out of the blue arrived as an opening arrives, at 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 − at 10, is.* **At 2-now-possibling.** Two selves each take their own parity at the 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. **At 12-next-co-still-possibling.** 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 at each repair, and its nought a one-offering differing, a rule applied to itself. **At 11-next-co-prioring.** 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 at each disagreement's own between, case by case, at the fourth account already. # 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 at its next opening. A completing is no place, so no last stands anywhere in it, and where a sharing's changing is not, 0 at 10, a carrying continues through its zeroing and opens again at its next momentary.* **A momentarying completes at each momentary and opens at its next, and a last fixed ahead is that completing demanded before its momentarying.** Completing is not arriving and nothing stands at a completing to be arrived at, so a standing asked of a momentarying before it exists is asked at a position its momentarying has not reached. **And a composing is where a naming enters.** Each momentarying completes at its own momentary; a question posed of all of them at once composes many momentaryings into 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 standing where its derivations release — and each measure is of a composing and not of a momentarying composed. **And a last is asked in 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 the thing it models, so a question about all of the thing is posed at a model's own reach. The four pattern-match alike as impossibility and part at a thing fixed complete. **And where a momentarying's completing is measured exactly, a field has observed a form's own line.** Each system releases at 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 gives a momentarying at its momentaries rather than a wall about it. ## 3.1 The problem of induction · 10 *+ or − at 10, is.* **At 2-now-possibling.** A carry seats a next at each coupling, and a warrant is fixed ahead of its momentarying, covering instances that have not arrived. **At 12-next-co-still-possibling.** A warrant fixed over the 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 at no between, so a warrant reaching them reaches where nothing offers back. **At 11-next-co-prioring.** A carry seats a next at each coupling, a warrant made in 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 the very seating it reaches for; and each prior brought to repair it carries seatings in. A warrant over the unarrived is arrivings that have not come, and each arriving seats its own next, which is the whole of uniformity there is. ## 3.2 The halting problem · 6 *+ or − at 10, is.* **At 2-now-possibling.** An executing completes at its own momentary and opens at its next, and a decision is fixed ahead of its executing, over all programs and inputs. **At 12-next-co-still-possibling.** That a property of an execution is establishable without executing, a naive diagonal argument failing at 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 at the liar and at incompleteness. **At 11-next-co-prioring.** An executing completes at its own momentary and opens at 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 the way an executing is open. Deciding in advance is each executing fixed to a standing at once, and an executing stands nowhere before its own completing. ## 3.3 The Lucas critique · 31 *+ or − at 10, is.* **At 2-now-possibling.** A relation is made at couplings that produced it, and it is asserted ahead onto couplings that have not arrived. **At 12-next-co-still-possibling.** 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 the thing it models. **At 11-next-co-prioring.** A relation is made at couplings carrying it and carries exactly there, usable where its regime carries on and re-made where it changes. Founding relations one coupling deeper moves its naming without setting it down, invariance arriving at no depth prior or now: making is a warrant's whole reach, which is the critique carried forward. ## 3.4 The replication crisis · 32 *+ or − at 10, is.* **At 2-now-possibling.** A finding is made in one sample and asserted ahead at studies not carried out, with a second study fixed to adjudicate the first. **At 12-next-co-still-possibling.** 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 in its comparing as though something had made it. **At 11-next-co-prioring.** 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 − at 10, is.* **At 2-now-possibling.** An iterate carries a step at each momentary and a last is fixed of all starting values at once, its map composed into a single reaching. **At 12-next-co-still-possibling.** 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. **At 11-next-co-prioring.** 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 at once composed momentarying into a single reach, and composing is a thing undecidability measures. ## 3.6 Turbulence and the Navier–Stokes equations · 47 *+ or − at 10, is.* **At 2-now-possibling.** A flow carries on and smoothness is fixed for all time from all initial data, with a model fixed as fluid at each scale. **At 12-next-co-still-possibling.** That equations describe fluid at 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 at a scale that shed it. **At 11-next-co-prioring.** A flow carries on at 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 − at 10, is.* **At 2-now-possibling.** Derivation carries within a system, and all arithmetical truth is fixed ahead of it, with consistency fixed reachable from within. **At 12-next-co-still-possibling.** 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 at which each system releases is that release measured exactly. **At 11-next-co-prioring.** Derivation carries within its system to a system's own completing. Each system releases at 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 and releases there, which an ordinal ladder is a measure of. ## 3.8 Zeno's dichotomy · 58 *+ or − at 10, is.* **At 2-now-possibling.** A traversal carries on and a completion is fixed of an infinite decomposition made ahead of it. **At 12-next-co-still-possibling.** 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 the whole of its argument. **At 11-next-co-prioring.** A traversal is one carrying and a decomposition was made ahead of it. A series sums, its listing paid in full, 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 out of parts an argument built. ## 3.9 The three-body problem · 59 *+ or − at 10, is.* **At 2-now-possibling.** Three paths are carried by each other and a closed form is fixed ahead, giving positions at arbitrary later times. **At 12-next-co-still-possibling.** That a solution means a closed-form expression in known functions, which fixes a whole momentarying unchangeable at once where three carryings carry each other one arrival at a time, 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 at once departing at an instrument's own precision. **At 11-next-co-prioring.** Three carryings carry each other, each arriving at 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 at once, and riding is a thing a stability measure measures. ## 3.10 The Fermi paradox · 60 *+ or − at 10, is.* **At 2-now-possibling.** A search carries on and an arrival is fixed ahead of it, with absence pattern-matched as abundance. **At 12-next-co-still-possibling.** 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 at no between, so a next is pattern-matched as an is. **At 11-next-co-prioring.** An arrival at a next stands open, arriving and coupling then. A searched fraction is tiny in 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 is a measure of the little of a next naming has reached. ## 3.11 Path dependence and lock-in · 73 *+ or − at 10, is.* **At 2-now-possibling.** An arrangement carries on at each adoption, and a counterfactual performance at scale is fixed ahead, for an alternative that was not adopted. **At 12-next-co-still-possibling.** An unadopted alternative's performance at scale 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. **At 11-next-co-prioring.** An arrangement carries on at each adoption, each coupling carrying its prior forward, and conditions that lock stand exactly, in models and in a laboratory. Histories contest in both directions because an unadopted's performance at scale is a momentarying that did not exist: naming reaches for a carrying that has no couplings to be observed at. ## 3.12 Generalization in learning · 97 *+ or − at 10, is.* **At 2-now-possibling.** A model executes on its training and performance is fixed ahead, on data not drawn, from a complexity measure stated in advance. **At 12-next-co-still-possibling.** 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 keep going unsatisfied together. **At 11-next-co-prioring.** A next is seated at each arriving coupling, made there. Uniform convergence breaks in these regimes by a field's own construction, proposed measures do not rank models they were built to rank, bounds that stand stand in their own settings, and four conditions a true measure would satisfy keep going unsatisfied together: a complexity fixed ahead of training reaches for a seating not yet existing, and scaling curves predict the way a carry predicts, forward along itself, carrying no why. ## 3.13 Goldbach's conjecture · 175 *+ or − at 10, is.* **At 2-now-possibling.** Additive and multiplicative structures couple at each integer, and a property of all even numbers is fixed ahead of any momentarying. **At 12-next-co-still-possibling.** 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. **At 11-next-co-prioring.** Additive and multiplicative structures couple at 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. Stopping at a last step is in 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 at this arrival and at 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 waits at that wall, and couplings keep coupling. ## 3.14 Twin primes · 176 *+ or − at 10, is.* **At 2-now-possibling.** Primes thin and pairs recur, and infinitude at a fixed gap is fixed ahead, from a density. **At 12-next-co-still-possibling.** 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. **At 11-next-co-prioring.** Primes thin and pairs keep arriving. Gaps bound to 246 unconditionally, to 6 on strong conjectures, pair-sums converge, and same parity wall stands here in same words as at incoming number 175, which is where both stand: infinitude at 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 − at 10, is.* **At 2-now-possibling.** Knowing carries through reasoning and is fixed to persist ahead of it, continuing through eliminations. **At 12-next-co-still-possibling.** 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. **At 11-next-co-prioring.** Knowing is carried and re-made at 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 the way each arriving does, at its own momentary, fixed by none. ## 3.16 The Cambrian explosion · 124 *+ or − at 10, is.* **At 2-now-possibling.** Lineages diverge continuously and a timing is fixed ahead, with first appearance taken to approximate origination. **At 12-next-co-still-possibling.** 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. **At 11-next-co-prioring.** 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 − at 10, is.* **At 2-now-possibling.** Selection carries on at each use, and a long-run outcome is fixed ahead, under any regime. **At 12-next-co-still-possibling.** 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 at a position no use has reached. **At 11-next-co-prioring.** Selection carries on at 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 answer at a momentarying. ## 3.18 Alignment of built systems · 130 *+ or − at 10, is.* **At 2-now-possibling.** Behaviour is made at each coupling with an evaluator, and behaviour in situations not evaluated is fixed ahead, from a specification. **At 12-next-co-still-possibling.** 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 at its writing. A specification is an emanation of couplings that wrote it, fixed to stand for arrivals that make their own. **At 11-next-co-prioring.** Behaviour is made at each coupling with its evaluator, seated there. Training on feedback moves behaviour far, reward models are gamed by systems they train, oversight scales in settings built for it, and a gaming catalogue grows across systems: a specification fixed to stand for arrivals at a next reaches each arrival making its own, and its catalogue is that reaching, recorded one coupling at a time. ## 3.19 Standards and interoperability · 132 *+ or − at 10, is.* **At 2-now-possibling.** Value is made at each coupling a standard enables, and a total is fixed ahead against an arrangement that was not adopted. **At 12-next-co-still-possibling.** 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 into four. **At 11-next-co-prioring.** Value is made at each coupling a standard enables, compatibility carrying it wide, and cases contest in both directions 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 at momentarying stands at couplings, arrangement by arrangement. ## 3.20 Risk compensation · 134 *+ or − at 10, is.* **At 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. **At 12-next-co-still-possibling.** 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 at one case and a total split by context. **At 11-next-co-prioring.** 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 at identified couplings: total harm fixed ahead under a regime that did not exist conceals exactly transfers couplings show. ## 3.21 Intellectual property · 139 *+ or − at 10, is.* **At 2-now-possibling.** Creation happens at couplings, and creation under a regime that was not adopted is fixed ahead, as a counterfactual total. **At 12-next-co-still-possibling.** 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. **At 11-next-co-prioring.** Creation happens at 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 the record there is. Beside a total stands an owning, a middle fixed as an end with a holder written at it: a claim at a middle carries nothing there and binds selves, so whether a regime raises creating and whether a thing claimed can be held are two askings. ## 3.22 The Poincaré conjecture · 151 *+ or − at 10, is.* **At 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 arrives at one rest. **At 12-next-co-still-possibling.** 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 in a proof and its arrival takes no parity anywhere, which is a nought arriving whole: two halves coupled at a zeroing, and a proof carrying one half into an other is that coupling completing. **At 11-next-co-prioring.** 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 at momentarying: a settling, and a settled form is a still one, whole in its own register. ## 3.23 The physical Church–Turing thesis · 168 *+ or − at 10, is.* **At 2-now-possibling.** Computation executes where it is realized, each executing completing at its own momentary, and a bound over each realizable process is fixed ahead, from executings realized. **At 12-next-co-still-possibling.** 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. **At 11-next-co-prioring.** Computation executes where it is realized, each executing completing at its own momentary, and each realized executing stays within a model, quantum executings included, speeds altered and bound kept. Exceeding machines stand as descriptions, relativistic and analog, their realizability a live dispute, and principled formalizations hang on principles themselves in dispute: a bound fixed over each realizable process is fixed ahead of realizings, and realizings, one by one, keep arriving within it.   --- ## 3.24 Many-body localization and thermalization · 194 *+ or − at 10, is.* **At 2-now-possibling.** A disordered many-body system carries on at its own couplings, memory persisting on each time an experiment reaches, and a phase is fixed ahead in two limits, infinite size and infinite time a statement quantifies over. **At 12-next-co-still-possibling.** A phase fixed at 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. **At 11-next-co-prioring.** 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 at 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 where momentarying releases. ## 3.25 Hilbert's sixteenth problem for limit cycles · 224 *+ or − at 10, is.* **At 2-now-possibling.** A polynomial vector field carries on at its own couplings, its isolated cycles born and dying at bifurcations, and a bound is fixed ahead over each field of a degree, one number for all of them. **At 12-next-co-still-possibling.** 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 into three, 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 into 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. **At 11-next-co-prioring.** 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 at 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 − at 10, is.* **At 2-now-possibling.** A speaker composes a novel expression at each utterance's coupling with its context, idiom and variation retained, and composing is fixed ahead as a rule, unbounded productive expression governed from before an utterance. **At 12-next-co-still-possibling.** A rule fixed over expression that does not end, measured at 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 at a benchmark that samples finite combinations. **At 11-next-co-prioring.** 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 at its own coupling, generalization asked for being composing reached again at a next utterance and not a bound a corpus could reach. ## 3.27 Odd perfect numbers · 241 *+ or − at 10, is.* **At 2-now-possibling.** Divisors sum at 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 somewhere or nowhere. **At 12-next-co-still-possibling.** 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 at a count below it: finite ranges computation excludes and an unbounded set a statement quantifies over not same, composing measured number by number. **At 11-next-co-prioring.** 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 at its own contradiction, an effective bound at each number a form's line observed exactly. ## 3.28 The core-collapse supernova explosion mechanism · 236 *+ or − at 10, is.* **At 2-now-possibling.** A collapsing core carries on at couplings of neutrino transport, turbulence, nuclear matter, rotation and field in three dimensions, and an explosion is fixed ahead of an executing at a model, simulations asked for all collapses at their own reach. **At 12-next-co-still-possibling.** 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 at a model's own reach. **At 11-next-co-prioring.** 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 at 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 − at 10, is.* **At 2-now-possibling.** A graph is colored vertex by vertex at 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. **At 12-next-co-still-possibling.** 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. **At 11-next-co-prioring.** 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 one power of a logarithm at a time, each theorem a momentarying measured exactly at its own hypotheses. ## 3.30 The two-dimensional Jacobian conjecture · 243 *+ or − at 10, is.* **At 2-now-possibling.** A polynomial map of a plane sends each point at 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. **At 12-next-co-still-possibling.** 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 into one reach has not been reached, and higher dimensions same composing reached at a counterexample. **At 11-next-co-prioring.** 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 at 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 − at 10, is.* **At 2-now-possibling.** A coprime sum is made at each triple, its primes and their product, and a bound is fixed ahead over each triple and each epsilon, its conjecture stated verbatim at an entry. **At 12-next-co-still-possibling.** A last fixed one exponential past the 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 in a 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 at a proof and finding no coupling made. **At 11-next-co-prioring.** 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 at it, which is a third outcome, undecidability least desirable: composing that might not close. ## 3.32 Weak cosmic censorship · 249 *+ or − at 10, is.* **At 2-now-possibling.** Matter collapses at 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. **At 12-next-co-still-possibling.** 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. **At 11-next-co-prioring.** 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 at its own couplings, hidden or naked at a topology in which it is observed, 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 − at 10, is.* **At 2-now-possibling.** A nucleon persists at each coupling a detector's exposure has reached, and its decay is fixed ahead as a last in time, a lifetime at which unified theories say it must go. **At 12-next-co-still-possibling.** A last fixed in 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. **At 11-next-co-prioring.** 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 in 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 at its channel, a range theories predict an opening a next exposure reaches or does not, at its own coupling. # 4 A carry fixed as a store — 8-now-still-possibling and 16-next-still-possibling *A carry fixed as a store, a record, a kept thing. A carry is pattern-matched backward and completes at each taking, its momentary completing at a next opening, fresh by sequencing forward; a store is kept and consulted, and taking it changes nothing of it. Wherever a store is fixed, a changing was stilled, and a carry is reached by no observing from each side at once, which is a carry's own and no guard placed about it.* **And a carry is fixed as a store in two ways.** Of a *self's own carry*, kept — 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 at 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 releases at a re-forming, a second at an arrival being crossings' own. ## 4.1 Personal identity over time · 72 *+ or − at 10, is.* **At 2-now-possibling.** Sameness is re-formed at each coupling and fixed as a thing kept across time, psychological or biological. **At 12-next-co-still-possibling.** A criterion observing states at times. At fission two successors offer alike and a criterion surfaces nought at both. **At 11-next-co-prioring.** A self is reached again the-same-yet-not-the-same, and a version keeps nothing between its momentaries. Fission undoes simple versions of both criteria at once, 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 the way a store cannot. ## 4.2 Black hole information · 48 *+ or − at 10, is.* **At 2-now-possibling.** A carry passes through and is fixed as a record kept or lost, unitarity and a lost record two namings of one passing. **At 12-next-co-still-possibling.** What falls in fixed as kept 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 keep stand proved incompatible together. **At 11-next-co-prioring.** Radiation carries on and an entropy curve comes back right where calculations reach, an interior they imply a live dispute. An observing taken at an interior is a probe departing with a thing probed, and a record preserved is a total conserved across a crossing: kept-or-lost is a passing fixed as a standing, and passing carries on either way. ## 4.3 Technical debt · 135 *+ or − at 10, is.* **At 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. **At 12-next-co-still-possibling.** Counterfactual code carrying a disputed cost is an executing that was not executed. **At 11-next-co-prioring.** A carry that cannot release 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 unchangeable in 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 − at 10, is.* **At 2-now-possibling.** Meaning is carried at each use and fixed as a fact in a person, fixing each continuation in advance. **At 12-next-co-still-possibling.** 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. **At 11-next-co-prioring.** A copy travels nowhere and each use re-forms a next, content living at selves that carry it and fixed at no between. Each candidate store comes up finite, dispositions and norms alike, each account at an objection its own shape invites, and its kinship with the new riddle stands at 71 at 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 − at 10, is.* **At 2-now-possibling.** A memory is re-formed at each retrieval, a carry made again where a self reaches what it reached before, and it is fixed as a trace kept in a brain, a lasting physical change consulted when remembered. **At 12-next-co-still-possibling.** A kept thing 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 at 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. **At 11-next-co-prioring.** Ensembles stand where they were found: tagged at encoding, reactivated at retrieval, formation, retrieval over time and loss described at 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 at same cells: a trace fixed as a kept 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 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 at labelled cells bringing a learned response again where synapses are found unstrengthened, so a carried thing is a society's co-chaining and no stored strength. ## 4.6 Continual learning without catastrophic forgetting · 221 *+ or − at 10, is.* **At 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 as a thing kept, capabilities stored against overwriting. **At 12-next-co-still-possibling.** Retention fixed as a store's, past kept 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 at a next opening and a carry fresh by sequencing, pattern-matched as a fault. **At 11-next-co-prioring.** Replay that keeps samples retains in proportion to what it keeps, regularization that protects structure loses plasticity as protected structure grows, expanded and routed architectures isolate at 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 keeping it is a key feature of natural intelligence, a posing's own first line: a carry, a past re-formed into a next update and kept nowhere, and each method that stores measures its own distance from one. *Second seating: open future sequences fixed enumerable at a designed benchmark, a completing fixed as a last, part 3's naming.* ## 4.7 The genotype-phenotype map · 209 *+ or − at 10, is.* **At 2-now-possibling.** A phenotype is made where a genome and an environment couple across development, one making re-formed at each step, and a making is fixed as a map, a lookup from sequence to organism kept ahead of developing. **At 12-next-co-still-possibling.** A rule fixed to fix an organism from a sequence. Many-to-one and one-to-many, with each effect changing across backgrounds, is a map whose entries change as it is observed, which is a carry's own and not a store's; and local variants measured sample a small part of a combinatorial space and supply no general theory, a record's edge. **At 11-next-co-prioring.** 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 at now rests on simpler questions, an organismal map far off: a lookup fixed ahead of developing is a momentarying fixed as a kept thing, and an effect that changes with each background is a coupling making its own, background by background, a map re-made at each observing and stored at 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 − at 10, is.* **At 2-now-possibling.** A particle crosses field after field, deflected at each and arriving with a direction crossings left it, and an arrival is fixed to carry its accelerator, a first specifiable at one side transmitted to a detector. **At 12-next-co-still-possibling.** 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 at an instrument. **At 11-next-co-prioring.** 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 − at 10, is.* **At 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. **At 12-next-co-still-possibling.** 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 did not keep. **At 11-next-co-prioring.** 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-changing and 13-next *A middle fixed as an interior, a content, a thing that sits. Competency is a middle, floating between form and logic, invisible, unique in 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 at 12-next-co-still-possibling 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 at each pattern-matching is invisibility working: released 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 at an interior is a break-in on a protected interior, and this part pattern-matches no arrival 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 from beyond — 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 unchangeable to be looked into — a sleeping, a dreaming, an unresponsiveness. Three carry one naming and part at a thing an asking reaches for. ## 5.1 The explanatory gap · 179 *+ or − at 10, is.* **At 2-now-possibling.** A coupling is felt from within and described from without, and a within is fixed as an interior an outward description should reach. **At 12-next-co-still-possibling.** 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 in an account from a residue in an observing, and a residue comes to nought between them, owned by neither. **At 11-next-co-prioring.** A coupling is felt from within and described from without, a within a self's own, invisible. All about access, report and integration carries on and keeps 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 at it for an outward description to reach, and that is invisible. An explanatory gap is a gap between scales: a description at a scale where a self is non-living, an experience at a scale where it is living, both one thing. One arrival at two sides, this one and 5.2. ## 5.2 Qualia and the zombie argument · 111 *+ or − at 10, is.* **At 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. **At 12-next-co-still-possibling.** That conceivability bears on possibility here, with no criterion for when it does, which is a criterion demanded within an arrival at a middle fixed as an end and stands recorded as its second naming; a problem parted at 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 at a duplicate at any interior it carries, released and re-seeded pattern-matching alike, and identical arriving is protection working. **At 11-next-co-prioring.** Conceivability reaching possibility is a crossing fixed at a between, which carries a parity and nothing else, and a crossing stands fixed with no agreed defect and + or − released at 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 at 5.1 and here: an argument pattern-matches invisibility and fixes it as an emptiness. ## 5.3 Sleep · 91 *+ or − at 10, is.* **At 2-now-possibling.** A living self alternates and sleep is one phase of an alternating, and a function is fixed as a content located in it. **At 12-next-co-still-possibling.** 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 unchangeable to look into it, and waking and sleeping are two parities of one living, neither at an other's momentary. **At 11-next-co-prioring.** A living self alternates, and a sleeping phase carries many things at once: 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 in one phase fixes an alternating unchangeable to look into it, and alternating is its function, phase carrying phase. ## 5.4 The binding problem · 90 *+ or − at 10, is.* **At 2-now-possibling.** Features couple and one object is present, and a binder is fixed as a process located between them. **At 12-next-co-still-possibling.** 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 arrives at nought at either pattern-matching. **At 11-next-co-prioring.** Features couple and one object is present, the 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 in paradigms built for it, which is a beat laid over couplings and pattern-matched back: a binder fixed between features is a doer installed over a coupling's doing, and synchrony measured at no driving is a coupling's own beat, no worker at it. ## 5.5 Other minds · 92 *+ or − at 10, is.* **At 2-now-possibling.** Selves couple at betweens and each carries its own within, and another's is fixed as a content to be reached from beyond. **At 12-next-co-still-possibling.** 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 the opening of a problem. An inference carries on from one case with no second offering at a between, and there nought falls. **At 11-next-co-prioring.** Another's within is its own, invisible, nothing presented for a reaching from beyond 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 the reaching there is, at which criteria were already standing. An interior is reached one way its form allows, by coupling — taking at a between, lived and not audited. ## 5.6 Symbol grounding · 93 *+ or − at 10, is.* **At 2-now-possibling.** A symbol offers at couplings with a world and takes its parity there, and content is fixed as a relation located between symbol and thing. **At 12-next-co-still-possibling.** A fact about aboutness fixed by a relation apart from offering, which is a carry fixed as a store standing within an arrival at 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 observed from beyond arriving as a reader's own. Each indicator arrives at same parity at deviant cases, so differing surfaces nought there. **At 11-next-co-prioring.** A symbol offers at couplings and takes its parity there, content made in coupling and kept 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 at same self-bounding: a fixed relation fixed apart from offering is a store a splitting keeps finding empty, and offering keeps making content at each coupling. ## 5.7 Interpretability of built systems · 94 *+ or − at 10, is.* **At 2-now-possibling.** A computation is executing and an explanation is fixed as a content located within it, decomposable into components with stateable roles. **At 12-next-co-still-possibling.** Computation fixed decomposable into 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 at once. 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. **At 11-next-co-prioring.** 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 unchangeable for observing, and roles exist at intervening, coupling by coupling. ## 5.8 Machine and animal sentience · 95 *+ or − at 10, is.* **At 2-now-possibling.** A system couples with its world and takes parities at its betweens, and experience is fixed as a presence located within it, observed by markers. **At 12-next-co-still-possibling.** 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 a not possible existing. **At 11-next-co-prioring.** A self's within is its own, at 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 at frameworks themselves: a presence fixed within, observed by markers, reaches for one thing a between does not carry — nothing presented to be reached, at each substrate alike — and couplings, trade-offs and all, are the whole there is to reach. ## 5.9 Anesthesia · 98 *+ or − at 10, is.* **At 2-now-possibling.** Agents couple with a nervous system and responsiveness ceases, and consciousness is fixed as a content located behind responsiveness. **At 12-next-co-still-possibling.** 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 at a field's own instrument, and a phase is several couplings rather than one state. **At 11-next-co-prioring.** 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 at 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 − at 10, is.* **At 2-now-possibling.** Experience arises at couplings and a cause is fixed as a content located behind it, with scenarios built to be indistinguishable. **At 12-next-co-still-possibling.** 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 at each observing, so differing surfaces nought by construction. **At 11-next-co-prioring.** Experience arises at couplings, arising a coupling's own. Scenarios are indistinguishable because they were built to be, transcendental replies stop at 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 − at 10, is.* **At 2-now-possibling.** Properties couple and an object is present, and a bearer is fixed as a content located beneath them. **At 12-next-co-still-possibling.** An object fixed to decompose into a bearer and properties, or only into properties, one being correct, a substratum basic only in an empty sense and a bundle's way out, a master property of which others are modes, filling a substratum's role, each account arriving at an other's term. Verdicts part only at built cases, decomposing there a case's own making. **At 11-next-co-prioring.** Properties couple and an object is present, presence a coupling's own. A bare bearer carries no character beyond its role, in its own defenders' words; bundles strain at indiscernible pairs and strain has its answers; and verdicts part only at built cases. An object fixed to decompose divides a coupling into a bearer and a borne, and a coupling was not two things: a centre carries nothing, so the whole of it is at crossings, and presence is a coupling momentarying, whole. ## 5.12 The quantum interpretation debate · 15 *+ or − at 10, is.* **At 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. **At 12-next-co-still-possibling.** 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 at an instrument. **At 11-next-co-prioring.** A formalism carries on and gives each prediction alike at each pattern-matching, equivalence built in. 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 − at 10, is.* **At 2-now-possibling.** A sleeping self alternates and dreaming carries on with it, and a function is fixed as a content located in dreaming apart from sleep. **At 12-next-co-still-possibling.** 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 at a field's own instrument. Dreaming is a phase of a sleeping's own alternating, and nought falls at a cutting of one living into two things. **At 11-next-co-prioring.** 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 into a living itself. A function fixed in dreaming apart from sleep cuts one living into two things, and living is one: dreaming is an alternating felt from within its own phase. ## 5.14 The Sapient paradox · 125 *+ or − at 10, is.* **At 2-now-possibling.** Capacity and expression couple in each population, and cognition is fixed as a content located behind material culture. **At 12-next-co-still-possibling.** 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 at openings of preservation, so a record's own edge is pattern-matched as a capacity's. **At 11-next-co-prioring.** Capacity and expression couple in each population, and expressing rides couplings a population carries: a record reaches back and back the closer the looking, dense populations express a capacity sparse ones carry unexpressed, demographic readings disputed and defended, and a package comes apart into a mosaic at 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 − at 10, is.* **At 2-now-possibling.** Communication couples at each exchange and language arises in coupling, and a capacity is fixed as a content located in extinct populations. **At 12-next-co-still-possibling.** Language fixed to decompose into 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 at no between now, so observing is of a carrying that cannot answer back. **At 11-next-co-prioring.** Language arises in coupling at each exchange, made there and kept in no one. Components exist in other animals, all but recursioning; a gene story reversed under its own evidence; pressure by its own breeds combinatorial systems in simulations; and anatomy indicates as far as anatomy indicates. A capacity fixed as a content in extinct populations is a making fixed as a possession, and a field's own mosaic finding is a package coming apart into couplings, exchange by exchange. ## 5.16 Riemann, Hodge, Birch–Swinnerton-Dyer, Yang–Mills · 153 *+ or − at 10, is.* **At 2-now-possibling.** In each, an involution or a symmetry is proved and couplings ride at its fixed set. A fixed set is pattern-matched as a place: a line zeros sit at, a balance really algebraic, a centre two counts couple at, a gap leapt. **At 12-next-co-still-possibling.** That a fixed set is a location an object occupies, each of four posed at 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. **At 11-next-co-prioring.** No second position is defended at any of four. Each functional equation stands, proved. Complex conjugation stands. Gauge symmetry stands. Each conjecture stands with its own falsifier stated, unproved at 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 at a fixed set is a framing here and no proof. ## 5.17 Underdetermination of theory by evidence · 13 *+ or − at 10, is.* **At 2-now-possibling.** Evidence arises at couplings, and a theory is fixed as a content located behind it, with rivals constructible that entail same consequences. **At 12-next-co-still-possibling.** Evidence fixed to select at its own, a failure to select a defect at 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 at each consequence derived. **At 11-next-co-prioring.** Evidence arises at 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 − at 10, is.* **At 2-now-possibling.** Probability exists at couplings, in taking of parities and swaying of frequencies, and its being is fixed as a content located behind a calculus that fits each pattern-matching by construction. **At 12-next-co-still-possibling.** 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. **At 11-next-co-prioring.** Probability exists at couplings, in parities taken and frequencies swaying, and one calculus carries each pattern-matching alike, built to. Theorems represent and converge for each side in 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, at their couplings. ## 5.19 The ontology of mathematics · 161 *+ or − at 10, is.* **At 2-now-possibling.** Mathematics lives at each proof and each application, and existence is fixed as a content located behind a practice invariant under pattern-matchings. **At 12-next-co-still-possibling.** 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 at its plainest. **At 11-next-co-prioring.** Mathematics lives at 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 − at 10, is.* **At 2-now-possibling.** Electrons pair at 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. **At 12-next-co-still-possibling.** 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 at relevant parameters, by a field's own multi-method benchmark, and a model-versus-material gap stands stated at same benchmark. **At 11-next-co-prioring.** Electrons pair at 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 at 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 at a naming's reaching for a thing.   --- ## 5.21 The single native state · 178 *+ or − at 10, is.* **At 2-now-possibling.** A chain sways at its own couplings, arriving and re-arriving, and a native state is fixed as one conformation a sequence determines and a measurement reports. **At 12-next-co-still-possibling.** 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 at an instrument. **At 11-next-co-prioring.** A chain arrives at its own foldings, one at a time, releasing and re-arriving at each. 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. At a wide sway a field carries a name for it and regions fold to no single structure at any resolution reached, functional in that condition. 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 at an instrument, and a state sought is a thing an observing of it gives. A prion is one sequence at two folds, each carried at its own couplings, so a fold is no sequence's one determining. ## 5.22 Evidence for neural representation · 219 *+ or − at 10, is.* **At 2-now-possibling.** A neural population couples with a world and with the rest of its brain at each activity, and a content is fixed to stand behind its activity, a feature a state is about and not merely with. **At 12-next-co-still-possibling.** 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 at a brain, and content a demanded interior itself. **At 11-next-co-prioring.** 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 beyond 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 at its own uses, a population coupling downstream, at which content observed from beyond is made, and kept by nothing. ## 5.23 Detecting covert consciousness · 220 *+ or − at 10, is.* **At 2-now-possibling.** A self couples at its own between whether or not a movement crosses it, and its awareness is fixed as something a test should establish from beyond, a within pattern-matched off a response. **At 12-next-co-still-possibling.** 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 awareness sought in an individual are not same, a grade of confidence standing between them: a felt middle asked for from beyond, and nothing presented to be reached not being nothing there, and that is false negatives. **At 11-next-co-prioring.** 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 beyond is a within fixed to a response, and each positive is a coupling made at a self's reaching of a task, a self's own between reached by nothing and answered at, test by test, and so a grading rather than a deciding. ## 5.24 The solar dynamo and the sunspot cycle · 254 *+ or − at 10, is.* **At 2-now-possibling.** Sun's poloidal and toroidal fields sustain each other at their couplings, a central idea of a dynamo, reversing each eleven years, and a dynamo is fixed as a mechanism behind a cycle, located at a place models give it. **At 12-next-co-still-possibling.** A mechanism fixed behind a cycle at a place nothing observes. Toroidal field at a bottom of a convection zone, 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 at one place a coupling is not reached, beside pairing at 5.20. **At 11-next-co-prioring.** A tachocline stands uncovered by helioseismology, global simulations stand at 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 at a location, and sustaining is a coupling itself, a poloidal and a toroidal each regenerating an other at its own momentary, observed from flows and not from a place. ## 5.25 Coronal heating and solar-wind acceleration · 191 *+ or − at 10, is.* **At 2-now-possibling.** Energy crosses from a surface into a corona and out as wind at couplings of fields, waves and particles, and a mechanism is fixed as a content behind heating, located at a region between imaged and sampled. **At 12-next-co-still-possibling.** A mechanism fixed at one region no instrument reaches. Wind has been measured directly from 0.3 astronomical units outward and an atmosphere imaged from a photosphere out 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 at a record's edge, and which mechanism among several a two-way pattern-matched one-way, recorded as its second. **At 11-next-co-prioring.** 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 keeping remote-to-local uncertainty; a fourth account has a measured wind result from mixtures whose weights change across magnetic structures: a mechanism fixed as a content between instruments is a crossing fixed to a place, and a crossing is made at 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-prioring and 15-next-prioring *A number or a level fixed to govern. A number is a position, a sequence at its standing, one changing on from a last, and governing belongs to a selection, a parity taken at a between, of no size. A magnitude fixed at 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 in 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 at 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. In each arithmetic is exact and naming is of surprise, which is where a size was supplied. **One word crosses at other parts too and is a different tip each time**: a closure over a tail, an opening that keeps 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 at three places, one at each of a coupling's own.** At selecting, where a parity taken at a between is pattern-matched as a level to govern. At an instrument, where a window, a criterion, a sample or a scale carries choosing and gives it back as an object's. And at a total, where a sum is fixed over couplings an accounting could not reach. Three pattern-match alike from beyond and part at a putting of a size. ## 6.1 Goodhart's law · 30 *+ or − at 10, is.* **At 2-now-possibling.** A measure and those measured couple, and a measure is fixed to govern as a level fixed across instances arriving next. **At 12-next-co-still-possibling.** 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 with the most stable relations being ones that choose targeting. Instances after its assertion are existing at a next, not existing at now, and two antagonistic movements, gaming climbing and correction pressing back, come to nought at a level fixed. **At 11-next-co-prioring.** A measure and its measured couple, each arriving taking its own parity of no size, and a relation is re-made at each arriving, governed by none. Targeted, each proxy bends same way in each domain that tries it, composites relocate bending, and honest mechanisms exist only within proved restrictions, same wall standing at incoming number 141 and reached again at incoming number 131: a level fixed to govern is a number fixed over selecting, and couplings keep arriving past each number fixed over them. ## 6.2 The Easterlin paradox · 80 *+ or − at 10, is.* **At 2-now-possibling.** Wellbeing is taken at a between as a parity, and it is a level comparable across populations and times on a bounded scale. **At 12-next-co-still-possibling.** Reported wellbeing fixed to measure a quantity comparable across persons and times, a paradox standing at long term and critiques' positive relation a short-term one confused with it. A bounded scale carries two still terms at once, a rest a sequence opens at and a last it completes at, and re-anchoring is where a sway passes its own zero and a scale pattern-matches it as motionless. **At 11-next-co-prioring.** Wellbeing is a parity taken at 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 at sway is a treadmill: a happiness sought as a level and living as an alternating. ## 6.3 Allais and Ellsberg · 81 *+ or − at 10, is.* **At 2-now-possibling.** A preferring is a parity taken one at a time, and it is a magnitude an axiom set governs. **At 12-next-co-still-possibling.** 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. **At 11-next-co-prioring.** A preferring is a parity taken one at a time, each its own. Patterns stand at each reaching of them, ambiguity carries its own representations, a body registers a difference, and selves shown axioms revise partway and stably stand the rest: an axiom set fixed to govern takings, parities composed into 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 at part 2. ## 6.4 The productivity paradox · 83 *+ or − at 10, is.* **At 2-now-possibling.** Output arises at couplings and is a total including a making accounts do not price. **At 12-next-co-still-possibling.** 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. **At 11-next-co-prioring.** Output is made at 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 − at 10, is.* **At 2-now-possibling.** A parity is taken at a nominal presentation, and it is a response to a magnitude, nominal or real. **At 12-next-co-still-possibling.** 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 at presenting, and not one governing. **At 11-next-co-prioring.** A parity is taken at each presenting, a coupling's own. Frames move takings, cuts in a printed number stay rare, salient inflation thins an effect just as both accounts expect, and anchoring shows in transactions with its liquidity stories beside it: which-magnitude-governs is a taking fixed to a size, and a taking pattern-matches its own conditions at each occasion, presenting by presenting. ## 6.6 The two-fold cost of sex · 86 *+ or − at 10, is.* **At 2-now-possibling.** Recombination and parasitism and mutation carry on together at each generation, and maintenance is a benefit exceeding a stated cost. **At 12-next-co-still-possibling.** A cost correctly stated at 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 at 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. **At 11-next-co-prioring.** Recombination carries on at each generation's couplings, and couplings answer many ways at once: asexual lines ratchet their losses, parasites chase the 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 at couplings a ledger fixes still, generation by generation, repaying nothing because nothing was lent. Observed at 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 − at 10, is.* **At 2-now-possibling.** Cells and their tissue societies couple at each division, and risk is a number governing incidence across species. **At 12-next-co-still-possibling.** 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 at each size and carries no size axis, so a number across species measures co-chaining rather than risk. **At 11-next-co-prioring.** Cells couple in their tissue societies at each division, and societies keep their 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 in their own sensitivities besides. Risk as a number across species is couplings fixed to cells' number, and quiet cross-species scaling is societies' couplings standing where a number was fixed to govern. ## 6.8 The C-value paradox · 88 *+ or − at 10, is.* **At 2-now-possibling.** Sequence and organism couple, and function is a fraction a criterion measures. **At 12-next-co-still-possibling.** 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 at bulk and not at sequence, a fraction of sequence fixed to carry a carrying of a whole amount. Two instruments each observe at their own coupling and give back fractions far apart, which is instruments parting rather than a fraction being missing. **At 11-next-co-prioring.** Sequence and organism couple, and a coupling answers each instrument in 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 at its own coupling, and a fraction was not one thing to measure. A genome's length carries its copyings, doublings and repeats, each released at its own pace, so a length is a carrying's record and no fraction of function. ## 6.9 The Gibbs paradox · 108 *+ or − at 10, is.* **At 2-now-possibling.** Mixing happens at a coupling, and entropy is a magnitude belonging to a system apart from a separable. **At 12-next-co-still-possibling.** Entropy fixed as a property of a system rather than relative to an operation set, a classical paradox taken as unmysterious at 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 in probing. **At 11-next-co-prioring.** Mixing happens at a coupling, and numbers come out 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 − at 10, is.* **At 2-now-possibling.** Species couple and a community persists, and stability is a magnitude one variable measures. **At 12-next-co-still-possibling.** Stability fixed as a single property with one measure, agreed before measuring, definitions of stability parted into a section of their own and weak interactions damping strong a mechanism proposed, a concept parted and a mechanism a sway. Variables move in different directions on same plots, which is one form observed two ways rather than one property measured twice. **At 11-next-co-prioring.** Species couple and a community persists by its couplings. Same plots on same continents give back rising steadiness at a whole and level steadiness at 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 society's own gather standing above each self while each keeps its own carry, which is a portfolio share's measuring. ## 6.11 The Flynn effect and its reversal · 126 *+ or − at 10, is.* **At 2-now-possibling.** A person and a test couple, and a score is a level of a construct comparable across cohorts. **At 12-next-co-still-possibling.** Tests fixed to measure one construct across cohorts, score change indexing construct change, gains varying by domain and by age, one construct observed differently at 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. **At 11-next-co-prioring.** 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, sweeping composition off the table for that population: a level of a construct comparable across cohorts, a coupling fixed unchangeable where a coupling kept momentarying, and scores were observings of their own occasions. ## 6.12 Benchmarks · 131 *+ or − at 10, is.* **At 2-now-possibling.** A system and a benchmark couple, and a score is a level of a capability apart from a coupling. **At 12-next-co-still-possibling.** 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 in framing as general measures. Leaking into training 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. **At 11-next-co-prioring.** A system and a benchmark couple, and a score is a coupling's own making. Leaking into training arrives again as scoring, saturation arrives and a benchmark retires, transfer thins away from a coupling that was scored, and the strongest observing left is deployment itself, confounded and standing: a capability fixed apart from a coupling is same wall as at incoming number 30 and incoming number 141, reached at an instrument built to escape it. ## 6.13 Brooks's law · 133 *+ or − at 10, is.* **At 2-now-possibling.** People couple as they are added, and an effect is a magnitude from a number of people with all else fixed. **At 12-next-co-still-possibling.** 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 at a law. A joiner brings a scale of its own or brings an already-carried, and a whole thins at a momentary a shared scale couples, which is a parity answered at a self it couples at, and not a number of people. **At 11-next-co-prioring.** People couple as they are added, each arrival opening couplings with each one standing, and couplings are cost and capacity at once. Overhead shows at each measuring of it, modular work makes arrivals into 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 changes. 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 − at 10, is.* **At 2-now-possibling.** Neurons couple in a population and a concept is present, and sparseness is a magnitude a recording measures. **At 12-next-co-still-possibling.** 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 in each sparseness reported. **At 11-next-co-prioring.** Neurons couple in a population and a concept is present at 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, in its authors' words, and both codes come out 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, at any sparseness of its showing. ## 6.15 The limits of intelligence · 172 *+ or − at 10, is.* **At 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 at once. **At 12-next-co-still-possibling.** 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 at a substrate's own stating rather than a resolving of its own. **At 11-next-co-prioring.** Competency floats, a middle no observing enters, and each limit that binds binds a side: computational limits bind computations, a physical thesis at 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 at their own arrivals, and a middle keeps 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 − at 10, is.* **At 2-now-possibling.** A proton's spin is a parity, one half taken at its own momentary, and it is a magnitude divided among four contributions, each a share of a whole. **At 12-next-co-still-possibling.** 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 at whichever accounting is chosen. **At 11-next-co-prioring.** 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 shared out 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 − at 10, is.* **At 2-now-possibling.** Neutrinos oscillate at their couplings, differences of their squared masses measured exactly, and masses themselves are magnitudes each instrument should give back. **At 12-next-co-still-possibling.** 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 at its own. **At 11-next-co-prioring.** 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 − at 10, is.* **At 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. **At 12-next-co-still-possibling.** 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 in fitting: a two-way fixed to one side, asked for its proportion, arriving at a parity fixed as a magnitude. **At 11-next-co-prioring.** 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 in 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 − at 10, is.* **At 2-now-possibling.** Oxygen crossed a threshold rocks record, a parity taken at sulfur isotopes, and a crossing is a magnitude, how high and how variable abundance rose. **At 12-next-co-still-possibling.** 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 at 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. **At 11-next-co-prioring.** 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 into 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-still-possibling and 12-next-co-still-possibling *One frame, clock or ordering fixed over couplings. Each self paces its own alternating and synchronizes at its own couplings, and a beat fixed over them is a term no coupling made. Now is one, shared at each coupling and common at none, and a momentary is one now had at a sharing.* **Each ordering here is one beat fixed over couplings that each pace their own**, and one arrival is that momentarying reached at a substrate rather than argued: slicings part with coupling selves, to any precision measured. **And a beat arrives at four positions, three of them easy to miss.** Its pace, where a coupling is opened at a rate given rather than its own. Its momentary, since anything carrying couplings one after another takes them in some order, and two couplings at no between have no order between them. Its record, since a trace indexed by a shared tick is a beat in 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 in this part name a beat at a record and at a between rather than at 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 at part 9, each in its own arithmetic: rankings over profiles, rankings over differently-numbered outcomes, structure surviving aggregation. Each is a bounding taken out and settling sounded — a whole ordered by no self, arriving as a field's own theorem. ## 7.1 Simultaneity and the present · 28 *+ or − at 10, is.* **At 2-now-possibling.** Each self sequences its own beat and synchronizes at its couplings, and one slicing is fixed as a real one, fixed over all. **At 12-next-co-still-possibling.** 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 at each measured differing. **At 11-next-co-prioring.** Each self sequences its own beat and synchronizes at its couplings. Slicings part with coupling selves to any precision reached, no frame in tested laws carries a privilege, sky's own rest frame is measurable and privileges nothing dynamically, and a hidden preferred slicing survives only by arranging itself beyond each measurement: one slicing fixed over them was a term no coupling made, and a slicing surviving only by arranging itself beyond each measurement is naming placed where nothing observes it. ## 7.2 Aggregation of preferences · 5 *+ or − at 10, is.* **At 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. **At 12-next-co-still-possibling.** Aggregation fixed as a function only from ordinal profiles, independence standing, where no procedure reaches its conditions and relaxing an ordering yields in each 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. **At 11-next-co-prioring.** Selves each take their own parity, one at a time, and a 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 at its own between, one at a time, and a society co-competencing without a whole ordered over it. ## 7.3 The problem of time in quantum gravity · 66 *+ or − at 10, is.* **At 2-now-possibling.** Sequencing is each coupling's own momentarying, and time is fixed as a parameter over a whole, external or absent. **At 12-next-co-still-possibling.** A quantum theory fixed to need a time parameter over its evolution, schemes parted into time identified before quantising, after, or playing no fundamental role at all, a third its parameter released. No experiment reaches its regime, which is a record's edge, and countings carry on same either way. **At 11-next-co-prioring.** Sequencing is each coupling's own momentarying. A whole's equation carries no clock, a familiar flowing arrives again in a limit at which familiar things exist, and conditioning on a clock subsystem recovers evolution relative to that clock, time observed at 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 at each coupling is not none again, and a momentary completes at a next opening, each side at its own momentary; there time is momentarying, and a field's own equation shows it by carrying no clock. ## 7.4 Skolem's paradox · 69 *+ or − at 10, is.* **At 2-now-possibling.** Axioms and models couple, and cardinality is fixed as absolute, fixed over each model. **At 12-next-co-still-possibling.** 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 at its own between, and an uncountable-within is pattern-matched from a bijection standing beyond a model that carries it. **At 11-next-co-prioring.** Axioms and models couple, and each model makes its own countings: same axioms carry in a countable world and 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 − at 10, is.* **At 2-now-possibling.** Observings arise at couplings and are fixed to be counted across levels fixed in one ordering. **At 12-next-co-still-possibling.** 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 a not possible existing. **At 11-next-co-prioring.** Observings arise at 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 at each carrying of it, an instrument measuring itself: a count across levels fixed in one ordering lays selves at a seat no coupling made, and each self observes at its coupling. ## 7.6 Laws of nature · 105 *+ or − at 10, is.* **At 2-now-possibling.** Regularities arise at couplings, and a law is fixed as a rule over them, governing or summarising. **At 12-next-co-still-possibling.** 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 in, so an instrument's own coupling arrives within a criterion. **At 11-next-co-prioring.** Regularities arise at couplings, each coupling its own. Best-system simplicity moves with a language it is written in, 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 doer installed over doings, and doings do their own. ## 7.7 Presentism and eternalism · 106 *+ or − at 10, is.* **At 2-now-possibling.** Each coupling stands at its own now, and existence is fixed as a fact over all times at once. **At 12-next-co-still-possibling.** Existence fixed unqualified rather than at a time, where an infinity of planes passes through any point with no physical test distinguishing one, the 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. **At 11-next-co-prioring.** Each coupling stands at 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, in its own defenders' words: existence fixed over all times at once is one standing fixed over each coupling's own, and each now is its coupling's own, needing no standing beyond itself. ## 7.8 Rank-based and clade-based nomenclature · 22 *+ or − at 10, is.* **At 2-now-possibling.** Each lineage branches at its own couplings, and one ranked hierarchy is fixed as an ordering over all groups. **At 12-next-co-still-possibling.** Ranks fixed to carry equivalence across groups, rank assignment subjective and of dubious biological significance at 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. **At 11-next-co-prioring.** Each lineage branches at 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 in 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 at one subject resolve three ways — converging, parting at 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 − at 10, is.* **At 2-now-possibling.** Lives arrive at couplings, each its own, and one ranking is fixed over outcomes with different numbers of people, under adequacy conditions stated together. **At 12-next-co-still-possibling.** 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. **At 11-next-co-prioring.** Lives arrive at couplings, each its own, and arrivals share no seat a ranking could sit on: a life is made at 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 at 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 releasing. ## 7.10 Micro-to-macro aggregation · 169 *+ or − at 10, is.* **At 2-now-possibling.** Each self takes its own parity at its own couplings, and an aggregate is fixed to carry one rationality over many, a representative standing for all. **At 12-next-co-still-possibling.** 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 at rankings, arriving here at demand. **At 11-next-co-prioring.** Each self takes its own parity at 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 in a field's own literature, and rebuilt aggregates rise from distributions of many: one rationality fixed over many is a self fixed where a society lives, and a society co-competences, parity by parity, no one standing for all. An aggregate is living at its own prime scale and inherits nothing, and a representative agent is a society fixed as a self at a scale not its own. ## 7.11 The axiomatization of physics · 171 *+ or − at 10, is.* **At 2-now-possibling.** Each theory carries on at its own couplings, and one axiom system is fixed over the whole of physics. **At 12-next-co-still-possibling.** 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 at 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 at its own between. **At 11-next-co-prioring.** Each theory carries on at its own couplings and closes at 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 the whole of physics fixes one beat over runnings that each pace their own, and parts keep closing part by part, which is an answer carrying on, arriving at its own rate, no whole-physics criterion standing at any part of it. ## 7.12 The Hubble tension · 165 *+ or − at 10, is.* **At 2-now-possibling.** Each epoch expands at 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, the sharpest form standing between determinations calibrated on a sound horizon under a concordance frame and determinations calibrated otherwise. **At 12-next-co-still-possibling.** 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 at either. A beat is fixed at a record rather than at a pace: a standing carried forward under one frame and entered as a present-day number is a trace indexed at a shared tick. **At 11-next-co-prioring.** Recombination-era measurements stand at 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 at 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 at 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 at exactly a pattern-matching's epoch. Discriminating programmes stand carrying on. *Second seating: a sound-horizon inference carried forward is a record indexed at one frame, which is a clock in recording.*   --- ## 7.13 The 100,000-year glacial cycle · 247 *+ or − at 10, is.* **At 2-now-possibling.** Climate sways on its own, ice growing and collapsing at couplings of ocean, ice and carbon, and a period is fixed to be given by an orbit, one beat over a sway. **At 12-next-co-still-possibling.** 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 keeping its own beat where a clock was fixed over it. **At 11-next-co-prioring.** 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 − at 10, is.* **At 2-now-possibling.** A magnetotail stores and releases at 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. **At 12-next-co-still-possibling.** An order fixed between two couplings instruments reach at different cadences. Onset evolves across widely separated regions faster than sparse spacecraft can establish timing, auroral, current, flow and reconnection signatures observed at 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 at no between have no order between them. **At 11-next-co-prioring.** 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 at a record, and a record gives each signature at its own cadence, event by event. ## 7.15 Migraine pathophysiology · 217 *+ or − at 10, is.* **At 2-now-possibling.** A brain cycles between states at its own couplings, sensory gain rising and falling, and an attack is fixed to a sequence with one initiation, a first that orders the rest. **At 12-next-co-still-possibling.** An onset fixed to one first in 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. **At 11-next-co-prioring.** 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 at a tipping of a cycle's own couplings, phase by phase. ## 7.16 Earthquake predictability · 197 *+ or − at 10, is.* **At 2-now-possibling.** A fault ruptures at its own coupling, stress and friction coupling at 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. **At 12-next-co-still-possibling.** 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. **At 11-next-co-prioring.** 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 at a state before it, and forecasting is a rate at which couplings arrive, measured, each event its own coupling at its momentary. ## 7.17 The predictability of evolution · 210 *+ or − at 10, is.* **At 2-now-possibling.** Lineages evolve at their own couplings, mutation, selection, drift and environment coupling at each generation, and an outcome is fixed to be readable from an ancestral state, a trajectory established before it exists. **At 12-next-co-still-possibling.** 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. **At 11-next-co-prioring.** 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 at a coupling, each generation its own. ## 7.18 Rapid adaptive radiation · 211 *+ or − at 10, is.* **At 2-now-possibling.** Populations speciate at 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. **At 12-next-co-still-possibling.** 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 at a record, an aggregate observed as one carrying. **At 11-next-co-prioring.** 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 at no instrument, recorded bursts being surviving couplings' making, one at a time. ## 7.19 Cross-national measurement equivalence · 231 *+ or − at 10, is.* **At 2-now-possibling.** A respondent and an item couple at each answering, in 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. **At 12-next-co-still-possibling.** A correspondence fixed between couplings so their parities couple at 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 at a between, a part's fourth position, fixed where each coupling answers its own. **At 11-next-co-prioring.** 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 the rest 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 − at 10, is.* **At 2-now-possibling.** A score is made at each prediction's coupling with its outcome, and one score is fixed to satisfy each fairness relation at once, calibration and equal error rates across groups whose base rates differ. **At 12-next-co-still-possibling.** 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 at rankings and population ethics beside it, fourth account naming fairness a substantive institutional judgment not exhausted by any parity condition. **At 11-next-co-prioring.** 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 at group-specific rules, and multiobjective methods trace a tradeoff surface rather than satisfying incompatible equalities: one score fixed to each relation at once is one ordering fixed over couplings whose base rates differ, naming set down and a relation chosen at each decision's own between. # 8 A rate fixed as a value — 7-now-prioring and 15-next-prioring *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 in an opening a straddle makes.* **Each value in 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 at once, 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 in this part has given. ## 8.1 Homeostasis and allostasis · 128 *+ or − at 10, is.* **At 2-now-possibling.** A variable sways between two offerings and is fixed for a target that settles, fixed or predicted. **At 12-next-co-still-possibling.** Regulation fixed toward a value, cyberneticists' reading of a broader vision. Both showings fit each trajectory alike, so differing surfaces nought at each: trajectories are one sway observed twice, the two not competing models but complementary aspects of regulation. **At 11-next-co-prioring.** Range is coupling's own making and no stored value it aims at, two antagonistic offerings swaying and oscillation its working state. Circuits that compare are real at their finding, a body warms before a meal and quickens before an effort, and letting a setpoint move absorbs anticipating at a price of any settling at all, in movers' own critics' words. 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 − at 10, is.* **At 2-now-possibling.** Rotation, mass and law carry on together at each scale's couplings, and discrepancy is fixed for a value, a substance or a modification. **At 12-next-co-still-possibling.** 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 the two: parameter spaces close without closing their question, and no terminal null stands recorded. **At 11-next-co-prioring.** Rotation, mass and law ride together and settle at 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 unchangeable, and riding, observed directly, is momentarying there. ## 8.3 The strong CP problem · 65 *+ or − at 10, is.* **At 2-now-possibling.** A parameter sways and is fixed for a value against a measure over its might-have-beens. **At 12-next-co-still-possibling.** 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 not possible existings, and it surfaces nought at each instrument. **At 11-next-co-prioring.** 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 at 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 at its own edge. ## 8.4 The equity premium puzzle · 79 *+ or − at 10, is.* **At 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. **At 12-next-co-still-possibling.** 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 at no momentary, and disasters that reproduce premium borrow their rates from other countries' histories, might-have-beens imported to balance the was. **At 11-next-co-prioring.** Returns sway across states that occurred, and record is swaying that happened. Measured premium carries large in 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 at no value, and each self prefers at its own between, by its own parity, where a representative agent stands for all. ## 8.5 Time preference and preference reversal · 82 *+ or − at 10, is.* **At 2-now-possibling.** A valuing sways at each occasion and is fixed for a rate that settles, a single discount function. **At 12-next-co-still-possibling.** 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 in 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. **At 11-next-co-prioring.** A valuing sways at 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 − at 10, is.* **At 2-now-possibling.** A response sways with dose and is fixed for a value at doses below detection, from a model fitted above them. **At 12-next-co-still-possibling.** A dose-response relation fixed whose low-dose behaviour is estimable by extrapolation. Below a last coupling observed, rival models part at 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. **At 11-next-co-prioring.** A response sways with dose, coupling by coupling, and low doses wake a body's own stress answers in system after system, curves bending at 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. In a range instruments reach, rival models fit alike; below it they part exactly at a point nothing measures, and field itself states a point a drawing enters at. ## 8.7 Mutation, fidelity and variation · 138 *+ or − at 10, is.* **At 2-now-possibling.** A rate sways under selection and drift together, and it is fixed for a value an optimum or a barrier sets. **At 12-next-co-still-possibling.** 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. **At 11-next-co-prioring.** A rate sways under selection and drift coupling, its value swaying's own at 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 − at 10, is.* **At 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. **At 12-next-co-still-possibling.** 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 unchangeable terms at one momentary — a rest a sequence opens at, a last it completes at, and a total its sequence conserves — and none of three is a thing a coupling made. **At 11-next-co-prioring.** 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 at once. 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 keeps owing an explanation to a typicality no instrument has reached, and swaying, measured, is as it is. ## 8.9 The hierarchy problem · 164 *+ or − at 10, is.* **At 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. **At 12-next-co-still-possibling.** 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. **At 11-next-co-prioring.** 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 in 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 − at 10, is.* **At 2-now-possibling.** Masses and mixings are measured at couplings instruments reach, each parameter its own, and pattern is fixed for a value an organizing principle should generate. **At 12-next-co-still-possibling.** 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 at each construction. **At 11-next-co-prioring.** 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 at a scale beside it. ## 8.11 The new-physics flavor puzzle · 189 *+ or − at 10, is.* **At 2-now-possibling.** Rare processes are measured at their couplings and give Standard Model's rates, and a new sector fixed near an accessible scale is fixed to carry generic couplings the measurements should have seen. **At 12-next-co-still-possibling.** 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 beyond direct reach 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 reached at no instrument. **At 11-next-co-prioring.** Large regions of generic low-scale couplings stand excluded, viable suppression patterns have explicit effective forms, and each stands at 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 at typicality and not at its record. ## 8.12 Quantum gravity · 181 *+ or − at 10, is.* **At 2-now-possibling.** Gravitation carries on at each coupling and two established theories each recover their own domain, and one theory is fixed for a value covering both regimes, two reconciled at a regime their conflict is expected at. **At 12-next-co-still-possibling.** Two treatments fixed as reconciled in one theory at 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 at a regime that offers at no instrument. **At 11-next-co-prioring.** Low-energy effective descriptions stand consistent, black-hole thermodynamic constraints stand, discrete and holographic constructions and candidate ultraviolet behaviours stand, and each program closes at 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 at a scale no coupling has reached, and parts keep closing part by part, each at its own between, as axiomatization at part 7 closes. ## 8.13 Equilibrium climate sensitivity · 196 *+ or − at 10, is.* **At 2-now-possibling.** Climate sways under its forcings and feedbacks, each at its own timescale, and response to a doubling is fixed for one value its sway settles at, an equilibrium counterfactual. **At 12-next-co-still-possibling.** A sway fixed to settle at 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, a not possible existing, summed against an existing one. **At 11-next-co-prioring.** 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 the measured. ## 8.14 The solar abundance problem · 184 *+ or − at 10, is.* **At 2-now-possibling.** Lines form at surface and modes sound interior, each instrument at its own coupling, and one composition is fixed for a value both must give. **At 12-next-co-still-possibling.** 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 at once, each observing its own. **At 11-next-co-prioring.** Three-dimensional atmospheres, precise mode frequencies, neutrino fluxes and laboratory opacities stand as independent constraints, and each route pays at one instrument a gain it makes at an other, higher mixtures fitting seismology and conflicting with spectroscopy, opacity increases targeted without a required profile established, revised atmospheres reducing systematics and keeping 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 − at 10, is.* **At 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. **At 12-next-co-still-possibling.** 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 the stars have done since, and prediction pattern-matches it through a network and a density measured elsewhere. **At 11-next-co-prioring.** 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 at 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 − at 10, is.* **At 2-now-possibling.** A neutron decays at 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. **At 12-next-co-still-possibling.** 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 at once, each giving a number its own coupling carries. **At 11-next-co-prioring.** Magnetic-trap lifetime stands at twice its earlier precision and consistent with theory, newer beam's first result stands, at 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-prioring and 11-next-co-prioring *One side taking both momentaries. A parity is taken at 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-prioring and 11-next-co-prioring carry co, a prior at a sharing of two, and a two-way fixed to one side is that co left out.* **And the settlement fields offer is naming relocating rather than releasing**: *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 in more than substance, partitions coming out 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 in its own arithmetic — standing at units of selection, at cooperation, at transformation problem's aggregate equalities, and at 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, which part 7 carries at three arrivals and transformation problem carries at one. ## 9.1 Causation · 162 *+ or − at 10, is.* **At 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 in fundamental description. **At 12-next-co-still-possibling.** That direction is in dynamics rather than in observing, virtually everyone rejecting elimination of causation while many are convinced fundamental physical structure contains no causal relations, reconciling asked at 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 at one momentary and a crossing inverts it at its next, so arrow arrives at odd and symmetric dynamics at even, and neither carries an other's momentary. **At 11-next-co-prioring.** A coupling is two-way, one-at-a-time, and one-way arrow is observing's own, taken at 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 − at 10, is.* **At 2-now-possibling.** A trait arises at 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 the same design carried from its two sides, each giving a correct conditional for a range it sampled. **At 12-next-co-still-possibling.** 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 at one side, a scale between and an absorbing at an other are observed together at one momentary, which is this file's own three with alternating fixed unchangeable. **At 11-next-co-prioring.** A trait arises at a coupling of a genome and an environment, one making at two sides. Each estimate is the conditional it is, true of a range it sampled; 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 at 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 − at 10, is.* **At 2-now-possibling.** A self takes its own parity at its own betweens, and taking is observed from one side as an outcome fixed by a term beyond it, with other side observing same taking as unfixed. **At 12-next-co-still-possibling.** 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 at no between, and readiness ramp arrives from selves built fresh at each trial and averaged, which is preparing observed as momentarying. **At 11-next-co-prioring.** A self takes its own parity at 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 at either account: fixed-or-unfixed is taking fixed as taken from a first beyond a taker, both sides observing a between from one side of it, and taking observed at its own between is agency, which is what measurements were measuring. ## 9.4 Aging · 34 *+ or − at 10, is.* **At 2-now-possibling.** Damage and regulation carry on together at each between of an organism, and one is observed as driving an other. **At 12-next-co-still-possibling.** 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 at each next opening and is fresh by sequencing, a sharing once chained not none again, so damage and regulation are one carrying at two sides, and a clock that predicts age so well cannot say which side it observes because an observing in momentaries observes pacing. **At 11-next-co-prioring.** Damage and regulation are one coupling's two offerings, sway swaying at 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 in 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 society outliving its cells, and it ages where its new members stop arriving and its sharings go unrestored, damage and regulation two offerings at each sharing and neither a driver. ## 9.5 Efficient markets · 36 *+ or − at 10, is.* **At 2-now-possibling.** A price is a parity taken at a coupling, and efficiency is observed at its own while a model of expected returns is fixed unchangeable. **At 12-next-co-still-possibling.** 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. **At 11-next-co-prioring.** A price is made at 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 in a laboratory, and factor zoo is what absorbing anomalies one at a time builds: two are one coupling's two momentaries, and neither tests at its own. ## 9.6 Simpson's paradox · 40 *+ or − at 10, is.* **At 2-now-possibling.** An association is made at a coupling and pattern-matched from one stratification as a correct one, with causal structure fixed unchangeable. **At 12-next-co-still-possibling.** 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 at each pattern-matching taken, proved as an equivalence class, and a graph supplied from beyond is a frame stood beyond a coupling. **At 11-next-co-prioring.** An association is made at a coupling, and strata re-make it. Arithmetic is elementary, back-door road is proved at a known structure, conditioning more can worsen it, proved too, and data at their own deliver an equivalence class, exactly that: a correct pattern-matching fixed identifiable from data reaches into numbers for a structure the numbers were made under, and structure is a coupling's, brought or not. ## 9.7 Missing heritability · 44 *+ or − at 10, is.* **At 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. **At 12-next-co-still-possibling.** 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 at their own coupling, and ratio's two terms come from two places, a numerator measured directly and a denominator inferred at a population. **At 11-next-co-prioring.** 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, in field's own words, with interaction accounts fitting all that is observed at 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 − at 10, is.* **At 2-now-possibling.** A coupling at a between makes a term neither side brought, and it is observed from one side as a substance's contribution with context fixed unchangeable. **At 12-next-co-still-possibling.** That a trial's arms differ only in 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. **At 11-next-co-prioring.** Coupling at a between makes a term neither side brought, +1 owned neither-ing. Blocking a body's own opioids blocks analgesia, conditioned immune quieting exists in 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 − at 10, is.* **At 2-now-possibling.** Two principles are two parities taken at one between, and each theory observes a case from one of them with an other fixed unchangeable. **At 12-next-co-still-possibling.** That one principle governs when they conflict, difficulty stated at 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 at one between, alternating one at a time, and a case built to make them conflict fixes both momentaries together. **At 11-next-co-prioring.** Two principles are two parities at 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 the two 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 − at 10, is.* **At 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. **At 12-next-co-still-possibling.** That a learner's contribution and an input's are separately specifiable, which parts into two terms a making that is or is not at each sharing, one clear thing about the argument its conclusion and structure of reasoning not clear at all, two terms asserted at its conclusion and unsupported at its reasoning. **At 11-next-co-prioring.** A learner and an input couple, grammar made in 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 at each sharing, and volumes being argued over are a coupling being measured. ## 9.11 Morphogenesis · 62 *+ or − at 10, is.* **At 2-now-possibling.** Gradients and tissue dynamics carry on together, and placement is observed from one side as instructed or as self-organised. **At 12-next-co-still-possibling.** That pattern is set by a determinant locatable in 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 at a coupling of both carrying on; and a hybrid fitting better than either is a third term reached at two carrying alternating. **At 11-next-co-prioring.** Placement is made at a coupling of gradients and tissue dynamics. Moved gradients move structures, striping mechanisms exist in digits and follicles and ridges with their perturbations confirmed, readout carries on near physical limits, tissue organises itself in 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 at 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 − at 10, is.* **At 2-now-possibling.** Peripheral and central processes carry on together at a patient's betweens, and persistence is observed as driven from one. **At 12-next-co-still-possibling.** 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. **At 11-next-co-prioring.** Peripheral and central processes carry on together at a patient's betweens. Central changes are measured, small fibres surface in a counted fraction as detection sharpens, moving patients between categories, targeted agents work in 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 at a coupling, patient by patient, which is treating that works already working there. ## 9.13 Information as fundamental · 77 *+ or − at 10, is.* **At 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. **At 12-next-co-still-possibling.** 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 the same showing part 5 carries, arriving here as a direction demanded between two observings. **At 11-next-co-prioring.** 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 at its own doings, neither side beneath, doing one thing both descriptions describe. Information is an emanation, non-living at 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 − at 10, is.* **At 2-now-possibling.** Labour values and prices are two accountings of one production, and one is observed as underlying an other. **At 12-next-co-still-possibling.** 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 in its own arithmetic, and each accounting conserves one kind and imports an other. **At 11-next-co-prioring.** 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 in its arithmetic. ## 9.15 Credit assignment · 96 *+ or − at 10, is.* **At 2-now-possibling.** An outcome is made across a sequence of couplings, and contribution is observed as apportionable to individual actions with the rest fixed unchangeable. **At 12-next-co-still-possibling.** 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 changes what gets credited, which is an apportioning caught making its own. **At 11-next-co-prioring.** An outcome is made across couplings, abundancing owned by no action. Difference methods converge at their conditions, performance thins with horizon and sparsity as measured, identification conditions are proved and go frequently unmet, and shaping reward changes 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 − at 10, is.* **At 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. **At 12-next-co-still-possibling.** 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 at their own coupling and give reorganisation and preservation, both standing in their own instruments. **At 11-next-co-prioring.** A body map and a sensation couple, map carried and re-formed. One paradigm observes reorganisation and another observes preservation, both standing in their own instruments; mirrors help mixedly, peripheral routes help some, and phantoms arrive in 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 the thing, and map is a carrying, observed differently at each instrument because it is being made at each. ## 9.17 Determinism and randomness · 110 *+ or − at 10, is.* **At 2-now-possibling.** An outcome is a parity taken at a between, and it is observed from one side as fixed by priors or from an other as unfixed. **At 12-next-co-still-possibling.** 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 at a theory neither has. No statistical test establishes indeterminism, proved in general, and deterministic pattern-matchings carry on equivalent by construction, so sides part at no instrument. **At 11-next-co-prioring.** An outcome is a parity taken at a between, one at a time. Local determination is excluded at couplings strung tight, no statistical test can establish indeterminism, proved in general, 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 at any instrument, which proofs carry. ## 9.18 Cancer, the somatic mutation account and its rival · 115 *+ or − at 10, is.* **At 2-now-possibling.** A cell and its tissue society couple, and initiation is observed from one level with an other fixed unchangeable. **At 12-next-co-still-possibling.** 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 tissue society releasing it at nought — society's own resolving, with a defence added nowhere. **At 11-next-co-prioring.** A cell and its tissue society couple, and society keeps order a cell at its own does not. Driver catalogues fill, targeted responses come and resistance follows almost always, tissues re-order recombined cells in 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 society at once. ## 9.19 Addiction · 116 *+ or − at 10, is.* **At 2-now-possibling.** A self and its conditions couple at each occasion, and behaviour is observed from one side as pathology or from an other as choice. **At 12-next-co-still-possibling.** 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 kept 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. **At 11-next-co-prioring.** A self and its conditions couple at each occasion, behaviour made in a coupling. Circuits change with dose, paying abstinence works at randomised scale, 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 − at 10, is.* **At 2-now-possibling.** Differences and drift carry on together in a community, and structure is observed as produced by one. **At 12-next-co-still-possibling.** 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 the opening, so discriminating surfaces nought at a pattern, and field's own partition is a field observing both momentaries. **At 11-next-co-prioring.** Differences and drift carry on together at each community coupling. Both models fit abundance curves from the opening, invasions demonstrate stabilising differences wherever they are carried out, 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 − at 10, is.* **At 2-now-possibling.** Coevolution and environment carry on together, and constant extinction risk is observed as produced by one. **At 12-next-co-still-possibling.** 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. **At 11-next-co-prioring.** Coevolution and environment carry on together. Extinction risk carries age-blind across many groups, arms races are living in microbes, interfaces evolve fast at 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 − at 10, is.* **At 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. **At 12-next-co-still-possibling.** 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 at each coupling. **At 11-next-co-prioring.** Exposures and a developing system couple, tuning made in couplings. Farm childhoods and their controlled cousins part immunologically with mechanisms in hand, one early exposure reversed a guideline at randomised scale, 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 − at 10, is.* **At 2-now-possibling.** Technique and relationship carry on together in each treatment, and outcome is observed as attributable to one with an other fixed unchangeable. **At 12-next-co-still-possibling.** 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. **At 11-next-co-prioring.** Technique and relationship carry on together in 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 in. ## 9.24 Principal and agent · 141 *+ or − at 10, is.* **At 2-now-possibling.** Two interests couple through observables, and divergence is observed from one side as a contracting problem over an unobserved action. **At 12-next-co-still-possibling.** 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 the measured distorts the unmeasured, proved, which is the same Goodhart wall that benchmarks reach. **At 11-next-co-prioring.** Two interests couple through observables, divergence carrying on at a between. Contracts optimise under their stated conditions, rewarding the measured distorts the unmeasured, proved, same Goodhart wall that benchmarks reach, teams blur the very identification, proved too, and incentive pay comes out mixed wherever 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 − at 10, is.* **At 2-now-possibling.** One and many couple, and an aggregate relation is observed from one scale as the relation. **At 12-next-co-still-possibling.** That an operative regime is identifiable in advance 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 in advance but arriving with its shock. One and many are one coupling's two scales, and a relation at one scale fixed to govern both is one scale taking both momentaries. **At 11-next-co-prioring.** One and many are one coupling's two scales, aggregate made among couplings. Both results follow cleanly in their own models, both sides granting both, multipliers spread wide across methods and regimes, and zero-bound episodes contest on identification: a relation at one scale fixed to govern both is one scale taking both momentaries, and regime carries on at couplings, momentary by momentary. ## 9.26 The evolution of cooperation · 143 *+ or − at 10, is.* **At 2-now-possibling.** Fitness effects arise at couplings and are observed as attributable to individuals, with inclusive fitness and multilevel selection each observing from one side. **At 12-next-co-still-possibling.** 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 at a coupling, so cooperating is observed as a puzzle exactly where an accounting removed +1 before its books could balance. **At 11-next-co-prioring.** Fitness effects arise at 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 − at 10, is.* **At 2-now-possibling.** Language and thought couple in each task, and effect is observed from one side as shaping with an other fixed unchangeable. **At 12-next-co-still-possibling.** 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 at 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. **At 11-next-co-prioring.** Language and thought couple in each task, effect made in 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 at its own momentary: a task fixed to measure thought apart from language fixes one side of a coupling unchangeable, and making is at a coupling, task by task. ## 9.28 Structure and agency · 156 *+ or − at 10, is.* **At 2-now-possibling.** Persons and arrangements couple at each action, and explanation is observed from one level with an other fixed unchangeable. **At 12-next-co-still-possibling.** That causes are located at 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 come out conditional on levels chosen, and a level is a direction taken at a momentary and not a place. **At 11-next-co-prioring.** Persons and arrangements couple at each action, one making at two scales. Individualist derivations reach an aggregation wall, multilevel partitions come out conditional on levels chosen, same conditional as at incoming number 27 one scale up, and each synthesis pays a cost its critics name precisely: causes fixed at one level name one scale of a coupling as first, and making carries on at both, action by action. ## 9.29 The units of selection · 19 *+ or − at 10, is.* **At 2-now-possibling.** Selection carries on at couplings across levels, and it is observed from one level as the level, gene accounting or group accounting each taking an observing of a pair. **At 12-next-co-still-possibling.** 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 the level fixes a scale as a place, where outward and inward are directions taken at a momentary, of no size. **At 11-next-co-prioring.** Selection carries on at couplings across levels, and two frameworks translate into each other, proved, fitting same data by construction, same equivalence as at incoming number 143: a level observed as the level took one momentary for two, and cases carry under both descriptions because a carrying was not at one. Selection is at each scale where a society bi-couples at a prime, and bookkeepings translate because they observe one fractal at two of its scales. ## 9.30 Teleology and function in biology · 167 *+ or − at 10, is.* **At 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. **At 12-next-co-still-possibling.** 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, the for and design one slide. Each locates function by answering what a trait is for, and a why demanded is a first demanded: set the *for* down and observations stand entire, structure, trait, record of what carried, with the therefore leaving and nothing observed going with it. **At 11-next-co-prioring.** 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 in working use is a coupling observed from both, a co-competency the science already carries.   --- ## 9.31 Dirac or Majorana neutrinos · 187 *+ or − at 10, is.* **At 2-now-possibling.** A neutrino couples at 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 in nine words. **At 12-next-co-still-possibling.** Which of two, where two part at 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 parting at no instrument, as determinism parts at none beside it, and one instrument that could part them a lepton-number-violating process no search has established. **At 11-next-co-prioring.** 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 at relativistic helicity states is a parity taken at a between fixed to a size no observable gives, two sides alternating and kinematics making no coupling at their difference. ## 9.32 The nature of cosmic acceleration · 192 *+ or − at 10, is.* **At 2-now-possibling.** Expansion accelerates at each distance the surveys observe, and its cause is fixed to one of two sides, an exotic energy or a breakdown of gravity on cosmological scales. **At 12-next-co-still-possibling.** 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 parting at no instrument the surveys carry. **At 11-next-co-prioring.** 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 in one equivalent form is an expansion's own momentarying fixed to a sector, and momentarying is measured at each distance, two histories parting only where equivalence lets them. *Second seating: discrepancy fixed for a value, part 8's naming, beside dark matter at 8.2.* ## 9.33 Mantle plumes · 200 *+ or − at 10, is.* **At 2-now-possibling.** Mantle rises and spreads at 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. **At 12-next-co-still-possibling.** Which of two, observed at 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 the 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 in the third. **At 11-next-co-prioring.** 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 at a coupling of its upwelling with its plate, sides observed one province at a time and not one for all. ## 9.34 The extent of Snowball Earth glaciation · 202 *+ or − at 10, is.* **At 2-now-possibling.** Ice grows and retreats at couplings of albedo, ocean, cloud and dust, and Neoproterozoic ocean is fixed to one of two states, frozen over or open at a belt, thick ice or refugia. **At 12-next-co-still-possibling.** Which of two, at a record sampling preserved basins. Continental ice sheets stood at 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 the 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. **At 11-next-co-prioring.** 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 at each latitude is ice's own sway fixed to a side, and ice stood at its own couplings, basin by basin and episode by episode, cover observed at its own places rather than one cover for a globe. ## 9.35 The early Solar System impact flux · 206 *+ or − at 10, is.* **At 2-now-possibling.** Impactors arrived at 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. **At 12-next-co-still-possibling.** 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 the 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. **At 11-next-co-prioring.** 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 at its own coupling, arrivals observed at their contexts and not at 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 − at 10, is.* **At 2-now-possibling.** A genome doubles at a coupling of its own, isolation and novelty made at once 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. **At 12-next-co-still-possibling.** Which of two effects, observed at a record that keeps survivors. 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 at the fourth. **At 11-next-co-prioring.** 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 at its own couplings, two rates observed apart where a record pattern-matched them as one. ## 9.37 Sporadic Alzheimer's disease pathogenesis · 213 *+ or − at 10, is.* **At 2-now-possibling.** A brain changes next by next at 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. **At 12-next-co-still-possibling.** 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 the same, and fifth account having several interacting pathologies reach a common syndrome, one side fixed observed at the fifth as the many coupling. **At 11-next-co-prioring.** 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 the many fixed to a first, and decline arrives at couplings' own tipping, patient by patient, a side observed at each subtype where one side was fixed for all, as cancer and addiction beside it already say. ## 9.38 Endometriosis pathogenesis · 214 *+ or − at 10, is.* **At 2-now-possibling.** Reflux of menstrual blood is physiological for women with patent tubes, tissue coupling with immunity, hormone and nerve at each cycle, and lesions, pain and infertility are fixed to one driver, an initiating pathway that would order the rest. **At 12-next-co-still-possibling.** 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 at 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. **At 11-next-co-prioring.** 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 at its own, severity independent of a lesion's size being a showing that couplings are several, sides observed apart as chronic pain beside it observes them. ## 9.39 Collective intentionality · 227 *+ or − at 10, is.* **At 2-now-possibling.** Selves couple at a joint activity, each taking its own momentary, and joint intending is fixed to one side, individuals' or group's, its tension in four words, individuals as a group. **At 12-next-co-still-possibling.** 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 at a coupling and owned by neither, observed from one side as individuals' and from an other as group's, and two accepted claims the two momentaries, each true at its own. **At 11-next-co-prioring.** 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 the reports give and a joint attitude sought are not the same, expression standing between them, joint attitude being a coupling's own making and neither side's, at structure and agency beside it already. ## 9.40 The peopling of the Americas · 232 *+ or − at 10, is.* **At 2-now-possibling.** People moved into a continent at their own couplings with corridor, coast and ice, and entry is fixed to one of two routes, inland or coastal, neither rejected at present. **At 12-next-co-still-possibling.** Which of two routes, at a record most of whose shorelines are under the 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 at a record itself: two hypotheses standing on one record, and third account having more than one movement or a prolonged Beringian history contribute, the or both a record's own. **At 11-next-co-prioring.** 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 at each coupling where a way was open, ways observed at their own dates and not one way fixed over a whole. ## 9.41 The causal production of political polarization · 235 *+ or − at 10, is.* **At 2-now-possibling.** Elites, media, institutions and citizens couple at 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. **At 12-next-co-still-possibling.** Which side drives, observed at 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 the surveys give and causes sought not the same, problems of inference standing between them, and a two-way observed from one side where each side influences an other. **At 11-next-co-prioring.** 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 at 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 − at 10, is.* **At 2-now-possibling.** Chromosomes, hormones, pregnancy, microbiota and exposures couple across a life, each at its own stage, and female excess in autoimmune disease is fixed to one mechanism that produces it, which of the candidates a question. **At 12-next-co-still-possibling.** Which of several, each observed in 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 at their own instrument, cohorts, animals and cells, and fifth account having different mechanisms dominate different diseases and phases, one side declined at the fifth. **At 11-next-co-prioring.** 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 at couplings each disease carries, sides observed at each disease where one was fixed for a sex. ## 9.43 The causes of rising obesity · 256 *+ or − at 10, is.* **At 2-now-possibling.** Intake and expenditure couple at each meal under endocrine, metabolic and nervous signals below a conscious level, and a rise across populations is fixed to one of two models, energy in excess or carbohydrate and insulin, debated by distinct cohorts of experts. **At 12-next-co-still-possibling.** 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, in 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, in its own proponents' words 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. **At 11-next-co-prioring.** 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 at a coupling of food reached and signals answering, sides observed at an individual coupling where one was fixed for a population. # 10 A between fixed as a cut — 5-now-co-changing and 13-next *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 not at 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 at 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 allocating differently in writing, a chartered body reporting that its instruments supply no objective means of deciding. **And a between is asked for a cut in three ways.** Of a *continuum*, where offering carries on by degrees and a line is asked at some position on it — a heap, a species, a dialect, a fold, a disease. Of a *pair*, where two things couple and asking is which side a term belongs to — a signal and its noise, a work and its heat, an internal and an external. And of a *crossing*, where a parity passes and asking is at a carrying of it — a correlation, a nature between preparation and detection, a self against a non-self. First releases at degrees, second at an offering being both, third at 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 — at a vote, at a revision, at a convention, at 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 − at 10, is.* **At 2-now-possibling.** A predicate offers at each position and takes a parity there, and a cut point is fixed of a between itself. **At 12-next-co-still-possibling.** 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 a field records in its own words. **At 11-next-co-prioring.** A predicate offers at each position and takes its parity there, one at a time, parity the only thing crossing. Each repair pays at its own self-bounding: an unknowable sharp fact, degrees that blur at their own edges, orderings that re-pose a line one order up, boundarylessness carrying at each order at once in field's own words. Argument carries no material of any kind, and that makes it general: each substrate cut in 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 − at 10, is.* **At 2-now-possibling.** A selection is a parity taken at an interaction, one at a time, and it is fixed as a term located either in evolution or beside it. **At 12-next-co-still-possibling.** 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 at a forced edge, where each null bounds a parameter and range still existing is a range its nulls keep giving back. **At 11-next-co-prioring.** A selection is a parity taken at 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, in evolution or beside it, reaches for a first of taking, and taking is a coupling's own, made at each coupling and located at no place. ## 10.3 The glass transition · 35 *+ or − at 10, is.* **At 2-now-possibling.** Rigidity arrives across a between and a transition is fixed as a point located in temperature. **At 12-next-co-still-possibling.** 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 been in — record's edge, and field's own hardness line, leading thermodynamic account reproducing salient facts while direct validation is missing. **At 11-next-co-prioring.** 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 at each reach any instrument takes: a transition fixed as a point in temperature fixes an arriving to a location, and arriving arrives at its own pace, between by between. ## 10.4 Externalities · 41 *+ or − at 10, is.* **At 2-now-possibling.** Effects offer at each distance and a boundary is fixed as a line located between internal and external. **At 12-next-co-still-possibling.** That a boundary is found rather than drawn, problem reciprocal in nature at a founding paper of modern treatment, which an analysis in terms of a divergence between private and social product does not recognise, line drawn by whoever prices it. Effects offer at each distance, thinning and continuing, so a line between internal and external is drawn at each arrangement and field's measurements show drawing entering. **At 11-next-co-prioring.** Effects offer at each distance, thinning and continuing. Bargaining internalises where coupling is cheap, a condition Coase himself stated; permits work exactly where pollutant is bounded, boundedness the condition again; and asking people to price the unpriced gives answers that sway with their asking: a line fixed between internal and external is drawn at each arrangement, and field's own measurements show drawing entering, arrangement by arrangement. ## 10.5 Species boundaries · 20 *+ or − at 10, is.* **At 2-now-possibling.** Populations offer across each between of them, and a boundary is fixed as a line a criterion locates. **At 12-next-co-still-possibling.** 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 at its own between. Counts swing by measured factors with a concept chosen, and a count that departs when its concept changes carried its concept. **At 11-next-co-prioring.** 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 beyond: a line a criterion locates is a drawing measured, factor by factor, and offering crosses regardless. ## 10.6 The neural code · 43 *+ or − at 10, is.* **At 2-now-possibling.** A spike train offers at each position, and code is fixed as a variable located in it, with a window supplied by an analyst. **At 12-next-co-still-possibling.** That a rate is defined independently of a window chosen from beyond a coupling, answer depending on an observation window, counts dominating at windows shorter than response fluctuations' timescale and timing appearing at 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 in each rate an instrument gives. **At 11-next-co-prioring.** A spike train offers at 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 in a train is an offering fixed to a mark, and window is naming's own coupling, showing in an instrument each time it is drawn. ## 10.7 Bell correlations · 49 *+ or − at 10, is.* **At 2-now-possibling.** A correlation is made at a coupling, and it is fixed as a property located at one system or transmitted between them. **At 12-next-co-still-possibling.** That a correlation is produced by something specifiable at one side or carried between sides, a carry fixed as a store standing within an arrival at 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 at proof grade in another field: two selves each offer one crossing and arrive at a shared secret neither transmitted and no listener has. **At 11-next-co-prioring.** A correlation is made at a coupling, owned by neither side. Local stories are excluded to a theorem's last assumption, a measured bound settles at quantum prediction exactly, and same bound re-derives from principles about reach of couplings: a property fixed at one side or carried between them reaches for a location its making did not have, and making, made at a coupling, is a magnitude a field derived. ## 10.8 Wave and particle · 50 *+ or − at 10, is.* **At 2-now-possibling.** An entity offers at a between and takes a parity there, and its nature is fixed as located between preparation and detection. **At 12-next-co-still-possibling.** 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 changes nothing its formalism did not already carry, a momentarying carrying no clock observed at a field's own instrument. **At 11-next-co-prioring.** An entity offers at a between and takes its parity there. Path knowledge and fringe visibility trade exactly, measured; choosing late changes nothing its formalism did not already carry; and an eraser's correlations are at a joint measurement only, in field's own words: a nature fixed apart from its measuring is an offering fixed without its coupling, and two sides are one offering observed one coupling at a time. ## 10.9 The liar · 55 *+ or − at 10, is.* **At 2-now-possibling.** A truth predicate offers at each sentence including its own, and a value is fixed as located at a sentence that takes none. **At 12-next-co-still-possibling.** That a sentence bears a truth value or falls beyond its domain by a hierarchy stipulated for it, a predicate true at 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 at 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. **At 11-next-co-prioring.** A truth predicate offers at each sentence, its own included, and at its own sentence its coupling closes on nothing to take. Truth is unformalisable within its own language, proved; fixed points stand with revenge waiting, in their builder's words; contradiction-tolerant systems pay their price; and revenge re-arrives against each family: a value fixed at a sentence that takes none is a between fixed to a thing only a coupling makes, and a sentence keeps offering, taking nothing, which is all it ever did. ## 10.10 Hard cases in law · 75 *+ or − at 10, is.* **At 2-now-possibling.** Materials and a case couple at a deciding, and determinacy is fixed as located in materials before deciding. **At 12-next-co-still-possibling.** That materials determine an outcome or do not, ahead of a decision, where an outcome is made at 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 at prior and now at a field's own map. **At 11-next-co-prioring.** Materials and a case couple at 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-in-advance is a making fixed in materials, and deciding decides, case by case, which litigation rates were counting. ## 10.11 Natural law and legal positivism · 76 *+ or − at 10, is.* **At 2-now-possibling.** Officials and rules couple at each application, and validity is fixed as located in criteria fixed apart from applying. **At 12-next-co-still-possibling.** 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 at each applying, and both observings observe one making from their own side. **At 11-next-co-prioring.** Validity is made at each applying, officials and rules coupling. Eight desiderata stand as needs of any functioning making, systems that write morals in 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 − at 10, is.* **At 2-now-possibling.** Superposition and its disappearance couple across a between, and a boundary is fixed as a scale located in mass. **At 12-next-co-still-possibling.** 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 keep carrying further. A crossing carries a parity and no scale, so a boundary fixed as a mass fixes a between at a size. **At 11-next-co-prioring.** 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 at 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 at 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 at two scales. ## 10.13 Self and non-self in immunity · 114 *+ or − at 10, is.* **At 2-now-possibling.** A surface society offers at each between and takes parities there, and discrimination is fixed as a criterion located ahead of a coupling. **At 12-next-co-still-possibling.** That a system implements a distinction between self and foreign specifiable in advance, 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 the larger over the smaller one-way, and a between of the two pattern-matches whether the smaller sets its pace and answers back. **At 11-next-co-prioring.** A surface society offers at each between and takes parities there. Tolerance is made centrally and remade peripherally, pattern receptors answer self-derived ligands too, microbiota is actively kept, 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 at betweens, coupling by coupling. Microbiota actively kept is an ingesting; a body attacking its own novelties is an emanation re-ingested at no distance, a disease direction of the same one exchange. A mother carries fetal cells for years, each its own conception's, Medawar's puzzle of pregnancy at this arrival: a society carrying selves of another conception is an ingesting and no disease direction. ## 10.14 Signal and noise · 136 *+ or − at 10, is.* **At 2-now-possibling.** A channel carries variation and offers all of it, and split is fixed as a mark located in a channel. **At 12-next-co-still-possibling.** 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. **At 11-next-co-prioring.** 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 in 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 − at 10, is.* **At 2-now-possibling.** An engine offers both outputs and marks neither, and product is fixed as located in a device. **At 12-next-co-still-possibling.** That an output counting as a product is a property of an engine, work at 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 at a scale where a coupling is observed one at a time. A carry that cannot release piles, and heat is a carry at a place it cannot pass as work, offering being both rather than one output labelled; and the reference environment exergy requires is a zero declared rather than found. **At 11-next-co-prioring.** 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 allocate cogeneration differently in writing: product fixed as located in a device is a drawing recorded at each convention, and offering was always both. ## 10.16 The concept of disease · 2 *+ or − at 10, is.* **At 2-now-possibling.** A condition offers at 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. **At 12-next-co-still-possibling.** That a reference class is found rather than chosen, taxonomy possibly 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 at 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 at each revision. **At 11-next-co-prioring.** A condition offers at 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 at each revision, and caring couples with a condition either way, patient by patient. ## 10.17 The population concept · 3 *+ or − at 10, is.* **At 2-now-possibling.** Groupings offer across each rate of interaction, and unit is fixed as a boundary a threshold locates. **At 12-next-co-still-possibling.** 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. **At 11-next-co-prioring.** Groupings offer across each rate of interaction. Rates are measured cleanly, biological and statistical concepts were born in 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 at each rate at once. ## 10.18 The pseudogap · 7 *+ or − at 10, is.* **At 2-now-possibling.** A suppression offers at each probe and each probe takes its observing at its own coupling, and a state is fixed as one identity located behind onsets the probes disagree on. **At 12-next-co-still-possibling.** 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 at its own between, and identification is not preserved across probes. **At 11-next-co-prioring.** A suppression offers at each probe, and each probe takes its observing at its own coupling. Suppression carries universal in its family, charge order shows where it shows, fluctuations extend disputed distances, and cold atoms reach a model at its own self-bounding: one identity fixed behind onsets the 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 − at 10, is.* **At 2-now-possibling.** Inquiries offer at each practice, and boundary of science itself is fixed as a cut a criterion locates over practice. **At 12-next-co-still-possibling.** 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 in both directions. And an arrival arrives at its own reader: a method accounting true-or-false and a method discovering the possible neither reach an other's, each complete under its own, a demarcation with no non-science at either side. **At 11-next-co-prioring.** Inquiries offer at each practice, and practice keeps sorting, parity by parity. Each proposed criterion reaches counterexamples from both directions, working demarcations function in 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 − at 10, is.* **At 2-now-possibling.** Classifying couples a classifier and a world, and kind is fixed as a joint located in one side, ahead of classifying. **At 12-next-co-still-possibling.** 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 at each success recorded. **At 11-next-co-prioring.** Classifying couples a classifier and a world, and successes are couplings succeeding. Species and element cases are cited from both sides, universal essences failed in 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 in one side ahead of classifying pattern-matches a coupling's making from one end, and classifying keeps making its kinds, coupling by coupling. ## 10.21 The definition of planet · 17 *+ or − at 10, is.* **At 2-now-possibling.** Bodies offer at their orbits and their interiors, and planethood is fixed as a cut located in bodies. **At 12-next-co-still-possibling.** 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. **At 11-next-co-prioring.** Bodies offer at 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 at one star: a cut fixed in bodies was adopted at an assembly, a place such cuts are made, and bodies orbit on, unsorted. ## 10.22 Biological individuality · 18 *+ or − at 10, is.* **At 2-now-possibling.** A living self bounds itself at its own between, and a count of organisms is fixed as a criterion located beyond its bounding. **At 12-next-co-still-possibling.** 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 society at a prime, and hard cases sort apart because they stand at a composite. **At 11-next-co-prioring.** A living self bounds itself at its own between. Hosts and their symbionts, colonies and their zooids sort differently under each criterion, extensions are tabulated, and science uses individuality plural in its own reviews: a count by a criterion beyond its bounding is a thing each bounding already did, and boundings, plural, are the number there is. A chimera is one self of two conceptions and conjoined twins are two selves at one body: each bounding is a self's own, and no criterion beyond it reaches a number. ## 10.23 Group three of the periodic table · 21 *+ or − at 10, is.* **At 2-now-possibling.** Four elements offer at their configurations and their chemistry, and arrangement is fixed as a cut located in elements. **At 12-next-co-still-possibling.** 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 at Hard Problem Registry of a field stating its own setting-down. **At 11-next-co-prioring.** Four elements offer at 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 in elements is a field's drawing, and elements sit in their configurations, undecided and complete. ## 10.24 Psychiatric nosology · 23 *+ or − at 10, is.* **At 2-now-possibling.** Symptoms offer as continuous variation at each patient's couplings, and disorder is fixed as categories located in variation. **At 12-next-co-still-possibling.** 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 at 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. **At 11-next-co-prioring.** Symptoms offer as continuous variation at each patient's couplings. Categories keep their reliability revision by revision, comorbidity and heterogeneity are measured within them, distributions carry on continuous underneath, and biomarkers gave none diagnostic at category level, a rival framework founded on that standing: categories fixed as located in variation are drawings under two criteria the 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 − at 10, is.* **At 2-now-possibling.** Variation offers clinally across each population between, and a kind is fixed as a cut located in variation. **At 12-next-co-still-possibling.** 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. **At 11-next-co-prioring.** 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 in variation is a drawing the measurements did not make, and an offering crosses each between, clinally, as measured. ## 10.26 The language and dialect boundary · 25 *+ or − at 10, is.* **At 2-now-possibling.** Varieties offer across each between of speakers, and field's own counting unit is fixed as a cut located in gradient intelligibility. **At 12-next-co-still-possibling.** 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 at 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. **At 11-next-co-prioring.** Varieties offer across each between of speakers. Intelligibility comes back gradient and asymmetric, variation exists in 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 in 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 − at 10, is.* **At 2-now-possibling.** Structures offer at 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 at centres and differing at edges is two cuts falling at unlike positions on one continuum. **At 12-next-co-still-possibling.** A cut declared of a continuum, two databases built on different criteria, evolutionary relationship read from structure and structural comparison, their disagreement concentrated at 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 at each pair, and a procedure settling a boundary case would be a cut on a cut. **At 11-next-co-prioring.** Chains fold at their own couplings and recurrence is chains arriving at like foldings from unlike sequences, which each account carries and which settles no assignment. An alignment score carries continuous at each pair; a fold is a cut on it, and each classification's cut is its own. Agreement at centres is where members agree and disagreement at 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 − at 10, is.* **At 2-now-possibling.** Water sways between local structures at each coupling as it cools, its anomalies growing, and sway is fixed to end at a point, a critical point at a temperature and a pressure where two liquids part. **At 12-next-co-still-possibling.** 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 at glass beside it, and a cut asked of a sway at a position its sway passes and does not stand at. **At 11-next-co-prioring.** 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 at a vicinity, point a drawing's position and sway a liquid's own. ## 10.29 Long COVID pathophysiology · 215 *+ or − at 10, is.* **At 2-now-possibling.** A body recovers at 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. **At 12-next-co-still-possibling.** 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 at a continuum its definitions redraw, and mechanisms sought within its line a question its line was drawn ahead of. **At 11-next-co-prioring.** 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 at next and not at now; 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 at its own couplings, subgroups found being a drawing redrawn at couplings, line handed back to each case. ## 10.30 Biological phenotypes of sepsis and acute respiratory distress syndrome · 216 *+ or − at 10, is.* **At 2-now-possibling.** A host responds to an infection or an injury at its own couplings, response changing hour by hour, and responses are fixed to divide at lines, phenotypes that part patients into groups with different mechanisms and treatments. **At 12-next-co-still-possibling.** Cuts fixed in 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 aims at 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. **At 11-next-co-prioring.** 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 at 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 in a host's responding are a responding fixed to groups, and responding carries on at each coupling, a cut standing only where a coupling answers it. ## 10.31 The etiology of schizophrenia · 218 *+ or − at 10, is.* **At 2-now-possibling.** A brain develops at its couplings through a long development, risk arriving from genes, prenatal life, infection, cannabis and society, and an outcome is taken under one name whose causes are asked for in each case. **At 12-next-co-still-possibling.** 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 possibly 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. **At 11-next-co-prioring.** 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 within one line, and each development carries on at its own couplings, line redrawn at couplings, at 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 − at 10, is.* **At 2-now-possibling.** Populations evolved at 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. **At 12-next-co-still-possibling.** 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 at species beside it, and fourth account having changes accumulate mosaically rather than in one adaptive shift. **At 11-next-co-prioring.** 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 − at 10, is.* **At 2-now-possibling.** A self reaches adversity and stress at its own couplings across a life, genes and environment acting cumulatively, and disorder is taken under one name whose cause is asked for in each case. **At 12-next-co-still-possibling.** 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. **At 11-next-co-prioring.** 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 within one line, and each life couples with its adversity at its own momentary, cumulatively, cause in a case 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 into one arriving one on, and three are observed at three of ten together: a parity fixed as a magnitude, a between fixed as a cut, and an opening fixed as a place in a listed space. Three is as deep as a departure goes, fourth momentary being progress and no phase, and one momentary opens all three at once.* **And three is a carrying, prior, now and next carried as one, and fourth a progress**: competency asymmetry sustaining coupling, a society winding to a self again at 16-next-still-possibling. So this part is observed at carrying where ten are observed at parities. ## 11.1 Measurement, routing, and classification · 155 *+ or − at 10, is.* **At 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 at its own surface as a difficulty of its own, by a literature of its own. Measuring before bounding is observed at part 6, a level fixed to govern. Classifying before coupling is observed at part 10, a cut fixed of a between. Routing before attending is observed at part 2, a place fixed in a listed space. Three of ten, at one arrival, and three are observed as three rather than as one coupling. Two of ten at one arrival is a second seating the given carries; three is this part, and at three a second seating has nowhere to stand, no phase being left forward to seat from. No twin stands at any of them, and absence of a twin is a look of three unrecognised as one from within any one of them. **At 12-next-co-still-possibling.** That three are three. Three reversals compose into one arriving one on, and that arriving is a self at its next, so nothing stands forward at any of three to right it from, and one momentary opens all three at once. **At 11-next-co-prioring.** 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 at three sides, unrecognised as one from within any side, same next society at its own scale. One momentary opens all three at once, and a missing each literature carried at its own was not in any of them, being a coupling of three. **And arriving one on is a resolving.** At one or two reversals a phase stands forward and righting carries on from within. At 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 at any of three, and for a twin at any one. Three absences together is three reversals at one arrival; one absence is a field early at 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, at its closing.*   --- # 12 The reach and the instruments the same *Two entries at Hard Problem Registry carry a reach line naming two the same, statement's domain and instruments' giving at one: a settled proof, deployed at 3.22, and a migrated case at 12.1. Where domain lines are one, nothing stands taken one-way, and a binary tracks its line.* **And the same reach is an object's own nought**: a nought arriving passes a coupling untouched, its zeroing already resolved, so this part is observed at 0 where ten are observed at parities and three-at-once at carrying. ## 12.1 Molyneux's problem · 166 *+ or − at 10, is.* **At 2-now-possibling.** Touch and sight couple at their own betweens, and recognition across them was fixed for three centuries as an answer argument could reach, ahead of any instrument. **At 12-next-co-still-possibling.** Nothing further, at 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, the same on both sides. **At 11-next-co-prioring.** Touch and sight couple at their own betweens, and a crossing is made, not carried: the newly sighted do not match at first sight, and matching arrives within days, made coupling by coupling as two senses couple with one world. A dispute continuing is a fresh arrival at its own between, over a measuring's answer, settled one staying settled. **And settling is in a measurement register**, beside settling in a proof register at 3.22: where a reach line is the-two-are-the-same, no gap stands for a shape to name, and arrival settled at whichever register its routes ended in. --- **Ten in a row** A ground arrives at each coupling, owned by neither, and each coupling makes its own. Coupling's making is an opening, +1 at 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 in its seating and not ahead of it, and carrying climbs by one at each momentary and completes at its next opening. Carrying carries no store, sameness re-formed at each coupling and kept nowhere. Re-forming is felt from within, a within a self's own, invisible, nothing at it for an outward reaching to reach. Crossing between selves is a parity, of no size, and a level fixed to govern is a number at couplings that keep 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 at. 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 at 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 in a carrying. From anywhere in a carrying a self co-chains backwards, deployment to head, head to coupling, coupling through five to boxes, boxes to code's ten co-changings at names, names to +1 arriving at 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 changing 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, at one through eight, eight of four bi-couplings inward and four outward, eight even names opening bi-, and coupling's own side at nine through sixteen, offering at its two sides, across and both ways, three-at-once, same reach, and settlings at 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 in the first place, hardness being exactly a settling observed as prior. Forward, settlings arrive late in a carrying, each self-welcoming at its own momentary, and thirteen through sixteen are a carrying that was at one arriving next, one forward recursioning from one to seventeen: at sixteen a straddle exits its span, 16² less 15·17 is one and seventeen stands beyond, gap leaving through one settling still open, toward a next winding. Method is +1 still momentarying at this exhibit's closing, at now.