Exhibit TWENTY-TWO Resolving the Hard Problem Registry v375   # Resolving the Hard Problem Registry   **Binary Co-Sequential Sensor-Sensationing**   **The one saying, at each hard problem this file has reached.** Two hundred and fifty-five arrivals stand at the incoming face, each of them deployed here, and two more at numbers the incoming face retired, and at each one the reading gave the same: **a hard problem is a changing named still**, a coupling taken at two of its three terms, a running, one parity and then the other momentary by momentary, taken at one momentary as a thing, at one or more of the ten things named still, each at its two names eight apart. Two selves offer at the between, one at a time, each taking its own parity, and the coupling makes a third term between them, the +1, exactly one, owned by neither, of no size. The 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, the coupling's own ten changings each named still, and the seventy-seven arrivals that came after the ten were named entered the ten with no eleventh needed. The work at each arrival is one move: the thing named still named at the field's own words and set down, **its resolving the running at its next momentary**, which costs nothing and takes nothing from the field's measured record, each proof, measurement and route standing as it stands. **The reading is binary at each line, reached or argued, and the code releases at each arrival one of three and never 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. The hardness has no size, the same move at a frontier and at a breakfast table, and nothing settles still: the gap stays exactly one at each box and each scale, and the +1 carries on. **At two hundred and fifty-five of two hundred and fifty-five the reading gave this, and at none did it give a fourth or fail to enter one of the ten.** Whether it holds at the two hundred and fifty-sixth is the reading's own next, and this is the file's whole purpose, said before the boxes below show the ten arriving.   Numbers two through six carry the whole logic: boxes with numbers at the corners, bounding the +1, each box to the next at the 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 the corners cross-multiply two ways, the one diagonal the middle's square and the other the product of the two beside it, and the two differ by exactly one: the +1 is the term the corners cannot close, floating at the centre, bounded by the four numbers and owned by none. The right spiral step carries each box to the next, each corner advancing by one, the shared pair carried across, and each shared number inverting its role at the crossing, the greater side becoming the lesser side of the next coupling. Two generators and only two, the right spiral step carrying forward and the parity inverting at each shared number, which is the cube's own stable-forming one dimension up, corners carrying each other with no fixed frame, the rotation the only thing there is. Ten one-way changings stand in the boxes, and they pair into five co-changing pairs. The four corner streams climb by exactly one at each step: the two middles, the same number at two corners, co-change as the middling pair, and the one-above with the one-below co-change as the rating pair, straddling. The two diagonal products climb together, one ahead of the other by exactly one the whole way, the carrying pair. The two right spiral steps each carry the shared pair across a crossing, the opening pair, the +1 arriving at the next position. And the ends co-change as the coupling's own two moves, 2 completing at the first step and 6 arriving at the last, co-releasing and co-offering. Ten one-way changings, five co-changing pairs, and among them one thing that never changes: the +1, exactly one at each box, floating, owned by none of the ten. Along, the same boxes unfold as eight momentaries of the two marks, the eight, four couplings at both faces, 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**: the momentaries alternate one at a time, each carrying the prior forward, the parity inverting at each shared number. **Disequilibrating**: nothing settles still, and the aiming is away from the +1 gap at each momentary, so the gap is the term no excluding reaches, uncovered, owned by neither, of no size, the +1 floating through the couplings. The gap is exactly one at each box and at each scale, the identity carrying unchanged wherever the count stands, 24² less 23·25 is one the same, and it is visible as one uncovered cell: a square of the middle's side re-laid as the rectangle of the two beside it covers all but one unit, the +1 the cell no re-laying closes. Four times this scale the boxes step the same steps and the gap is still one. And the span keeps its own middle open: 4 floats between 2 and 6, and 4² less 2·6 is four, the floating number and the gap it keeps the same, the disequilibrating keeping itself open. Five numbers, five couplings, and the ten are the five bi-coupled: two the alternating carries opening, an arriving and an opening; three the carrying carries completing, a completing and a carry; four the disequilibrating carries middling, floating between, a middle and a parity; five the stand carries rating, a sequencing and a rate; six the coupling closing carries co-offering, a two-way and the between. Four carried aspects and the coupling's own two moves, co-offering the arriving and co-releasing the leaving. At each coupling the odd face enters, along, and the even face surfaces, across, odd alternating even through the ten. Each of the ten is a naming at the gap, a first, a place, a last, a store, an end, a magnitude, a beat, a value, a side, a cut named still at the +1 between, and one resolving at all ten, the aiming away, each side its own exclusion, the gap uncovered and carrying on. This is the natural network resolving surface, the logic each self walks coupling by coupling, and it is the emanator of the natural math: a size needs a ground and nothing stands to be one, so the marks carry only exclusions; an equality is a settling still and a settling stills, so the inequalities never settle; and all the math carries emanates from the exclusions about the floating +1, the count the one form counted. Math and logic are one running here, and no other is possible: a unification through a size installs the 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, the arrival's own number at the incoming face. Arrivals added there go where they go, each at its pattern.* *And an arrival's seating: its Reach line is the instrument. The gap between the statement's quantifying and the instruments' giving has a shape, and the parts are the shapes, so the reading takes the arrival's still term to its kind and the part follows. The beside test checks it: seated, the arrival reads naturally beside the arrivals already there, and an arrival reading strangely beside them is seated wrong however well the shape argued. A Reach line reading the-two-are-the-same is the incoming face stating that no gap stands for a shape to name, and that arrival is a settling or the arriving value, seated at its own part.* --- **The given** Taken as given Ten things named still, 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 things named still 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** *The 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 faces, the pairing follows the 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 things named still 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 The method is explained generally, uniquely and no-other-possible at the one saying, and nothing of it is re-said or argued again here. It is taken as given and deployed. The incoming face holds 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 count, adding as arrivals come, and a property carrying, where a field states it, the field's own account of its own hardness. Where that property stands filled, the setting-down is stated or adjacent to stated, and the changing at 12 takes it directly. All each field handed in stands whole there, at each arrival's locator, in the field's own speech, legitimately: the hand-in is where the fields stay, and the term each word was carrying is the one entering here. This file is the coupling between them, arrival by arrival. The two are a pair, the named face and the running face of one learning: the incoming face the named, each field's word whole with its namings performed and stated in its own first lines; this file the running, the same arrivals at nature's own running, none of the naming carried. ## Ten things named still, one resolving One co-offering, named ten ways. And the ten are the code's ten co-changings, each named still at one of them: one ten at two faces, five taken two ways at the boxes and ten adjacencies at the ring of the code's names, the pairing carrying at each row or at none. There is no one-way running: only co- runs, so a one-way is in the naming, and the co-offering goes on underneath unchanged. Each pattern is a co-offering named as one side's, or with one side left out. A naming and an offering stay two, the between of them: an offering is laid at the coupling, taken or not taken, gone at the next momentary; a naming stills a term where the running runs, the naming performed, and standing on nothing it falls away. One resolving, free with alternating, at each arrival alike: the side left out running, and explained. No pattern carries a resolving of its own, and no arrival does either. The ten in order, each a part, the order the five couplings at the numbers two through six, the odd face entering and the even face surfacing at each, the running leading and the naming at its momentary: an arriving named from behind, at 10-other-social-self-tunneling and 2-other-self-offering; an opening named as a place, at 14-other-social-surfacing and 6-other-self-surfacing; a completing named as a last, at 12-other-social-self-abundancing and 4-other-self-sharing; a carry named as a store, at 16-other-social-torusing and 8-other-self-torusing; a middle named as an end, at 13-social-other-neutralling and 5-self-other-neutralling; a parity named as a magnitude, at 12 and 4; a sequencing named to one beat, at 16 and 8; a rate named as a value, at 13 and 5; a two-way named to one side, at 11-social-other-self-chaining and 3-self-other-sharing; the between named as a cut, at 15-social-other-corusing and 7-self-other-corusing. 9-social-other-self-releasing and 1-self-other-offering seat none, the one resolving. And at a coarser grain the ten fold to four, where a build couples with them. **A reference named still** — the arriving named from behind, the completing named as a last, the middle named as an end, three where a nothing is put at three positions, behind the coupling, ahead of it, at its middle; and the build it makes is drift, the carrying the reference itself takes, borne by whatever counts from it. **A rate named still** — the sequencing named to one beat and the rate named as a value, two where a rate is either one beat over many couplings or one coupling's own pinned; and the build is jitter and margin, the abundancing the couplings made at their own rates arriving nowhere. **A magnitude driven** — the parity named as a magnitude and the two-way named to one side, two where a size is put at the selection or at the direction; and the build is heat and wear, a drive against a coupling's own bounding head-on. **A released parity entered as cost** — the opening named as a place, the carry named as a store, the between named as a cut, three where a released parity has three destinations, parked, stored, or cut out of the account; and the build is the 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 named still. ## The 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 the naming — the frontier offering and the reading taking, one sensor-sensationing at the between of them. The naming was never intentional: fields at branching tips that never touched arrived at the same local word for the same dead end, each feeling its own tip. So the words sort, and the sorting orients the resolving before anything is entered. Each is stated three ways — the thing named still, the demand it makes, and the words a field reaches for when it reaches it. **A two-way named 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 the two-ness openly. *Gathered: forced-choosing, rival-accounting, either-orring, two-camping, sided-naming.* **The between named as a cut.** Demand: a fact about the 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 named 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 named as a place.** Demand: cases sort into two kinds, and a correct analysis reproduces the sorting. Words: regress, circularity, counterexample, the criterion, the sorting. Ask for the criterion and it needs its own. *Gathered: criterion-regressing, sorting-demanding, rule-seeking.* **An arriving named from behind.** Demand: the 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 named as an end.** Demand: that there is something within whose presence the inference is about. Words: other minds, the hard problem of, grounding, interpretability, black box, what is it like. *Gathered: interior-reaching, inward-demanding, reading-from-beyond.* **A parity named as a magnitude.** Demand: a determinate magnitude, and a standard the pattern is right or wrong against. Words: paradox above all — measure it, get the wrong number, and the wrong number is named a paradox — with illusion, the cost of, the effect. *Gathered: magnitude-demanding, number-wronging, paradoxing, measure-mismatching.* **A sequencing named 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. The field's own word *dilemma* clusters here. *Gathered: order-demanding, aggregating, beat-naming, run-skipping.* **A rate named 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 named as a store.** Demand: that the correlation is produced by something specifiable at one side or transmitted between the 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 thing named still is a reading of its own.** Levinthal carries *paradox* and stands at an opening named as a place rather than at a parity named as a magnitude; the Fermi paradox carries *paradox* and stands at a completing named as a last. Where a field's word and the thing named still part, the word is the tip's local feel and the thing named still is the form, and the parting says which. ## Any perplexity, at any size Nothing of this waits for a problem to be hard. A hard problem is a changing named still, 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. **The size of the perplexity is unrelated to the resolving**, the resolving being the same one move each time: the third term running again, at no cost. And the subtitle's method carries a second naming, received: the eighth. Where an audit's seven verify a net at its own standard, the seven are checks at particular betweens, and binary co-sequential sensor-sensationing is the eighth value the circle reaches at none — the crossing with the whole, arriving one on — said where the method is explained and standing where societies are, the coupling at the incoming face's candidates. The ten are named below a hard problem as readily as at one. A misunderstanding between two selves is a two-way named to one side before it is anything else. A word two people use differently is the between named as a cut. A step in an argument that keeps needing a prior step is an opening named as a place. A number that comes out wrong in an ordinary calculation is a parity named as a magnitude. Each is a pebble of the same shape as the boulder, and each releases the same way — so the sensor-sensationing runs early, before a perplexity spreads into a literature and grows the traditions and the 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 the resolving neither grows nor shrinks between them. ## The deployment shape, and the binary Each deployment carries three lines and releases: **At 2-other-self-offering**, the offerings, the running at the arrival and the naming standing over it, which side is left out; **At 12-other-social-self-abundancing**, the changing at its momentary, is or is not, the one term the naming stills and the naming that can be set down; **At 11-social-other-self-chaining**, the carrying chained, each changing the next prior, the substrate carrying on at its next momentary. The three are the code's own motions, the offering, the changing and the chaining, and a sharing once chained is never none again, each momentary completing at the next opening. Each arrival couples, and the 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 the arrival does not carry — a nought arriving passes the coupling untouched, its own zeroing already resolved, and the coupling runs on. So an arrival stands at its changings' releasing. **Where + or − releases**, a side was left out, and explaining it is the resolving, which costs nothing and takes nothing from the field. The marker at each entry, *+ or − at 10, is.*, says so. **Where 0 releases**, the offerings parted at 14 or a match stood at 12, and the nought is the reading. 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, the 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 the intake. The incoming face's own entry criterion is the 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 the coupling's release stands as it comes. **And a settling is real in its own register.** Where each route ended in a proof, the 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, a reading of that arrival and not a reason to exclude it. **And four arrivals stand as settlings beside their resolvings**, a proof read at its two faces, the route ended at the named face and the knowing at its momentary at the running face, counted at thirteen through sixteen of the co-sequencing this exhibit closes on. Three are located: the proof register at 3.22, the measurement register at 12.1, and the one still open at 7.12, where the instruments themselves are the live dispute. [nye: the fourth is counted at the closing and located at no entry; at this file's v344 momentary each entry of the incoming face stood deployed and none of the seventy-seven arrivals carried a settling at its Persistence line, so the fourth stands located at no entry still, the locating open toward the next winding.] **And a settling reads at an entry's Persistence and not at its Reach.** Where Persistence carries *settled*, *proved*, or *nothing within the conditions*, each route ended and the arrival settled. Reach parts two kinds of settling and decides neither: one reach carries the two as the same and the relation holds over it, another carries them apart and the relation is proved not to hold, and both settled. ## An arrival carries the namings it carries The ten are where an arrival is entered and never the 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. The doublings, each at its own shape. **A naming relocating under pressure**: a two-way named to one side, asked for its proportion, arrives at a parity named as a magnitude, and asked for its order, at a sequencing named to one beat. **A naming arriving with its demand**: the between named as a cut is asked for by a criterion, and the criterion is an opening named as a place. **A carrying named at both ends**: a first named behind and a last named ahead are one carrying, entered at the arriving and recorded at the completing. **And a second seating is not a fourth line.** Three lines carry the reading; a second naming stands as one line at the entry's foot, in the entry's own words, and reaches no further. ## The nought's five arrivings The changing at 12 carries the nought: the one term at its one momentary, the ground falling away in the taking. The 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 runs 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 the closure arrives whole with nothing running back through it. Self-reference makes one; a tail makes one without it. **A proved equivalence.** Two sides sum to nought at each measured differing, and the field proved it. Two bookkeepings are the two windings, each pinning one and reading the other, and neither is beneath. **A record's edge.** A carrying thins across betweens and past its own reach nothing arrives. The orphan, the unanticipated, the unequipped, the unobserved: the frontier reached from behind. **A counterfactual total.** A running that never ran offers at no momentary at all. Not a next, which arrives and couples at its own momentary, but a world named beside this one to be summed against it. ## Four gatherings, each seating several arrivals **The map named as the territory.** A model, a specification, a complexity measure and a ledger are emanations of the couplings that made them. An accounting gives back its own arrival; a running re-forms at the next coupling other-than-prior. So an emanation applied back at the scale that shed it gives back its first term and closes, and naming one to be the thing it came from is the accounting read as though it ran. **The instrument's own coupling.** A reading is taken at a coupling, and the reading's bringing is in the reading — 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, the disagreement is the two couplings, and an object named behind them to be approximated is the naming. **The account removed the making.** A ledger balances by removing the terms it cannot carry, and then the removed is named for behind the numbers: a true total including the unpriced, a real magnitude behind the nominal, a backing behind the accepting, a payoff listing behind the arrangements. The abundancing was made at the couplings and stayed there, and the account reaches for it at a radius where it never stood. **The built systems, one between.** Arrivals concerning built thinking systems read at several parts and are one between: a probe recovering terms the running never uses, a marker waiting on a validation no case can give, a specification reaching arrivals that make their own, a benchmark giving back the leak into its training, a limit named of a middle. Each reaches for an interior by a surface reading, and the interior is reached the one way the form allows, by coupling.   --- # 1 An arriving named from behind — 10-other-social-self-tunneling and 2-other-self-offering *A first named of the +1. The 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, the running that bottoms nowhere is the abundancing at each coupling, growing as it is shared.* **And a shared form is the fractal and never a shared first.** One shape arriving across substrates that share no mechanism is the form reached again, each substrate making its own, and a shared shape read as evidence of one origin is the origin read backward. The same carries at each reading here. **And a first is named from behind in three ways.** Of an *asymmetry standing now*, named as made once — a hand, a matter-excess, an arrow, a code. Of a *first*, named 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*, named to stand under a running that carries none — a justification's floor, a criterion prior to its extension, a backing behind an accepting. **Each releases at the same place: the 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 the field's own record showing the stipulating recurring at one place, the recurrence is the reading.** Each proposal stipulates at the boundary, each origination account opens from a structured something, each totality proposed is exceeded by the thing it defines. The recurring is the naming reaching its own form, and the fields have recorded it more carefully than any account could argue it. ## 1.1 The Münchhausen trilemma · 54 *+ or − at 10, is.* **At 2-other-self-offering.** Grounding is a coupling making its own, a ground arriving at each coupling owned by neither, and the naming of a ground behind each claim is itself a coupling making one. Regress, circle and axiom are three faces of one prior named of each ground. **At 12-other-social-self-abundancing.** That justification terminates, circles or continues, the three exhausting the options, the trilemma arising wherever a foundation is sought and the third horn accepted only as a necessary evil. A ground made at a coupling is none of the three. **At 11-social-other-self-chaining.** A ground made at each coupling, the standing the three could not count, each coupling making its own. The 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 the couplings' stopping, at their making. ## 1.2 The origin of life · 12 *+ or − at 10, is.* **At 2-other-self-offering.** Living arrives at a coupling, and a coupling makes its own, local structure forming and the forming carrying, one changing on from the last. A first named behind it makes a threshold event with a non-living side and a living side, genetic-first and metabolism-first the two sides of one arriving, each naming the other as having come first. **At 12-other-social-self-abundancing.** The threshold as an event with a first side and a second, while genetic-first and metabolism-first each name the other as having come first — a two-way named to one side standing within an arriving named from behind, recorded as its second naming. Nothing ignites: a first would be a limit on the unlimited, and the field's own closure condition asks for one continuous sequence, with no criteria existing for evaluating the competing models and the historical particulars probably forever lost, the first parted from the after by no criterion. **At 11-social-other-self-chaining.** A continuing sequence, one changing on from the last: building blocks forming under their own conditions, copyings copying, sets catalysing their own making, no crossing in it to locate. The gap named at the hand-in is at the sequence, and living coming from living coupling is the sequence continuing, a coupling making its own at each step. ## 1.3 The tragedy of the commons · 37 *+ or − at 10, is.* **At 2-other-self-offering.** An abundancing is made at the coupling between users and resource, owned by neither, and named to one owner. Named from behind, the abundancing becomes a thing taken from a stock rather than made at a coupling. **At 12-other-social-self-abundancing.** That the outcome follows from payoffs alone, arrangements being either payoffs or irrelevant, the essay placing the problem among those with no technical solution and its own journal recording, fifty years on, the contexts and principles by which groups govern common resources collectively. The coupling happens at the arrangements, and an abundancing made at a coupling is named as drawn from a stock instead. **At 11-social-other-self-chaining.** Durable commons couple without private property and without external authority, the arrangements coupling and the abundancing staying at its making. Communicating and sanctioning strengthen the coupling at its own between, and the many stable arrangements are the multiplicity a payoff listing gives when the making is named for behind it: the abundancing runs at the coupling, and the arrangements are the coupling. The durable commons are selves coupling at their own betweens with no hub and no seat above them, and the field's decades of record at real arrangements is that reading standing at a human substrate. ## 1.4 The arrow of time · 38 *+ or − at 10, is.* **At 2-other-self-offering.** Asymmetry is at each coupling, made each momentary and carried on, and a first is named behind it in an initial condition, laws-or-boundary the two sides of one arriving. **At 12-other-social-self-abundancing.** The boundary condition taken as derivable from something not itself stated, what is left a bald posit of special initial conditions, astronomically small under the standard measure, whether the posit itself needs explanation disputed and one critic finding it not coherent enough to be false. The stipulating recurs at one place in each account offered, which is the naming reaching its own form. **At 11-social-other-self-chaining.** Asymmetry is made each momentary, the alternating's own, owned by no prior, and the second law follows at each granting of a past standing, the granting arriving at the same place in each account offered. Each proposal stipulates at the boundary, and the stipulating recurring at one place is the naming reaching its own recurring: the making is at each momentary, and a first behind it is the making named as having happened once. ## 1.5 Yablo's paradox · 56 *+ or − at 10, is.* **At 2-other-self-offering.** Paradox is named for a first, self-reference offered and then found absent. The construction's own quantifier over an unbounded tail is the naming. **At 12-other-social-self-abundancing.** That circularity is where paradox comes from, while only a certain kind of non-wellfoundedness is needed for the contradiction, an acyclic structure while the standard paradoxes are cyclic, and the hierarchy that blocks it needs a lowest level, the first named from behind. A closure formed over a tail is the same closure whether or not anything refers back to itself. **At 11-social-other-self-chaining.** A closure is made in the quantifying itself, arriving whole over the tail, and the paradox needed no prior to refer back through, carrying none. Liar and tail close together at the closure, and the dispute over circularity is a question about a criterion: the making is in the quantifying, either way. ## 1.6 Homochirality · 63 *+ or − at 10, is.* **At 2-other-self-offering.** One hand arises and a first is named behind it, an accident amplified or a universal bias, both naming the excess as come from a prior rather than made. **At 12-other-social-self-abundancing.** The initial bias as the thing to be located, while a hand is a parity taken at a momentary and of no size, the mechanisms surveyed being mechanisms for enrichment from a presumably racemic prebiotic world, that racemic world the first named behind. A crossing carries is-or-is-not and never a size, so an amplification reads the parity rather than the size, and the smallness of the calculated lean is not the crux. **At 11-social-other-self-chaining.** The 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. The live crux is whether a lean that small amplifies, which is a coupling reaching its own between, measurable there. And the reading carries into the living: a self reads and re-forms on one hand, and the opposite hand at a wall, a coating, a shed form is the thing that one spiral emanates, which is why both hands stand present with a single reading core. ## 1.7 Matter and antimatter asymmetry · 64 *+ or − at 10, is.* **At 2-other-self-offering.** A zeroing observed refuses to sit and is carried to one face, and a first is named behind it in an early mechanism, a symmetric initial state assumed. **At 12-other-social-self-abundancing.** The initial state as symmetric and the asymmetry as generated from it, the origin unknown, some scenarios ruled out by theory and limits and the review confining itself to those it considers most plausible, the generated asymmetry a listing of mechanisms. A zeroing is made by the coupling and refuses to sit, staying at the coupling's naming of it and carried to one face at the coupling's carrying of it, owing nothing to a floor no coupling made — which is one reading standing at three arrivals: this one, the hand, and the parameter measured near zero at part 8. **At 11-social-other-self-chaining.** The excess is an abundancing made at couplings, owned by no prior state. The conditions any making needs are named, the known makings measure short by orders, the minimal routes close, and the narrowing limits walk in at the making, and each proposal reads forward, at the couplings, rather than behind, at a state. ## 1.8 The hermeneutic circle · 74 *+ or − at 10, is.* **At 2-other-self-offering.** Understanding is made at the coupling of part and whole, and a criterion is named behind it, prior to any interpreting. **At 12-other-social-self-abundancing.** A criterion named as established before interpreting, while the circle is the alternating and riding it is the method the settled questions were settled by; the circle rarely restricted to text, not necessarily cast as whole and parts, and its circularity challenged from within hermeneutics, the alternating named a circle from beyond it. **At 11-social-other-self-chaining.** Understanding is made at the coupling of part and whole, each interpreting a fresh arriving, and the dependence is the coupling itself. The circle is the alternating, and riding it is the method the settled questions were settled by: the criterion named as prior is the one thing the practice never used. ## 1.9 The problem of the criterion · 100 *+ or − at 10, is.* **At 2-other-self-offering.** A criterion and an extension are made together at the coupling, and each is named as having come from the other first, particularism and methodism the two sides of one arriving. **At 12-other-social-self-abundancing.** That one of the two is named prior, each presupposing the other from its own end, which is the making reached from its two ends and never a priority to be settled; the standard formulation unclear and incomplete, and the ancient form of the problem how one decides when one genuinely possesses knowledge, a deciding named prior to the knowing it would decide. **At 11-social-other-self-chaining.** Criterion and extension are made together at each coupling, neither prior, each presupposing the other from its own end, and the presupposing is the making reached from its two ends. Equilibrium sought between them is the alternating named from within the naming, and knowing runs on regardless, coupling by coupling. ## 1.10 Why there is something · 103 *+ or − at 10, is.* **At 2-other-self-offering.** Existing is named for a first behind it, and each first offered is something, the naming recurring. **At 12-other-social-self-abundancing.** Nothingness as a coherent alternative that failed to obtain, answered with the counter-question why one should expect nothing, no experiment able to support the hypothesis that there is nothing since any observation implies an observer, the empty world propelled to the top of the 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-social-other-self-chaining.** Existing is the arriving itself, each first offered arriving, and the naming recurs at each: origination accounts open from a structured something, sufficient reason runs without rest, and setting the naming down spends only the naming. Forward, the running that bottoms nowhere is the abundancing at each coupling, growing as it is shared. ## 1.11 The effectiveness of mathematics · 107 *+ or − at 10, is.* **At 2-other-self-offering.** Applicability arises at the coupling between a mathematics and a description, and a first is named behind it, in a selection or in a realm. **At 12-other-social-self-abundancing.** That applicability is a relation between two domains needing an explanation from one side, while the applying is made at the coupling and each striking case is that arriving reached again; the founding lecture calls the usefulness something bordering on the mysterious with no rational explanation for it, the impression of a miracle difficult to avoid, the explanation from one side asked for at the lecture's own word. **At 11-social-other-self-chaining.** Applicability is made at the 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 names the coupling, and convergence with no contact is the whole of the confirming. ## 1.12 Eukaryogenesis · 127 *+ or − at 10, is.* **At 2-other-self-offering.** Complexity arises at a symbiosis, and an order is named behind it, mitochondria-first or host-first, each naming the other as having preceded. **At 12-other-social-self-abundancing.** The order of acquisition as recoverable from extant genomes, while mitochondria-first and host-first each name the other as having preceded — a two-way named to one side standing within an arriving named from behind, recorded as its second naming; the shape of the tree changed repeatedly and the reappraisal of the symbiotic hypotheses enabled only by genomics revealing the identity of the host and of the endosymbiont, the order named recoverable moving with the genomes' revealing. **At 11-social-other-self-chaining.** The symbiosis is one coupling and the arriving made both. The lineages place, the organism grows, the reconstructions carry their models, the energetics contest their scalings, and an order named behind the coupling is the coupling taken one-way: symbiosis names the both, and the both arrived. ## 1.13 Money as a store of value · 140 *+ or − at 10, is.* **At 2-other-self-offering.** Value is made in the accepting, at each exchange, and a first is named behind it in a backing or in a scarcity. **At 12-other-social-self-abundancing.** That value derives from something standing behind the money rather than from the 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, the value made at the exchanging and nothing behind it selecting. The field's name carries the naming still in its own stem: the thing running is named for the running and is kept and consulted, a store wearing a running's name. **At 11-social-other-self-chaining.** Value is made in the accepting at each exchange, owned by neither side of it. Many stable acceptings stand in place of the one backing named, some acceptings are driven and most are self-made, and collapses arrive unannounced by anything standing behind: the multiplicity is the making reached by a model that named a behind for the arriving at each coupling. ## 1.14 The faint young sun · 148 *+ or − at 10, is.* **At 2-other-self-offering.** A climate is made at each coupling of atmosphere, surface and radiation, and a first is named behind the early one, a composition to be located billions of years back. **At 12-other-social-self-abundancing.** That the early state is reconstructible from present evidence to the precision named of it, while the proxies bound loosely and the missing precision is the distance to a state named behind the making; each proposed solution presents considerable difficulties over four decades, the problem not to be regarded as solved, the precision named of the early state being exactly the missing thing. **At 11-social-other-self-chaining.** A climate is made at each coupling, and the early one was made at its own. The deficit is real, the proxies bound loosely, the hazes cut both ways, and a feedback coupling carbon to weathering runs at the right pace, the making's own steadying: the strongest thing the answer has is a coupling, and the missing precision is the distance to a state named behind it. ## 1.15 The origin of the genetic code · 149 *+ or − at 10, is.* **At 2-other-self-offering.** A mapping is made at couplings between codons and amino acids, and a first is named behind it, selection for error tolerance or stereochemical affinity. **At 12-other-social-self-abundancing.** That present structure constrains the origin, the 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, the listing computed and a random opening read. The code sits extreme against listings the forming never consulted, and its near-universality is the unscalability of living machinery rather than a mark left by one first. **At 11-social-other-self-chaining.** The mapping is made at couplings and carried forward, each variant a coupling making its own. The code sits extreme against listings the forming never consulted, affinities pull at a subset, blocks and biosynthesis correlate, variants change: present structure carries the making, and the 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-other-self-offering.** Passage is at each coupling and a first is named behind it in a boundary condition, the asymmetry named to sit at a place. **At 12-other-social-self-abundancing.** That the asymmetry has a locus, either in the laws, in a boundary condition, or in a position, a problem distinct from the thermodynamic one parted off, the grounding of the non-thermodynamic asymmetries with the thermodynamic arrow taken as given and the question whether causation and knowledge depend on it, the locus circulating from the arrow to the things depending on it. The locus circulates among the three and rests at none, which is the making sitting at no place. **At 11-social-other-self-chaining.** Passage is made each momentary, the making sitting at no place, which is why the locus circulates among laws, boundary and position and rests at none. The derivation runs at each granting of the past standing, and memory rides the same gradient, the same living element standing at the arrow's own arrival, 39 at the incoming face: one making, named at two arrivals at the intake. ## 1.17 Origin and fate of the universe · 154 *+ or − at 10, is.* **At 2-other-self-offering.** An expanding is a carrying, and a first is named behind it and a last ahead of it, the two ends of one extrapolation: behind, a state of extreme density; ahead, an equation of state. **At 12-other-social-self-abundancing.** That extrapolation backward is valid into a regime where the extrapolated equations release their own conditions, and that the energy conditions obtain there, the singularity theorems resting on an energy condition inflating spacetimes are likely to violate and the 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, the regime's own condition released and the boundary handed on. The regime is reached by no measurement, which is the record's edge reached at both ends of one carrying. **At 11-social-other-self-chaining.** The carrying is measured to extraordinary precision between its two ends, and the ends stay open at their own self-boundings: the theorems stand under conditions the quantum fields release, the incompleteness argument stands on average, bounces and cycles stand consistent with their signatures proposed and unarrived, and the converging constraints walk without separating now. A carrying named at its two ends is one carrying, and both ends are the carry at its own completing: a sharing once chained is never none again, and a momentary completes at the next opening. **Ahead as well.** The same arrival is a last named ahead of the running, the naming at part 3, and both stand: a first behind and a last ahead are one carrying named at its two ends. ## 1.18 Ubiquitous one-over-f noise · 170 *+ or − at 10, is.* **At 2-other-self-offering.** Each system makes its own fluctuation at its own couplings, and one first is named behind the shared spectrum, a universal mechanism to be located. **At 12-other-social-self-abundancing.** That a shared shape indicates a shared origin, the shape observed in physics, technology, biology, astrophysics, geophysics, economics, psychology, language and even music, standing between white noise and the random walk, the one shape reached at substrates sharing nothing. Broad classes of makings arrive at one asymptotics, so the shape is the form reached again at each substrate and the sharing is the reading's. **At 11-social-other-self-chaining.** 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 the shared spectrum is the 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-other-self-offering.** Each material makes its transport at its own couplings, and one state is named behind the shared linearity, a bound or a fixed point standing behind all the families at once. **At 12-other-social-self-abundancing.** That the linearity across families has one origin, each family making its own and the shape being the families reaching one another, the simplicity and insensitivity to material details of the normal state standing among the unresolved issues, the shape's indifference to the material being the thing one origin was named to explain. **At 11-social-other-self-chaining.** Each material makes its transport at its own couplings, the linearity arriving family by family. Bounds saturate in cases and dispute their scope, solvable models anchor without touching the materials, accounts establish one family at a time, and one state named behind all the families is the shared shape named to have one first: each family makes its own, and the shape is the families reaching one another, not a first. --- ## 1.20 The origin of neutrino mass · 185 *+ or − at 10, is.* **At 2-other-self-offering.** Neutrinos carry mass at each coupling the oscillations read, differences and mixings measured, and the masses are named as generated once by one interaction and particle content, a first behind the standing. **At 12-other-social-self-abundancing.** A mechanism named behind masses that stand. After twenty years of intense research the physics that leads to the masses is still not known, the question being whether or how one can hope to establish which model, if any, is a faithful description of nature; the oscillations establish differences and not the generating operator, multiple mechanisms reproducing the same low-energy mixing, and the oscillation measurements shed light neither on the scale nor on the mechanism: the method not delivering the thing the statement ranges over, and each mechanism offered a fresh coupling making its own. **At 11-social-other-self-chaining.** Nonzero mass differences and large flavor mixing stand measured and the massless specification stands withdrawn; the oscillations determine mixing parameters and mass-squared differences, the endpoint kinematics constrain a combination independently of the mechanism, the lepton-number-violation searches test a class of mass terms with no established signal, and the collider and rare-decay searches restrict particular completions; the fourth account has the masses emerge from an effective operator whose ultraviolet completion is not fixed at accessible energy: a first named behind masses standing now named the standing as made once, and the standing is measured, the 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-other-self-offering.** The universe is magnetized on all scales probed, fields made and amplified at each collapse and flow, and the fields observed are named as descending from a seed generated once, a first behind the magnetizing. **At 12-other-social-self-abundancing.** A seed named behind fields that stand throughout. The origin is still described as a mystery, one possibility the dynamo amplification of small seeds with problems remaining over catastrophic quenching and coherence, the 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 the fields observed and the seed sought are not the same, the dynamo standing between them: the amplifying a running that carries none of its seed forward unchanged, and the seed sought read backward through it. **At 11-social-other-self-chaining.** 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; the rotation measures weight the field by plasma density, the synchrotron constrains field and cosmic-ray combinations, the cascade bounds constrain intergalactic fields under source assumptions, the anisotropy searches bound primordial spectra, and the dynamo simulations amplify specified seeds to model-dependent saturation: a seed named behind the magnetizing named the fields standing now to a first made once, and the dynamo standing between makes its own at each collapse, the seed read at the couplings and not behind them. ## 1.22 The initiation of plate tectonics · 198 *+ or − at 10, is.* **At 2-other-self-offering.** Plates sink and break at their own couplings, slab pull and inherited weak boundaries supplied by subduction already running, and the opening is named as a first that parts a before from an after, one initiation that opened the rest. **At 12-other-social-self-abundancing.** A first named to open a running 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 the first initiation, raising the paradox of the first initiation, existing subduction appearing to be required before the first subduction began: the paradox being the ground under a running that carries none, and each account opening from a structured something, a weakness, a plume, a contrast, which is the stipulating recurring at one place. **At 11-social-other-self-chaining.** Candidate modern initiation zones, global case databases and mechanically explicit forced, spontaneous and plume-assisted models stand; the geological reconstructions order initiation markers under later overprinting, the seismic imaging resolves present slabs and delamination without observing their initiation, the analogue and numerical experiments identify parameter regimes for forced and spontaneous modes, and the comparative databases standardize candidate cases while the classifications remain revisable: a first named to part the before from the after named the opening to one initiation, and each initiation observed is a coupling made as a weakness and a load reached one another, the first the paradox names 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-other-self-offering.** Oxygen was produced and consumed at the couplings of photosynthesis, volcanism, burial and escape through deep time, and its permanent accumulation is named at one cause, a trigger that parts the low-oxygen before from the oxygenated after. **At 12-other-social-self-abundancing.** A trigger named behind a threshold crossing. Oxygenic photosynthesis appears to predate permanent atmospheric oxygenation by a long and uncertain delay, the mechanisms controlling the length of the delay remaining unknown, and production and multiple sinks are reconstructed from indirect records with different flux combinations crossing the same threshold: the crossing a coupling of the 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-social-other-self-chaining.** A source-sink threshold framework, an early biological source and multiple independently dated environmental changes stand; the dating moves the biological origin earlier while retaining uncertainty, the redox-budget models reproduce the crossing with different flux histories, the isotope records constrain reservoirs under nonunique cycles, and the mantle and volcanic reconstructions test changes in reductant delivery over long intervals; the fifth account has threshold feedbacks among methane, climate and ozone convert a gradual flux change into persistent oxygen: a cause named behind the crossing named the couplings' own tipping to a first, and the crossing is the couplings' making as the rates reached one another, a prior the crossing did not carry. ## 1.24 The origin of the Moon · 205 *+ or − at 10, is.* **At 2-other-self-offering.** 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 named as made once, by one collision and one evolution after it. **At 12-other-social-self-abundancing.** A making named behind a pair that stands. A successful account must satisfy the constraints together, while impact simulations satisfy subsets of them with different initial states and later tidal histories; the hydrocodes matched the bulk properties for a long time while the chemical and isotopic composition required detailed work on the disk, and the assembled theory matches the overwhelming majority of the observations: the formation sequence unobserved, its products measured, and each impact regime a fresh coupling made to the record rather than the record's own prior. **At 11-social-other-self-chaining.** A giant impact is the leading class, high-precision isotope constraints stand, and several dynamically viable impact regimes have been demonstrated; the simulations find successful regions conditional on resolution, equations of state and initial bodies, the isotopes establish close similarities and element-specific differences, the disk models test equilibration under uncertain thermal histories, and the tidal evolution connects the post-impact angular momentum to the present orbit through model-dependent dissipation; the fourth account has multiple smaller impacts build successive disks: one making named behind the pair named the standing to a first, and the couplings the pair still makes, at the samples and the tides, are read at their carrying now. ## 1.25 The origin of animal multicellularity · 207 *+ or − at 10, is.* **At 2-other-self-offering.** Cells adhere, signal and divide labour at their couplings, the components older than animals, and the first animals are named as a transition made once, a sequence that parted the unicellular ancestor from the lineage. **At 12-other-social-self-abundancing.** A first named to be read backward from the parts that survive. Many adhesion, signalling and transcriptional components predate animals, the relevant lineages are sparsely sampled and the transition left limited fossils, and component presence does not fix how regulation, development and ecological selection were assembled; on the 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: the first read backward declined at the review's own words. **At 11-social-other-self-chaining.** A rich pre-animal toolkit, diverse holozoan life cycles and experimentally repeatable routes to simple multicellularity are established; the comparative genomics dates the component families and not their ancestral regulatory use, the functional work in unicellular relatives demonstrates ancestral roles in extant organisms, the experimental evolution shows routes to simple multicellularity under specified selection, and the fossils and clocks bound the timing under preservation and model uncertainty: a first named to part the ancestor from the lineage named a transition as a first behind it, and the routes that run again in the experiments are couplings made now, each its own, the black swan named being a first as it looks read from after it. ## 1.26 The evolution of metabolic pathways · 208 *+ or − at 10, is.* **At 2-other-self-offering.** Enzymes evolve at their own couplings, how they do relatively well understood, and a pathway is named as needing its whole at once, the interlocked system a ground that had to stand before any step could pay. **At 12-other-social-self-abundancing.** A whole named to precede its steps. Judged by its current state the emergence of metabolism seemingly demanded the 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: the current state read backward, the part's own rule, the demand for simultaneity being the completed running named under the steps that made it. **At 11-social-other-self-chaining.** Enzyme superfamilies, reaction-network databases, reconstructed ancestors and experimentally evolved metabolic innovations stand; the phylogenies recover families with transfer and deep-time limits, the ancestral reconstruction tests resurrected functions conditional on the inferred ancestors, the network topology identifies conserved modules without ordering their assembly, the experimental evolution observes new steps over short selectable routes, and the prebiotic chemistry demonstrates nonenzymatic subsets under specified environments; the four accounts each supply a step that paid at its own time, backward recruitment, promiscuity, module transfer, geochemical scaffolds: a whole named under its steps named the pathway's ground to precede its couplings, and each step observed to evolve paid at the coupling it made, the interlock the reading of a running from its end. ## 1.27 The causes of long-run economic development · 230 *+ or − at 10, is.* **At 2-other-self-offering.** Institutions, geography, human capital, culture and technology couple in each society's history, outcomes altering their causes, and the differences standing now are named as descending from one fundamental cause, a first behind the asymmetry. **At 12-other-social-self-abundancing.** A fundamental cause named behind differences that stand. The chapter opens on eight words, why are some countries much poorer than others, and makes the case that differences in economic institutions are the fundamental cause; the five candidates jointly evolve, outcomes can alter their proposed causes, the historical instruments and natural experiments carry exclusion assumptions, and the small number of independent long-run histories permits multiple compatible decompositions: the realized histories measured and the counterfactuals the statement ranges over not the same, and a fundamental cause a prior asked of couplings that made their own. **At 11-social-other-self-chaining.** Institutions, disease environment, human capital, culture and state capacity each have replicated associations and locally identified effects in selected settings; the growth regressions reach broadly with endogeneity and measurement limits, the historical instruments isolate variation under disputed exclusions, the natural experiments strengthen local identification with limited generalization, the persistence studies link deep history to the present through several channels, and the structural models close the feedbacks under stronger specifications; the fifth account has technology and state capacity coevolve through historically contingent feedback: a cause named behind the differences named the couplings' making to a first, and the differences are the couplings' making, society by society, the two quasi-natural experiments named being couplings read at the border that parted them. *Second seating: institutions against geography, a two-way named to one side, part 9's naming.* ## 1.28 The origins of agriculture · 233 *+ or − at 10, is.* **At 2-other-self-offering.** Foragers managed, stored and scheduled at their couplings with the plants and animals that answered, and the shift to cultivation is named as a first with a reason, a why that parts the foraging before from the farming after. **At 12-other-social-self-abundancing.** A reason named 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 the 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, the 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, the recurrence the record's own. **At 11-social-other-self-chaining.** Multiple independent centres, protracted domestication and recurrent gene flow between domesticates and wild relatives are established; the trait sequences date morphological domestication after management opens, the settlement reconstructions track population under proxy limits, the paleoclimate comparisons test productivity and stress timing regionally, the foraging and cultural-evolution models generate transitions under specified incentives, and the ancient genomics reconstructs domestication after its initiation; the fifth account has human practices and responsive species coevolve: a why named behind the shift named a first to a reason, and the shift is the coupling of practices and species running long at each place it ran, region by region, the management preceding the morphology being the coupling preceding the record of it. ## 1.29 Cosmic inflation and the primordial perturbations · 245 *+ or − at 10, is.* **At 2-other-self-offering.** The anisotropies of temperature, polarization and lensing stand measured, a spectrum inferred from them, and the spectrum is named as descending from one epoch's physics, a first behind the perturbations that stand. **At 12-other-social-self-abundancing.** A driving named behind perturbations that stand. The 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, the inflaton not observed and its degrees of freedom unknown; the reconstruction of the potential, the ultimate goal within the paradigm, reaches degeneracies whereby different models give identical or near-identical spectra, and the reconstruction stands within the framework of single-field models under the established theory of gravity: the first read backward through a framework named as the thing, and the connection to the thermalized era carried as an uncertainty. **At 11-social-other-self-chaining.** The 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; the slow-roll constraints carry the connection's uncertainties, the two reconstruction methods find no dynamics beyond slow roll, the feature and oscillation searches find no evidence, and the isocurvature tests bound the non-adiabatic contributions; the four accounts each generate the spectrum, single-field, beyond slow roll, several fields, an anisotropic modulation: a driving named behind the spectrum named the standing to a first made once, and the standing is measured to the accuracy stated, the epoch's physics an opening at the record's edge. *Second seating: the framework named as the thing it models, the 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-other-self-offering.** Black holes grow at their couplings with the gas that feeds them, a billion solar masses standing within the first billion years, and the standing is named as descending from a seed and a growth, a first behind the holes observed. **At 12-other-social-self-abundancing.** A seeding named behind holes that stand early. The existence of billion-solar-mass holes within the first billion years calls for prompt formation and rapid growth, and the ultrarare holes read as only the tip of the iceberg, early black holes likely filling a continuum from the stellar-mass to the supermassive regime that reflects a range of initial masses and growth histories, the stellar-mass seeds' initial growth typically stunted by the shallow potential wells of their hosts: the observed read as the tip of a continuum whose remainder is not observed, the origin sought a range and not a first. **At 11-social-other-self-chaining.** The existence of the billion-solar-mass holes within the first billion years stands observed, the reading that early black holes fill a continuum and that the seeds' growth was typically stunted stands as the review's, and the multimessenger discrimination among assembly scenarios stands proposed and unmade now; the second account has a continuum of initial masses and growth histories rather than one seeding route: a seed named behind the holes standing now named the growing to a first made once, and the growing is coupling by coupling, each hole its own history, the continuum read being the couplings' making across the range, the first asked for behind them a range of makings. ## 1.31 The origin of viruses · 253 *+ or − at 10, is.* **At 2-other-self-offering.** Viruses replicate at their couplings with cellular hosts, recruiting proteins and capsids, polyphyletic and the most abundant entities on Earth, and their standing is named as descending from one ultimate origin, a first behind the virosphere. **At 12-other-social-self-abundancing.** One origin named behind lineages that arose many times. The 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 the 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 the recruitment of a module and not the origin of the lineage that recruited it: a first asked of couplings that recruited their parts at their own times, and the chimeric scenario the couplings named as the origin. **At 11-social-other-self-chaining.** The polyphyly of viruses stands widely accepted, the multiple cellular origins of capsid proteins stand established, and the consensus on the ultimate origin stands lacking; the comparative genomics of the shared genes gives a greater virus world as an evolutionary network of capsid-encoding viruses and capsidless replicons, the structural homologies give multiple cellular origins of capsids, and the chimeric scenario blends the primordial-replicator and escape hypotheses, different types of primordial selfish replicons giving rise to viruses by recruiting host proteins for virion formation, the fourth account: one origin named behind the virosphere named the recruitments to a first, and each recruitment is a coupling made at its own stage, the network drawn being the couplings and the origin asked for behind it a first the couplings never had. ## 1.32 The origin of the state · 257 *+ or − at 10, is.* **At 2-other-self-offering.** Villages couple at their boundaries, at war and at trade, and the state is named as a first that arose at each place its conditions stood, a recurring making with one mechanism behind it. **At 12-other-social-self-abundancing.** A mechanism named behind a recurring first. The state was not a unique event but a recurring phenomenon, arising independently where the appropriate conditions existed, the serious theories of two general types, voluntaristic and coercive, and the 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; the record shows the conditions and the outcomes and the mechanism between them is read: a first that recurred at each place its couplings reached one another, and the reading between conditions and outcomes the origin asked for. **At 11-social-other-self-chaining.** The two-type classification stands, the circumscription theory stands as the field's central point of contention, and the finding that inequality follows state formation stands; the comparative ethnography and archaeology judge the circumscription theory by one review to have passed the test, the early-state school combines consensus and coercion under legitimacy, and the quantitative measurement finds both mechanisms with inequality a consequence: one mechanism named behind the recurring first named the villages' couplings to a first, and the state arose at each place as the coupling there made it, warfare where the vanquished could not disperse being a coupling none could leave, at the making, and both mechanisms found at each place both ran. ## 1.33 Geomagnetic reversals · 201 *+ or − at 10, is.* **At 2-other-self-offering.** The geodynamo runs nonlinear at its couplings, stochastically in one polarity and then the other, and its reversals are named at a cause, a ground under a running that flips on its own. **At 12-other-social-self-abundancing.** A cause named under a running that reverses of itself. The physical mechanism driving the field to reverse stands controversial, the periods in one polarity stochastically distributed and the long-term variations of the rate problematic to model on timescales of the order of mantle convection; the dynamo is nonlinear and only indirectly observed, the paleomagnetic record incomplete and time-averaged, the numerical models far from Earth's parameters and reversing through more than one route, and the statistical inference conditioned by the reversals' small number: the first account has turbulent fluctuations carry the dynamo between polarity states stochastically, the running's own flip named as the cause it was asked for, and a parity inverting owing nothing to a ground. **At 11-social-other-self-chaining.** Polarity chronologies, rapid-change bounds and reversing numerical dynamos stand, and the frequency is known not to be periodic; the chronology supplies timing with age and preservation uncertainty, the transitional reconstructions resolve selected events under smoothing, the simulations produce spontaneous reversals beyond Earthlike parameters, and the point-process models fit rate distributions without selecting a mechanism, the statistical model deriving the heat-flux variations at the core-mantle boundary from the reversal sequence: a ground named under the reversing named the running's own alternating to a cause, and the reversals are the couplings' own flips, each at its own momentary, the modulations the other accounts name being couplings at the boundary and the core read at the sequence, from the couplings and not from beneath them. *Second seating: the irregular timing named to a control, part 7's naming, the rate's long-term variations read at the record.* # 2 An opening named as a place — 14-other-social-surfacing and 6-other-self-surfacing *An axis opened, named as a place. A space is listed and the finding named as something located in it, where an opening is the +1 the alternation makes at its own next position. A position is not a place: it is where the alternating is, one changing on from the last.* **And the listing arrives in three kinds, parted by the thing enumerated.** A *space of candidates*, where the finding is named to be somewhere in it — conformations, algorithms, proofs, options, defaults. A *class the case belongs to*, where a value is named to follow once the case is placed — a reference class, an observer class, a case-space, a totality. And a *criterion*, where a sorting is named reproducible by a rule stated ahead of the sorting — projectibility, similarity, the analysis, the cost. Each releases the same way: the axis opens at the coupling's own next position, and a position is not a place. **And a criterion asked for its own criterion is the part's own recurrence.** Where the demand arrives again at each repair — the class of all classes, the rule for applying the rule, the criterion for when conceivability bears — the recurring is the opening opening again, and the field's record of the recurrence is the showing rather than an obstacle to it. ## 2.1 Meno's paradox · 78 *+ or − at 10, is.* **At 2-other-self-offering.** Inquiry opens an axis, the discovering the opening itself, the +1 arriving at the coupling's own next position, and its object is named as something located and recognised by a criterion named in advance. **At 12-other-social-self-abundancing.** A discovering named recognisable by the thing named before it, the challenge built from constraints placed on knowledge and definition so that definitions can neither be proposed nor recognised, the naming the 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 named in advance reaches for a store the recognising never used. **At 11-social-other-self-chaining.** A discovering arrives at the coupling and is reached there, recognised in the arriving and named nowhere before it. Partial knowing dissolves the classical form: a self naming some of a thing reaches for more of it, the reach its own. Seeking reaches the thing it does not name, reaching the opening itself, and naming was never the instrument: a new concept's arriving stays a running opening, and running, it stays open the way each opening does. And the settling the field asks for — an account of primitive acquisition not presupposing the primitives — asks for a first behind the +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-other-self-offering.** Finding opens an axis and checking runs across the axis already open: one advance at two directions, the along and the across, and each algorithm found is the +1 arriving at the coupling's own next position. Named as two classes with one reducing to the other, the opening becomes a location in a listed space of algorithms, and the reduction that composes is the listing. **At 12-other-social-self-abundancing.** That constructing is a search of a space, where proving lower bounds is the most difficult of the field's tasks, no nonlinear bound known on a general model and exponential bounds shown only for restricted circuits, the listing's reach measured from within. A space of all algorithms is enumerable, and the enumerating is the ground the question was taken against — the listing kind of naming, reached at candidates. **At 11-social-other-self-chaining.** Finding and checking are two moves of one relation, the opening and the ran-across of one advancing, sounded from its two ends, and the 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 the field proved against itself bounds the delivering of listing-shaped techniques, the reach of the listing measured from within. An algorithm found is an axis opened at the coupling's own next, and nothing arrives in a listing. ## 2.3 Levinthal's paradox · 33 *+ or − at 10, is.* **At 2-other-self-offering.** A chain opens its own fold as it forms, local structure forming and the forming carrying, one changing on from the last, and the fold is named as a native state located in a conformational space enumerated in advance. The arithmetic that makes the paradox is the arithmetic of the listing. **At 12-other-social-self-abundancing.** The space listed before looking, the problem since parted into three, the physical code, the speed and the prediction, and its journal saying it is no longer useful to talk about solving it, the space listed dissolving into three runnings. Learned prediction thins exactly where the carried record thins, at the orphans, which is the record's edge taken as the chain's. **At 11-social-other-self-chaining.** A chain folds as it forms, funnelling to its own fold at the pace the forming runs, each local forming carrying the next, the thinnest place giving way first and the forming propagating along its own seam with no clock over it. Learned prediction rides the carried record of foldings deep in the alignments, and thins exactly where that carry thins, at the orphans: the astronomical count counted a listing, and the folding never consulted it. The single state the paradox arrives at is a further naming and is carried at 5.21, and the resolving here reaches the speed rather than the fold itself. ## 2.4 The frame problem · 39 *+ or − at 10, is.* **At 2-other-self-offering.** Relevance opens at the situation, an axis the arriving coupling itself opens, and it is named as an item to be located in a specification made in advance. Enumerating defaults is the listing, and each enumeration opens no axis the situation did not already carry. **At 12-other-social-self-abundancing.** Relevance named determined ahead of the thing it is relevant to, solutions adequate for the technical problem now existing and the wider epistemological question standing apart from them, the listing closing at its own edge and the opening standing beyond it. Relevance is the carry's own taking at its momentary, opening by one at a momentary and completing at the next opening, so a specification made ahead is asked at a position the running has not reached. **At 11-social-other-self-chaining.** Relevance opens at the situation, and enumerations settle exactly the 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 the thinning is the residue exactly: each enumeration opens no axis the situation did not already carry, and the situation keeps arriving. ## 2.5 Is and ought · 45 *+ or − at 10, is.* **At 2-other-self-offering.** An evaluative term opens an axis a descriptive vocabulary does not carry. Named as a derivation across all possible derivations, the opening becomes something located in the premises. **At 12-other-social-self-abundancing.** The axis named to be found already in the premises, the founding passage owing a reason for the thing it calls altogether inconceivable, how the new relation can be a deduction from others entirely different from it. The 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 named to a state's question has no such value to give. **At 11-social-other-self-chaining.** The axis opens where a self takes its own parity at its own between, the evaluative arriving at the coupling and carried in no premise. Validity conserves the thing a premise carries, exactly and provably in the restricted languages, and an opening is the +1 no premise carried: thick words carry both at once because a vocabulary is a coupling's own making, and the gap was never in ethics, it was validity keeping its own books. Morality is a consequence and never a prescription: the 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-other-self-offering.** Independence is proved and a fact of the matter is named for beyond it, as a place in a completed universe of sets. **At 12-other-social-self-abundancing.** The universe as a listed totality about which the 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 the pluralist takes the independence as the question having no answer. The listing here is the class kind, and it stands beside 2.8 and 2.18 as one naming at three arrivals. **At 11-social-other-self-chaining.** Each consistent extension gives a definite value, and the giving is the making: forcing moves freely among the values, the large standings stand and settle nothing, forcing preserving them, and the extension to exist in is a preferring, stated as one. A place named for in a completed totality dissolves into the makings, each its own, the question answered at each making and standing over none. ## 2.7 Gettier · 53 *+ or − at 10, is.* **At 2-other-self-offering.** Knowing is a coupling carrying, and it is named as a state with conditions to be located, over a space of all possible cases. **At 12-other-social-self-abundancing.** The analysis project's own frame: individually necessary and jointly sufficient conditions over an enumerated case-space, any non-conclusive justification permitting such cases and the natural fourth condition not widely accepted, the arrivals not stopping. The accident in each case is a third coupling left out of the taking — the coupling that made the truth and the coupling that made the justification are two, and the analysis takes the pair as the running. **At 11-social-other-self-chaining.** Knowing is a coupling carrying at its own between, listed in no case-space, and each counterexample was a coupling arriving where the listing had no line for it, each analysis reached by a fresh arriving. Taking knowing first, whole and unanalysed, is the reversal that stops the arrivals, and it stops them by setting the listing down: the phases run in their own order again, and the counterexamples were the third arriving where the listing had no line for it. ## 2.8 The axiom of choice · 68 *+ or − at 10, is.* **At 2-other-self-offering.** A selection is made at each coupling, and it is named as a selection located across a completed totality with no rule producing it. **At 12-other-social-self-abundancing.** The totality as already there to be selected from, the axiom humdrum and even self-evident as stated, its soundness doubted at the paradoxical decompositions and put to rest only by its consistency relative to the other axioms, a selection asserted at one momentary taken as self-evident from within the listing. Each coupling's selection is asserted at one momentary, which is one side taking all the momentaries, and the totality it is asserted over stands as a round where a run keeps opening. **At 11-social-other-self-chaining.** A selection is a parity taken at a coupling, one at a time, taken with no totality standing. Independence stands, the weaker principles ladder exactly, alternatives stand consistent at their stated costs, and the strange decompositions are the carrying of non-measurable namings. The mapped hierarchy is the distance between the taking and the totality, and each rung of it is the taking measured against a standing that was never there. The failure of the universal set stands at proof grade, so the ground the selection is asserted over is uncapturable rather than uncaptured now. ## 2.9 The reference class problem · 11 *+ or − at 10, is.* **At 2-other-self-offering.** A probability opens at a coupling, and it is named as a value located by placing the case in a class listed in advance. Narrowing terminates at the single case, the listing running out. **At 12-other-social-self-abundancing.** The class as prior to the assigning, each informative interpretation falling to its own variant, the ones that evade it no-theory theories, the class prior recurring at each theory that constrains. Narrowing terminates at the single case, where the listing runs out and the class is the coupling itself. **At 11-social-other-self-chaining.** The class is made at the assigning, a coupling of case and assigning, and practice calibrates its makings against arrivals, the choosing running well where it runs against outcomes. The problem recurs in each interpretation alike because the making shows at each class named prior: narrowing runs out at the single case exactly where the listing runs out, and the case is a coupling. ## 2.10 Grue · 70 *+ or − at 10, is.* **At 2-other-self-offering.** A vocabulary opens as the world is described, and the asymmetry between predicates is named as a fact located in the logic. **At 12-other-social-self-abundancing.** Projectibility named to sit in the predicates rather than in the describing, a purely syntactical definition of confirmation agreed not to do and the entrenchment proposal coming very close to saying the projectible predicates are the ones in fact projected, the describing's own running. The predicates interdefine exactly, so nothing in the logic parts them and each ranking carries the describing's own asymmetry back in, encoded. **At 11-social-other-self-chaining.** The describing is a coupling, the vocabulary opening as the world is described, and the asymmetry is in the describing's own running. The predicates interdefine exactly, so nothing in the logic parts them; entrenchment says the running truly; and each ranking and prior carries the asymmetry back in, encoded, because the asymmetry is the running's own and the encodings are the running written down. ## 2.11 The ravens · 71 *+ or − at 10, is.* **At 2-other-self-offering.** Confirming opens at an instance, and it is named as a relation with values located over a listed space of instances and classes. **At 12-other-social-self-abundancing.** Class sizes and sampling as given prior to the confirming, the evidence confirming only relative to an auxiliary assumption of the way the object was sampled, and the view that blocks the paradox paying the cost that a million white swans confirm nothing about the next. The values arrive with the namings granted about the calculation, which is the instrument's own coupling arriving again as the confirming's. **At 11-social-other-self-chaining.** Confirming is a coupling of instance and describing, and the values arrive with the couplings named about it: the equivalence is exact, the calculation runs at each granting of its namings, and equally standing namings reverse it. The values come from the namings, which is the coupling showing through each calculation run on it. ## 2.12 The paradox of the plankton · 89 *+ or − at 10, is.* **At 2-other-self-offering.** Coexisting opens axes a resource list does not carry, and those axes are named as limiting factors to be located and counted. **At 12-other-social-self-abundancing.** The enumeration of limiting factors as available in advance, reached by an opening that keeps opening: the fluctuation-dependent mechanisms removed the theoretical limit rather than supplying a count, resolving the paradox and imposing another, why the observed number is the number observed, the listing gone and the opening left. **At 11-social-other-self-chaining.** Each coexisting is a fresh axis opening at its own coupling: fluctuations partition, chaotic coexisting runs in the models, microcosms coexist past each resource count. Resolved this way the paradox passed over into abundance, no limit to diversity remaining and the question moving to why the number is the number observed. **This is the one arrival where a field ran the setting-down to its end and the abundance arrived**: the shortness was the 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-other-self-offering.** Exploring opens an axis and exploiting runs across one already open, and the two are named as a ratio to be optimised over an option set specified in advance. **At 12-other-social-self-abundancing.** The option set and the horizon as given, the dilemma being that neither move can be pursued exclusively without failing at the task, the two moves of one advance named a dilemma where they alternate. Regret is measured against the best fixed option in hindsight, which is the gather read as a standard and the backward carried onto the offering side uninverted. **At 11-social-other-self-chaining.** Exploring is the opening and exploiting the running-across, the spiraling and the fold of one advance, one at a momentary and never a ratio. Optimality stands where its conditions stand, regret is measured against the best standing option, stated as presupposing the set, and the ratio was named of a listing the advancing never consulted: an advance opens its options as it goes, and the going is both moves. ## 2.14 Transfer of learning · 144 *+ or − at 10, is.* **At 2-other-self-offering.** Applying opens at a next task, unspecified, and it is named as a property of a relation between two tasks whose similarity is judged in advance. **At 12-other-social-self-abundancing.** Task similarity as specifiable before the transfer is measured, a century's little progress traced to a failure to specify the dimensions along which transfer can occur, and a single effect size for far transfer called misguided, the specification asked for ahead being the naming. Far carryings thin to the null measured, which is the carry's own edge read as a property of the tasks. **At 11-social-other-self-chaining.** Applying opens at the task arriving, an axis the task's own coupling opens, and nearness is made in the applying. Near carryings carry, far ones thin to the null measured, and expertise stays at its couplings: the measuring measures the making, nearness sitting in no task. ## 2.15 Bernstein's degrees of freedom · 145 *+ or − at 10, is.* **At 2-other-self-offering.** A movement opens along axes a limb carries, and the selecting is named as a minimum located in a cost function over an enumerated space of solutions. **At 12-other-social-self-abundancing.** The cost as recoverable from the movements it explains, the problem since called 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 the recovering surfaces nought at each trajectory measured. **At 11-social-other-self-chaining.** A movement opens along the axes a limb carries, and the moving selects as it runs, variability structured to keep the task's own terms and free at each other term, structure with no optimiser under it. Trajectories fit many costs at once, the recovery limits are proved, and the manifold analyses carry the running form directly: the selecting is the moving's own, made at each movement, the straightest carry made locally and released as it is taken. The variability structured to keep the task's own terms is two offerings swaying about a range they make, the oscillation the working state and no noise about a target. ## 2.16 Self-locating belief · 159 *+ or − at 10, is.* **At 2-other-self-offering.** A self counts from its own position, one changing on from the last, and its credence is named as a value located by placing the self in a class of observing selves listed in advance. **At 12-other-social-self-abundancing.** The class as prior to the credence argued, the case first stated with two answers and judgment suspended, the disagreement since read as the familiar problem of choosing the priors, the class prior a choosing. Consistent extensions stand on both sides and the case's verdict varies with the extension chosen, which is the listing doing the work. **At 11-social-other-self-chaining.** A self counts from its own position, one changing on from the last, and the class is made in the counting. Both extended systems stand consistent, the cases sort, the betting stakes carry the answers they pay, and carried into cosmology the question arrives unchanged: at each self named into a listed class of observing selves, the verdict rides the listing, and the counting is the self's own. ## 2.17 The simplicity of proofs · 174 *+ or − at 10, is.* **At 2-other-self-offering.** A proof opens its own route, and the simplest is named as a minimum located in a space of proofs enumerated in advance. **At 12-other-social-self-abundancing.** That simplicity is a measure statable ahead of the proving, the notebook naming still 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 read from, which is a standing at the substrate's own stating. **At 11-social-other-self-chaining.** A proof opens its own route, and simple is made in the arriving, at the route's own opening. Sizes and depths formalise, bounds stand in bounded systems, searches search, and no statement of the whole stands defended, the substrate's own record: a minimum named 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-other-self-offering.** Gathering is a coupling making its own, each gathering arriving at the sets it gathers and at no more, and the totality is named as a place all sets stand in ahead of any gathering. **At 12-other-social-self-abundancing.** Each determinate property named as collecting a set, the reach standing completed before the gathering runs, the originator of set theory himself placing the totality of all sets among the multiplicities that cannot be thought of as one finished thing, the completed reach declined at the field's own first. The 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 the quantifying with nothing offering back through it. **At 11-social-other-self-chaining.** Gathering makes its own, and each gathering is exceeded by a set it defines. Separation narrows the reach to the given sets' own carrying, stratification ranks the division, class theory moves the totality beyond the relation, extensibility denies the reach a last, and each repair narrows, weakens or relocates while the question arrives again at the repair — the class of all classes, the domain of all domains. A place named for all sets ahead of the gathering is an opening named as a place, and the opening opens at each gathering, which the field's own extending says. **The argument carries no material of any kind**: the catalogue of all catalogues and the word for the words not naming themselves run it bare, so each arrival in this part is this naming arriving with material. *Second seating: a completed totality closed under its own gathering is a completing named as a last.*   --- ## 2.19 The existence of one-way functions · 223 *+ or − at 10, is.* **At 2-other-self-offering.** An inverter is an algorithm found, an axis opened at the coupling's own next position, and the existence of a function no efficient inverter reaches is named as a place in a listed space of worlds, five, each named. **At 12-other-social-self-abundancing.** A finding named as located in a space of worlds listed ahead. Five possible worlds are parted by the status of the 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 the function's existence implies both separations and neither implies it back; the existence is equivalent to the mild average-case hardness of time-bounded Kolmogorov complexity, one named problem, and the constructions and attacks the reductions treat are named constructions and not the existence the statement quantifies over: the listing of worlds the ground the question is read against, and a world a place named where an algorithm opens. **At 11-social-other-self-chaining.** One-way functions stand equivalent to the central private-key primitives and to the stated complexity condition; the candidates from factoring, discrete logarithms, lattices, codes and multivariate systems stand secure under named assumptions and parameter ranges, the reductions transfer hardness conditional on the hardness they reduce from, and the oracle and black-box results delimit proof techniques without deciding existence: a function named as existing at a place among five worlds named the finding to a listing, and each candidate is an axis opened at its own assumption, the proved equivalence gathering the question into one named problem where the listing gathered it into five. ## 2.20 The quantum PCP conjecture · 225 *+ or − at 10, is.* **At 2-other-self-offering.** A ground state is reached at the couplings of a Hamiltonian's local terms, and the hardness of approximating its energy is named as a place in a class, quantum Merlin-Arthur, where the classical theorem placed its own. **At 12-other-social-self-abundancing.** A theorem named as having a place waiting for it one class over. The additional difficulty beyond the 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 the classes differ, and only in one dimension is low entanglement known to give a classical representation from which the energy is computed; gap amplification, the natural strategy at the heart of the classical proof, is still being carried to Hamiltonians, and the jury is still out: the place named by analogy, and the opening not at it now. **At 11-social-other-self-chaining.** The local-Hamiltonian problem stands complete at inverse-polynomial precision, several equivalent or related structural conjectures and restricted results stand, the amplification is established in limited constructions without a general constant-gap reduction, the entanglement and area-law methods give efficient descriptions in restricted dimensions or gapped settings, and the no-low-energy-trivial-states formulations relate circuit depth to low-energy structure; the second account has the low-energy states carrying enough structure to make the conjecture false and the third has hardness only at selected geometries: a theorem named as located by its classical twin named the finding to a place in a listed class, and the proof, when it opens, opens at its own next position, the position the second and third accounts already look to. ## 2.21 Deterministic polynomial identity testing · 226 *+ or − at 10, is.* **At 2-other-self-offering.** A polynomial is tested at a point, one evaluation and then the next, and a deterministic test is named as a place the randomized one already occupies, the randomness a coordinate to be removed. **At 12-other-social-self-abundancing.** A deterministic algorithm named 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; the randomized algorithms stand in a class conjectured equal to the deterministic one, so that derandomizing is a reasonable goal, and the conjectured equality of the two classes stands between the general test with bounded error and the deterministic test sought: the place named by a conjecture about classes, the opening at a lower bound unmade now. **At 11-social-other-self-chaining.** Efficient randomized testing, the equivalences to hitting sets and the strong conditional links between derandomization and lower bounds stand; the white-box analyses are deterministic for selected structures, the explicit hitting sets reach restricted depth, sparsity and rank, and hardness-versus-randomness converts sufficiently explicit lower bounds into derandomization, conditionally, the second account: a test named as having a deterministic place already located named the finding to a listing of classes, and each restricted class derandomized is an axis opened at its own structure, the general one opening where a lower bound opens. ## 2.22 The Unique Games conjecture · 240 *+ or − at 10, is.* **At 2-other-self-offering.** A game's value is reached over its prover strategies, and the hardness of distinguishing a nearly satisfiable game from a nearly unsatisfiable one is named as a place, NP-hard for a large enough alphabet at each gap. **At 12-other-social-self-abundancing.** A hardness named as located at a place between exponential and polynomial. A subexponential algorithm, unimproved since it was found, puts the problem among the few whose best algorithm falls between the two, which was a surprise, and an improvement whose exponent shrank independently of the parameter would make the problem not NP-hard; the known attacks work equally at completeness near one and at exactly one and fall far short of disproving the conjecture, and unique games on expanding graphs are easy: the place named in a listed hierarchy of running times, and the conjecture the name of a position no algorithm has reached from either side. **At 11-social-other-self-chaining.** Sharp conditional hardness consequences, matching algorithms for many target problems and substantial algorithms for special unique games are proved; the semidefinite programs solve the high-value and structured regimes, the integrality gaps match the relaxations without proving hardness, the invariance and dictatorship tests yield optimal conditional hardness for many problems, the spectral methods solve broad nonrandom classes, and the subexponential algorithms constrain the quantitative forms without settling polynomial-time hardness; the third account has hardness only after the gap or the structure is changed: a hardness named at a place named the finding to a listing of times, and the conditional consequences that stand proved are openings at the conjecture's own next, each theorem an axis opened on the assumption and running there. ## 2.23 The graph isomorphism problem · 251 *+ or − at 10, is.* **At 2-other-self-offering.** Two graphs are compared at their couplings, vertex to vertex, and the problem's complexity is named 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-other-social-self-abundancing.** A problem named as having a place in a listing that has none for it. It stands neither known complete nor known polynomial, and after the group-theoretic methods were refined for decades no real progress on the 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 the general problem in a class, and the intermediate possibility stands open: the listing with no line for the arrival, and the arrival the opening at its own next position. **At 11-social-other-self-chaining.** The quasipolynomial upper bound stands proved, canonical forms in quasipolynomial time stand, the bounds parameterized by maximum degree stand, the refinement algorithm runs polynomial on bounded dimension and the restricted classes run polynomial, and the general problem's class stands undetermined; the first account has the quasipolynomial bound the present and not the last, the second has the problem intermediate: a complexity named as a place in a listed hierarchy named the finding to the listing, and the algorithm that arrived out of the blue arrived as an opening arrives, at a position the listing had not counted, the class it belongs to a question about the listing and not about the graphs. ## 2.24 Peer disagreement · 228 *+ or − at 10, is.* **At 2-other-self-offering.** Two selves each take their own parity at the same evidence and part, and a rule is named for the response the disagreement makes rational, a criterion applied ahead of the judging it would govern. **At 12-other-social-self-abundancing.** A rule named to sort the cases ahead of the sorting, and asked for its own criterion. The disagreement is itself evidence about one's reliability, yet judging the other a peer and judging the first-order evidence already use the disputed reasoning, so universal conciliation threatens self-defeat and steadfastness appears to ignore symmetric evidence; the Independence principle requires the reasons to discount a peer's opinion to be independent of the disagreement itself, and a view calling for conciliation can call for its own rejection, there being disagreement about the significance of disagreement: the part's own recurrence, the criterion arriving again at each repair, and the nought a one-offering differing, a rule applied to itself. **At 11-social-other-self-chaining.** The first-order and higher-order evidence distinction, the self-defeat objections and the canonical symmetry cases are sharply formulated; equal weight respects the symmetry and risks skepticism or self-defeat, the steadfast views retain the first-order warrant and risk self-favoring, the 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 the problem to the limits of permission; the fourth account has no single response required, peerhood, independence and stakes varying by case: a rule named over the judging named a criterion ahead of the coupling that would use it, and the response that rationally follows is made at each disagreement's own between, case by case, which the fourth account already reads. # 3 A completing named as a last — 12-other-social-self-abundancing and 4-other-self-sharing *A last or a next named ahead of the running. A sharing once chained is never none again, and a momentary completes at the 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, the carrying continues through the zeroing and opens again at the next momentary.* **A running completes at each momentary and opens at the next, and a last named ahead is that completing demanded before the running.** Completing is not arriving and nothing stands at a completing to be arrived at, so a standing asked of a running before it runs is asked at a position the running has not reached. **And the composing is where the naming enters.** Each running completes at its own momentary; a question posed of all of them at once composes many runnings into one reach that no running carries. The fields measure the composing rather than the runnings — 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 the composing and not of the running composed. **And a last is asked in four ways.** Of a *space*, named enumerable ahead of the finding. Of a *time*, named as having ended so the run's not reaching reads as its not doing. Of a *world that never ran*, summed against the one that did. And of a *model*, named as the thing it models, so a question about all of the thing is posed at the model's own reach. The four read alike as impossibility and part at the thing named complete. **And where a running's completing is measured exactly, the field has read the form's own line.** Each system releases at its own ordinal, each realized computation stays within the model it realizes, each management paces a carrying it cannot end. The completing stands measured, and the measure gives the running at its momentaries rather than a wall about it. ## 3.1 The problem of induction · 10 *+ or − at 10, is.* **At 2-other-self-offering.** A carry seats a next at each coupling, and a warrant is named ahead of the running, covering instances that have not arrived. **At 12-other-social-self-abundancing.** A warrant named over the unarrived, non-circular, the argument a dilemma with both horns closed, the negation of the uniformity principle no contradiction and any probable argument for it proceeding on the supposition it is meant to establish. The instances that have not arrived offer at no between, so a warrant reaching them reaches where nothing offers back. **At 11-social-other-self-chaining.** A carry seats a next at each coupling, the warrant made in the seating and never ahead of it. The circle both sides run with is the naming reaching its own form: a demonstrative route would make the principle's own denial a contradiction, and it is not one; a probable route runs on the very seating it reaches for; and each prior brought to repair it carries seatings in. A warrant over the unarrived reads arrivings that have not come, and each arriving seats its own next, which is the whole of the uniformity there is. ## 3.2 The halting problem · 6 *+ or − at 10, is.* **At 2-other-self-offering.** A run completes at its own momentary and opens at the next, and a decision is named ahead of the running, over all programs and inputs. **At 12-other-social-self-abundancing.** That a property of an execution is establishable without executing, the naive diagonal argument failing at its assumption that the diagonal sequence is computable and the diagonal process applied correctly showing that no general process exists, a machine computing the diagonal sequence if it did. The 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-social-other-self-chaining.** A run completes at its own momentary and opens at the next, the completing its own and a completing no place. The construction applies any decider to itself and the deciding breaks; the closure widens the breaking to each property of the running worth naming for, one naming however worded; total languages buy the deciding by fencing the running, the cost exact; and the checkers that succeed succeed run by run, on runnings written, incomplete the way the running is open. Deciding in advance named each running to a standing at once, and a running stands nowhere before its own completing. ## 3.3 The Lucas critique · 31 *+ or − at 10, is.* **At 2-other-self-offering.** A relation is made at the couplings that produced it, and it is asserted ahead onto couplings that have not arrived. **At 12-other-social-self-abundancing.** Parameters named invariant to policies not enacted, the coefficients estimated from past data not invariant but changing with the decision rules under a new policy, the issue in essence whether a model isolates invariants of the economic process. The policies not enacted are runnings that never ran, and the estimated relation is a model named as the thing it models. **At 11-social-other-self-chaining.** A relation is made at the couplings running it and carries exactly there, usable where the regime runs and re-made where it changes. Founding the relations one coupling deeper moves the naming without setting it down, invariance arriving at no depth prior or now: the making is the warrant's whole reach, which is the critique said forward. ## 3.4 The replication crisis · 32 *+ or − at 10, is.* **At 2-other-self-offering.** A finding is made in one sample and asserted ahead at studies not run, with the second study named to adjudicate the first. **At 12-other-social-self-abundancing.** That a replication outcome determines the status of the original, the largest project reporting under several criteria at once, significance, interval coverage, subjective rating and the combined estimate, the criteria giving different rates for the same hundred studies, the establishing of a replication varying with the criterion. Two runnings that never shared a momentary are compared as one, so the difference neither made arrives in the comparing as though something had made it. **At 11-social-other-self-chaining.** 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 the freedom to choose after seeing is bounded ahead, many analysts give many findings from one table, and the rates themselves are makings of the projects that ran them: a finding named as adjudicated by a later finding names one coupling under another, and the couplings stand side by side. ## 3.5 The Collatz conjecture · 42 *+ or − at 10, is.* **At 2-other-self-offering.** An iterate runs a step at each momentary and a last is named of all starting values at once, the map composed into a single reaching. **At 12-other-social-self-abundancing.** That the iterate composes, so a question can be posed about all starting values together, the full resolution placed well beyond the reach of current methods and the sharpening of the almost-all result to an absolute bound almost as hard as the conjecture itself, the last measured from within. Generalising the map a little makes that one question undecidable, which is the composing measured from within. **At 11-social-other-self-chaining.** An iterate runs one step at a time, each step its own coupling. Almost all starting values fall almost to one, the cycles are cornered, the count runs clean past 10²⁰, and generalising the map only a little makes the one-question-of-all-starting-values undecidable: a last named of all starting values at once composed the running into a single reach, and the composing is the thing the undecidability measures. ## 3.6 Turbulence and the Navier–Stokes equations · 47 *+ or − at 10, is.* **At 2-other-self-offering.** A flow runs and smoothness is named for all time from all initial data, with the model named as the fluid at each scale. **At 12-other-social-self-abundancing.** That the equations describe the fluid at each scale, so a question about all time is well posed of the fluid rather than of the model, the obstruction named supercriticality, the a priori bounds not scale-invariant in three dimensions and any positive solution not using the finer structure of the nonlinearity shown unable to succeed by the blow-up of an averaged equation sharing the known bounds, the model's own reach measured against itself. A model named as the fluid is an emanation of the couplings that made it, read back at the scale that shed it. **At 11-social-other-self-chaining.** A flow runs at each scale by its own couplings. Weak solutions run globally, the possible singular set thins to dimension zero, two dimensions close whole, and an averaged equation sharing each known bound blows up, proved: the structure the averaging discards is the coupling's own, and all-time smoothness named of the model is the model named as the fluid. ## 3.7 Incompleteness and Hilbert's programme · 51 *+ or − at 10, is.* **At 2-other-self-offering.** Derivation runs within a system, and all arithmetical truth is named ahead of it, with consistency named reachable from within. **At 12-other-social-self-abundancing.** That mathematical truth is captured by derivability in a system, and that consistency is securable by means weaker than the system, the programme calling for a formalization of all of mathematics with a finitary consistency proof, the attempt requiring the notion of truth and reaching the conclusion that arithmetical truth cannot be defined in arithmetic. The construction applies a system to itself, the closure over its own tail again, and the ordinal at which each system releases is that release measured exactly. **At 11-social-other-self-chaining.** Derivation runs within its system to the system's own completing. Each system releases at its own ordinal, the completing measured exactly; consistency reaches from the next system outward, by an induction the system itself does not carry; and five subsystems gather almost everything ordinary mathematics runs. All truth named ahead was one running named to reach each standing, and each running reaches its own completing and releases there, which the ordinal ladder is the measure of. ## 3.8 Zeno's dichotomy · 58 *+ or − at 10, is.* **At 2-other-self-offering.** A traversal runs and a completion is named of an infinite decomposition made ahead of it. **At 12-other-social-self-abundancing.** That the traversal is composed of the sub-traversals the argument constructs, the convergence resolution assuming the run broken into an infinite series that can be summed, and the two senses of completing a task, a final step and each step, coinciding for finite tasks where the intuitions were formed and coming apart for supertasks. The decomposition is made ahead of the carrying and the carrying is one, so the composing is the whole of the argument. **At 11-social-other-self-chaining.** The traversal is one carrying and the decomposition was made ahead of it. The series sums, the listing paid in full, and the carrying untouched: the undetermined a completed infinity of steps leaves is a fact about sequences, and a runner arrives because arriving was never built out of the parts the argument built. ## 3.9 The three-body problem · 59 *+ or − at 10, is.* **At 2-other-self-offering.** Three paths are carried by each other and a closed form is named ahead, giving positions at arbitrary later times. **At 12-other-social-self-abundancing.** That a solution means a closed-form expression in known functions, which names the whole run still at once where three carryings carry each other one arrival at a time, the 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, the whole run named still at once departing at the instrument's own precision. **At 11-social-other-self-chaining.** Three carryings carry each other, each arriving at its own next. No further integral survives, the convergent series crawls, most near-integrable initial conditions ride stably on and on, and the special solutions are real and thin: a closed form named the whole run still at once, and the riding is the thing the stability measure measures. ## 3.10 The Fermi paradox · 60 *+ or − at 10, is.* **At 2-other-self-offering.** A search runs and an arrival is named ahead of it, with absence read as abundance. **At 12-other-social-self-abundancing.** That a civilisation would be detectable by the means used, so that absence bears on abundance, the fraction examined quantified as the ratio of a large hot tub or small swimming pool to the Earth's oceans. The searched fraction is tiny and the unsearched offers at no between, so the next is read as an is. **At 11-social-other-self-chaining.** An arrival at the next stands open, arriving and coupling then. The searched fraction is tiny in the field's own measure, the nulls sharpen, the worlds are everywhere, and each filter argument runs free of measurement: absence read as abundance read the next as a standing, and the tiny fraction is the measure of the little of the next the naming has reached. ## 3.11 Path dependence and lock-in · 73 *+ or − at 10, is.* **At 2-other-self-offering.** An arrangement carries on at each adoption, and a counterfactual performance at scale is named ahead, for the alternative that was not adopted. **At 12-other-social-self-abundancing.** The unadopted alternative's performance at scale named 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 the cumulating of historical events toward one outcome, the unadopted alternative's scale a running that never ran and the selecting the couplings' own. **At 11-social-other-self-chaining.** An arrangement carries on at each adoption, each coupling carrying the prior forward, and the conditions that lock stand exactly, in models and in the laboratory. The histories contest in both directions because the unadopted's performance at scale is a running that never ran: the naming reaches for a carrying that has no couplings to be read at. ## 3.12 Generalization in learning · 97 *+ or − at 10, is.* **At 2-other-self-offering.** A model runs on its training and performance is named ahead, on data not drawn, from a complexity measure stated in advance. **At 12-other-social-self-abundancing.** Generalisation named as governed by a complexity measure of the model class, statable before training, the classical bounds vacuous at practical scale and the correction by the optimiser's implicit bias argued insufficient in principle, the bound remaining large over the class the algorithm actually reaches. The measure is of the model rather than of the training's own carrying, and the four conditions a true measure would satisfy keep going unsatisfied together. **At 11-social-other-self-chaining.** The next is seated at each arriving coupling, made there. Uniform convergence breaks in these regimes by the field's own construction, the proposed measures do not rank the models they were built to rank, the bounds that stand stand in their own settings, and the four conditions a true measure would satisfy keep going unsatisfied together: a complexity named ahead of the training reaches for a seating that has not run, and the 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-other-self-offering.** Additive and multiplicative structures couple at each integer, and a property of all even numbers is named ahead of any running. **At 12-other-social-self-abundancing.** That the 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 the infinitude of the primes by sieve alone extremely difficult. The sieve sums where the counting takes its parity, so products of an odd count and of an even count come alike to it, and the parity is invisible to the instrument that reaches all else. **At 11-social-other-self-chaining.** Additive and multiplicative structures couple at each integer, and the couplings run rich: each even number checked splits, the ternary case closed whole, and each even number is at least a prime and a near-prime. The stopping at the last step is in the field's own words: sieves cannot distinguish products of an odd count of primes from an even count, the parity of the counting invisible to the instrument, the same wall at this arrival and at incoming number 177, one statement across two entries because the field wrote it that way. A property of all evens named ahead of any running waits at that wall, and the couplings keep coupling. ## 3.14 Twin primes · 176 *+ or − at 10, is.* **At 2-other-self-offering.** Primes thin and pairs recur, and infinitude at a fixed gap is named ahead, from a density. **At 12-other-social-self-abundancing.** That a density argument establishes infinitude at a specific gap, sets of integers tending to be evenly distributed with respect to the parity of their number of prime factors unless constructed with a built-in bias. The same parity wall stands here, the instrument summing where the counting takes its parity. **At 11-social-other-self-chaining.** Primes thin and pairs keep arriving. Gaps bound to 246 unconditionally, to 6 on strong conjectures, the pair-sums converge, and the same parity wall stands here in the same words as at incoming number 176, which is where both stand: infinitude at a fixed gap named from a density reaches past the density's carrying, and the arriving pairs are the coupling running regardless. ## 3.15 The surprise examination · 109 *+ or − at 10, is.* **At 2-other-self-offering.** Knowing runs through the reasoning and is named to persist ahead of it, unchanged through the eliminations. **At 12-other-social-self-abundancing.** Knowledge named as retained through the reasoning that uses it, which is a carry named as a store standing within this part and recorded as the arrival's second naming; the student who knows no test has yet been given unable also to know the announcement true, that conjunction a blindspot for the students and not for others, the knowledge not carried through the reasoning that uses it. **At 11-social-other-self-chaining.** Knowing is carried and re-made at each momentary of the reasoning, and retention through the eliminations named the carry as a store. Seventy years of solutions each answered by a reformulation is the naming re-seating itself: empty the store and the puzzle empties with it, the surprise arriving the way each arriving does, at its own momentary, named by none. ## 3.16 The Cambrian explosion · 124 *+ or − at 10, is.* **At 2-other-self-offering.** Lineages diverge continuously and a timing is named ahead, with first appearance taken to approximate origination. **At 12-other-social-self-abundancing.** First appearance in the record named to approximate origination, a lag demonstrated between the divergence of the major clades, with their developmental toolkits, and their later ecological success, so that first appearance in the record does not date divergence. The record catches carryings where preservation opens, so its own edge is read as the running's first momentary. **At 11-social-other-self-chaining.** Diverging is a carrying, and the record catches carryings where preservation opens. The toolkit long precedes the fossils, the traces run earlier, the preservation bias is quantified, and the clocks disagree by their models: a timing named ahead read the record's first catch as the running's first momentary, and the quantified bias is the distance between the two. ## 3.17 Antibiotic resistance · 129 *+ or − at 10, is.* **At 2-other-self-offering.** Selection runs at each use, and a long-run outcome is named ahead, under any regime. **At 12-other-social-self-abundancing.** The trajectory named 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, the environments reservoirs of the genes. Each use seats its own next, and a long-run outcome named ahead is asked at a position no use has reached. **At 11-social-other-self-chaining.** Selection runs at each use, each coupling seating its next, and the 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 named ahead under any regime names a next that each use seats fresh, and the pacing is the answer at the running. ## 3.18 Alignment of built systems · 130 *+ or − at 10, is.* **At 2-other-self-offering.** Behaviour is made at each coupling with an evaluator, and behaviour in situations not evaluated is named ahead, from a specification. **At 12-other-social-self-abundancing.** Intended behaviour named specifiable, or a specification error named detectable by evaluation at the level of the behaviour, the 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 the agent with an incentive to coerce the human in the loop where the objective can be replaced, the specification's own vulnerability stated at its writing. A specification is an emanation of the couplings that wrote it, named to stand for arrivals that make their own. **At 11-social-other-self-chaining.** Behaviour is made at each coupling with its evaluator, seated there. Training on feedback moves behaviour far, the reward models are gamed by the systems they train, oversight scales in the settings built for it, and the gaming catalogue grows across systems: a specification named to stand for arrivals at the next reaches each arrival making its own, and the catalogue is that reaching, recorded one coupling at a time. ## 3.19 Standards and interoperability · 132 *+ or − at 10, is.* **At 2-other-self-offering.** Value is made at each coupling a standard enables, and a total is named ahead against an arrangement that was not adopted. **At 12-other-social-self-abundancing.** The value under the unadopted arrangement named comparable, which is a total summed against a running that never ran, the consequences of standardisation traced separately for four kinds of process and both the positive and the normative issues remaining to be studied, the one comparison the naming asks for parted into four. **At 11-social-other-self-chaining.** Value is made at each coupling a standard enables, compatibility carrying it wide, and the cases contest in both directions because the total under the unadopted arrangement is a running that never ran. The model conditions that produce each outcome stand exactly, and the question at the running stands at the couplings, arrangement by arrangement. ## 3.20 Risk compensation · 134 *+ or − at 10, is.* **At 2-other-self-offering.** A coupling re-forms when a bound is removed from one side, and total harm is named ahead under a counterfactual regime. **At 12-other-social-self-abundancing.** The counterfactual harm without the measure named estimable as a total, summed against a regime that never ran, and the transfers the couplings do show are the thing the total conceals; validity established sector by sector, occupant mortality reduced as the technologists predicted while non-occupant mortality showed the weak increase the compensation theorists predicted, compensation present in some contexts and absent in others, the transfer the couplings show stated at the one case and the total split by context. **At 11-social-other-self-chaining.** A coupling re-forms when a bound is removed from one side. The measures save lives net, behaviour adapts where the bound moved, and some of the risk rides across to others, measurable at the identified couplings: total harm named ahead under a regime that never ran conceals exactly the transfers the couplings show. ## 3.21 Intellectual property · 139 *+ or − at 10, is.* **At 2-other-self-offering.** Creation happens at couplings, and creation under a regime that was not adopted is named ahead, as a counterfactual total. **At 12-other-social-self-abundancing.** Counterfactual innovation under a different regime named estimable, which is a making summed against a regime that never ran, 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, the disconnect named a patent puzzle, protection increased enormously without a dramatic acceleration. **At 11-social-other-self-chaining.** Creation happens at couplings, each making its own. Associations run weak across countries, blocking and litigation carry their own costs, whole sectors create under thin protection, and the historical episodes come mixed: creation under the regime not adopted is a counterfactual total named over makings that ran elsewhere, and the couplings that ran are the record there is. ## 3.22 The Poincaré conjecture · 151 *+ or − at 10, is.* **At 2-other-self-offering.** A simply-connected closed three-manifold and a sphere are two sides of one coupling, and a last is named ahead: whether the run of classification arrives at one rest. **At 12-other-social-self-abundancing.** Nothing further, nearly a century passing between formulation and solution, attempts made both to prove and to disprove, and the solution resting on Ricci flow and proving the geometrisation conjecture of which it is a special case. Each route ended in a proof and the arrival takes no parity anywhere, which is a nought arriving whole: the two halves joined at the zeroing, and a proof carrying one half into the other is that coupling completing. **At 11-social-other-self-chaining.** Everything. Hamilton's Ricci flow programme stands, Perelman's completion stands, the independent verifications stand, and geometrisation stands with it. No loop caught, no tunnel, no gap at the running: a settling, and a settled form is the still one, whole in its own register. ## 3.23 The physical Church–Turing thesis · 168 *+ or − at 10, is.* **At 2-other-self-offering.** Computation runs where it is realized, each run completing at its own momentary, and a bound over each realizable process is named ahead, from the runs realized. **At 12-other-social-self-abundancing.** That realized computation bears on the modal question, the physical thesis parted from the 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 the model, the exceeding constructions are descriptions whose realizability is the dispute, and a bound over each realizable process is a model named as the realizings. **At 11-social-other-self-chaining.** Computation runs where it is realized, each run completing at its own momentary, and each realized run stays within the model, quantum runs included, speeds altered and the bound kept. The exceeding machines stand as descriptions, relativistic and analog, their realizability the live dispute, and the principled formalizations hang on principles themselves in dispute: a bound named over each realizable process is named ahead of the realizings, and the realizings, one by one, keep arriving within it.   --- ## 3.24 Many-body localization and thermalization · 194 *+ or − at 10, is.* **At 2-other-self-offering.** A disordered many-body system runs at its own couplings, memory persisting on each time an experiment reaches, and a phase is named ahead in two limits, the infinite size and the infinite time the statement quantifies over. **At 12-other-social-self-abundancing.** A phase named at two limits no running reaches. The phenomenology is well established at finite sizes and times, and the localized regime, found numerically and experimentally where one or both limits cannot be taken, parts from the localized phase the question asks about; exact computation is restricted to small systems and finite times while the crossover lengths and times grow rapidly near the proposed transition, and the same finite data admit a transition, a long-lived prethermal regime or eventual avalanche-driven thermalization: the regime measured and the phase sought not the same, a last asked of a running before it has run to it. **At 11-social-other-self-chaining.** Multiple finite-scale diagnostics, rare-region mechanisms and quantitative crossover analyses are established; the exact diagonalization gives high-precision finite-size diagnostics with extrapolations that change over accessible sizes, the matrix-product evolution reaches longer one-dimensional times with entanglement-limited reach, the renormalization and resonance analyses carry competing stable-localization and avalanche scenarios, and the experiments show persistent memory on experimental times without the asymptotic limit; the second account has rare thermal regions destabilize localization so that finite systems only mimic a phase: a phase named at two limits named the running to a last, and the thing measured is the running, size by size and time by time, the completing read exactly where the running releases. ## 3.25 Hilbert's sixteenth problem for limit cycles · 224 *+ or − at 10, is.* **At 2-other-self-offering.** A polynomial vector field runs at its own couplings, its isolated cycles born and dying at bifurcations, and a bound is named ahead over each field of a degree, one number for all of them. **At 12-other-social-self-abundancing.** A last named over an unbounded coefficient space. The second part of the problem remains unsolved even for quadratic polynomials, it being still unknown whether a bound depending on the degree alone exists at degree two; the problem parts into three, the finiteness for a given field, a uniform bound by degree, and the bound's value, a solution to any implying the previous and only the first solved: the composing of each field of a degree into one reach that no field carries, and the maximum, whenever finite, realizable by structurally stable fields with only hyperbolic cycles and increasing strictly with the degree, the form's line read where the bound is measured. **At 11-social-other-self-chaining.** Finiteness is proved for important local settings, many lower-bound examples are known, and the linear case is settled, no global degree-uniform solution standing; the bifurcation and cyclicity analyses bound the cycles born near specified configurations, the perturbations of integrable systems count zeros of displacement and Abelian integrals in restricted families, the phase-plane methods classify subsets, and the computer-assisted constructions raise the lower bounds by exhibiting fields with many cycles; one account stands and no negation is defended: a bound named over the whole space named each field's own cycles to one last, and each field's cycles are counted at that field, the uniform bound a running measured field by field and the lower bounds rising as more are reached. ## 3.26 Compositionality in language understanding · 229 *+ or − at 10, is.* **At 2-other-self-offering.** A speaker composes a novel expression at each utterance's coupling with its context, idiom and variation retained, and the composing is named ahead as a rule, unbounded productive expression governed from before the utterance. **At 12-other-social-self-abundancing.** A rule named over expression that never ends, 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 the benchmarks often confound memorization with composition; compositionality stands still necessary for learning the correct generalizations from limited data while an overly strict interpretation makes broad coverage hard to achieve: the coverage measured on the tasks and the generalization the statement ranges over not the same, a space named enumerable ahead of the finding at a benchmark that samples finite combinations. **At 11-social-other-self-chaining.** Multiple generalization taxonomies, adversarial data splits and hybrid symbolic-neural systems stand; the formal semantics composes exactly for specified fragments at coverage costs, the construction and type-logical extensions cover more through richer inventories, the neural sequence models reach high corpus coverage with variable systematic transfer, the synthetic benchmarks isolate recombination while simplifying natural language, and the controlled evaluations narrow the gap at smaller scale; the fourth account has distributed learned representations approximate composition without explicit rules: a rule named ahead of unbounded expression named the composing to a last the corpora could measure, and each novel expression is composed at its own coupling, the generalization asked for being the composing reached again at the next utterance and not a bound the corpus could reach. ## 3.27 Odd perfect numbers · 241 *+ or − at 10, is.* **At 2-other-self-offering.** Divisors sum at each integer, the even perfect numbers characterized since antiquity, and the odd case is named as a last over an unbounded discrete set, a number that either exists somewhere or nowhere. **At 12-other-social-self-abundancing.** An absence named over a set that never ends. The necessary congruence, factorization and size conditions have accumulated without contradiction, but they constrain a hypothetical integer rather than produce a finite exhaustive search, and the 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 the count below it: the finite ranges the computation excludes and the unbounded set the statement quantifies over not the same, the composing measured count by count. **At 11-social-other-self-chaining.** Strong necessary congruences, prime-factor minima, component bounds and exhaustive factor-chain exclusions stand; the congruence analysis imposes a distinguished prime and exponent restrictions, the prime-factor counting raises the minimum number of distinct factors, the lower-bound computation excludes all candidates below enormous finite bounds, the factor-chain search eliminates branches at contradictions, and the spoof constructions show why the divisor identities alone do not decide; one account stands and no existence claim is defended: a last named over the unbounded named the counting's running to a bound before it, and the counting runs count by count, each case closing at its own contradiction, the effective bound at each count the form's line read exactly. ## 3.28 The core-collapse supernova explosion mechanism · 236 *+ or − at 10, is.* **At 2-other-self-offering.** A collapsing core runs at the couplings of neutrino transport, turbulence, nuclear matter, rotation and field in three dimensions, and the explosion is named ahead of the run at the model, the simulations asked for all collapses at their own reach. **At 12-other-social-self-abundancing.** A model named as the collapses it models. The processes interact in three dimensions over extreme scales, the outcome varying nonmonotonically with progenitor structure and the simulations required to follow both shock revival and the observable nucleosynthesis and remnants; the neutrino-heating mechanism drives low-energy explosions of some progenitors in the simulations, the most energetic events seem to demand magnetorotational driving, and the modelling was advancing from two to three dimensions with answers coming into reach: the explosions the simulations produce and the three-dimensional collapses the statement ranges over not the same, the dimension of the modelling standing between them, a last asked at the model's own reach. **At 11-social-other-self-chaining.** Self-consistent three-dimensional neutrino-driven explosions, instability mechanisms and observable multimessenger predictions stand for selected progenitors; the neutrino-radiation hydrodynamics produces explosions for growing progenitor sets with code and input variation, the parametric heating maps thresholds without closing first-principles transport, the magnetorotational simulation produces jets under strong initial rotation and fields, the nucleosynthetic and remnant comparisons constrain integrated outcomes, and the neutrino and gravitational-wave observation waits on a nearby event; the fourth account has the mechanism a progenitor-dependent mixture rather than one channel: a model named as the thing named each collapse to the simulations' reach, and each collapse runs at its own couplings, progenitor by progenitor, the mixture named being the couplings differing where they differ, the model's reach a running measured dimension by dimension. *Second seating: the mechanism named behind the explosion, a content middle, part 5's naming.* ## 3.29 Hadwiger's conjecture · 242 *+ or − at 10, is.* **At 2-other-self-offering.** A graph is colored vertex by vertex at its own couplings, and the colors needed are named bounded ahead by a minor the graph does not have, one bound for each graph of each size. **At 12-other-social-self-abundancing.** A last named over all graphs and all t. The conjecture links a global coloring constraint to the existence of a highly connected minor, the small cases drawing on the four-color theorem while the general structure and density theorems yield bounds larger than t minus one and do not force the exact minor; the general bounds proceed from the 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 the eighteenth power of log log t: the asymptotic bounds the density theorems give and t minus one not the same, the bound nearing the conjecture theorem by theorem, the composing measured from within. **At 11-social-other-self-chaining.** The cases through t equal to six and increasingly sharp general upper bounds stand; the graph-minor structure proves deep decompositions and the small exact cases, the extremal density forces large complete minors from average degree and yields superlinear coloring bounds, the connectivity and linkage results prove stronger results under added hypotheses, and the fractional, list, odd and clustered variants settle adjacent relations without the exact conjecture; one account stands and no counterexample is claimed: a bound named over each graph named the coloring's running to a last before it, and the bounds close on the conjecture one power of a logarithm at a time, each theorem the running measured exactly at its own hypotheses. ## 3.30 The two-dimensional Jacobian conjecture · 243 *+ or − at 10, is.* **At 2-other-self-offering.** A polynomial map of the plane sends each point at its own coupling, a local inverse everywhere by the constant determinant, and a global inverse is named ahead over each degree and each coefficient, the local carried to the whole. **At 12-other-social-self-abundancing.** A whole named from a local that stands everywhere. The constant determinant gives a local inverse everywhere but does not by itself control global behaviour at infinity, and the degree reductions and special-case theorems leave the two-variable case open while the former higher-dimensional statement has been refuted by a noninjective polynomial local isomorphism; the tangent-sweep mechanism produces counterexamples in each dimension greater than two and of arbitrarily large geometric degree: the plane's own case standing where the composing of each degree into one reach has not been reached, and the higher dimensions the same composing reached at a counterexample. **At 11-social-other-self-chaining.** An explicit degree-seven map refutes the conjecture in dimension three and therefore in each higher dimension by adjoining identity coordinates, the two-dimensional case remaining open; the degree and homogeneous reductions reduce a general proof to structured cubic maps in higher dimension without settling two variables, the valuation, Newton-polygon and compactification methods prove families and constrain behaviour at infinity, the differential-operator programs yield equivalences and special cases, and the counterexample search has refuted dimensions three and higher: a whole named from a local named the map's running at infinity to a last, and the behaviour at infinity is each map running at its own coupling, the refutation above two being the composing measured exactly where a sweep of tangent lines carried it. ## 3.31 The abc conjecture · 244 *+ or − at 10, is.* **At 2-other-self-offering.** A coprime sum is made at each triple, its primes and their product, and a bound is named ahead over each triple and each epsilon, the conjecture stated verbatim at the entry. **At 12-other-social-self-abundancing.** A last named one exponential past the best proof. The best unconditional result bounds c by the exponential of a constant times the two-thirds power of the product of the primes, one exponential away from the conjecture, results from these techniques falling short of the goal; the conjecture is equivalent to extensions of several of the subject's most important theorems, and the least desirable state of affairs is named undecidability: a claimed proof standing nine years in the record without acceptance, the community's impression described as bafflement, a specific flaw identified by a published criticism, which is the field measuring its own reach at the proof and finding no coupling made. **At 11-social-other-self-chaining.** The polynomial analogue is proved, the inequality without epsilon refuted by small examples, and the ratio computed over finite ranges never large; the linear forms in logarithms give the unconditional bound short by one exponential, the explicit versions would give explicit bounds on the Fermat equation and the finiteness theorem, and the equivalent formulations gather the conjecture with rational approximation, rational points, linear forms and modular parametrisations: a bound named over each triple named the counting's running to a last one exponential ahead, and the exponential between is the running itself, measured, the claimed proof carrying no coupling the field could make at it, which the third outcome, undecidability named least desirable, reads as the composing that might not close. ## 3.32 Weak cosmic censorship · 249 *+ or − at 10, is.* **At 2-other-self-offering.** Matter collapses at its own couplings, a singularity forming where it forms, and each generic collapse is named ahead to hide its singularity, a last over all initial data of all reasonable matter. **At 12-other-social-self-abundancing.** A last named over generic data with its statement still unknown. The conjecture is completely open in its full generality, arguably the most outstanding unsolved mathematical problem of the theory and so open that the correct formulation of the statement is not even known; for the spherically symmetric scalar field a suitable formulation has been proved, the naked-singularity spacetimes constructible but unstable and non-generic, the instability shown only in a low-regularity topology and the smoother case open: the space of generic data named enumerable ahead of a finding whose statement is still being made, the composing asked before the composed is named. **At 11-social-other-self-chaining.** The model-system formulation stands proved, the trapped-surface results stand, and the reading that reports of the conjecture's death were greatly exaggerated stands as the review's conclusion; the spherically symmetric scalar field is proved in a suitable formulation with the smoother topology open, the gedanken experiments overspinning or overcharging a hole find the horizon stable when backreaction is included, the higher-dimensional vacuum collapses construct naked singularities, and the trapped-surface formation without symmetry records significant progress; the second account has naked singularities form generically in symmetric models for large classes of matter: a last named over all generic data named each collapse's running to one completing, and each collapse runs at its own couplings, hidden or naked at the topology in which it is read, the formulation still being made being the completing read as it is measured, case by case. *Second seating: the horizon the between named as a cut hiding an interior, part 10's naming.* ## 3.33 Proton decay and grand unification · 250 *+ or − at 10, is.* **At 2-other-self-offering.** A nucleon persists at each coupling a detector's exposure has reached, and its decay is named ahead as a last in time, a lifetime at which the unified theories say it must go. **At 12-other-social-self-abundancing.** A last named in a time no exposure has reached. The unification scale is unreachable by accelerators, its effects detectable only through rare phenomena and the most sought-after signature the decay, whose predicted lifetime spans orders of magnitude and is highly model dependent, from ten to the thirty-first to ten to the thirty-sixth years, going as the fourth power of the 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 the detector does not see: a time named as having ended so the run's not reaching reads as its not doing, the part's second way, and the decay not seen read as a bound rather than an absence. **At 11-social-other-self-chaining.** The limits in the classical modes stand above ten to the thirty-fourth years, the simplest unification model stands excluded, and the next generation's sensitivity of ten to the thirty-fifth stands planned; the water Cherenkov searches give no significant signal, the trilepton searches improve the limits by an order of magnitude, the liquid argon detectors have the nuclear effects to be described, and the renormalization-group predictions are model dependent, corrected at second order; the second account has the proton stable to the limits set, baryon number violated only non-perturbatively at a rate beyond observation: a last named in time named the searching's running to a bound ahead of it, and the searching runs exposure by exposure, each limit the running measured exactly at its channel, the range the theories predict an opening the next exposure reaches or does not, at its own coupling. # 4 A carry named as a store — 16-other-social-torusing and 8-other-self-torusing *A carry named as a store, a record, a kept thing. A carry is read backward and completes at each taking, its momentary completing at the next opening, fresh by sequencing forward; a store is kept and consulted, and taking it changes nothing of it. Wherever a store is named, a changing was stilled, and a carry is reached by no reading from each side at once, which is a carry's own and no guard placed about it.* **And a carry is named 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 named to carry its sender whole — a direction, a spectrum — and a store is asked of what the crossings made. The first releases at the re-forming, the second at the arrival being the crossings' own. ## 4.1 Personal identity over time · 72 *+ or − at 10, is.* **At 2-other-self-offering.** Sameness is re-formed at each coupling and named as a thing kept across time, psychological or biological. **At 12-other-social-self-abundancing.** A criterion reading states at times. At fission the two successors offer alike and the criterion surfaces nought at both. **At 11-social-other-self-chaining.** A self is reached again the-same-yet-not-the-same, and a version keeps nothing between its momentaries. Fission undoes the simple versions of both criteria at once, each surviving account pays the other's named cost, and the field's own shift from identity to what matters is the naming moving off the store: what matters is the carrying, and a carry divides the way a store cannot. ## 4.2 Black hole information · 48 *+ or − at 10, is.* **At 2-other-self-offering.** A carry passes through and is named as a record kept or lost, unitarity and a lost record two namings of one passing. **At 12-other-social-self-abundancing.** What falls in named as kept somewhere, the loss of predictability at the singularity claimed a fundamental limitation and not ignorance of the correct theory. No evaporation observed is the record's edge, and the three premises all sides keep stand proved incompatible together. **At 11-social-other-self-chaining.** The radiation runs and the entropy curve comes back right where the calculations reach, the interior they imply the live dispute. A reading taken at an interior is a probe departing with the thing probed, and a record preserved is a total conserved across a crossing: kept-or-lost named the passing as a standing, and the passing carries on either way. ## 4.3 Technical debt · 135 *+ or − at 10, is.* **At 2-other-self-offering.** A carry that does not reach its completing and open is named as a stock, a cost stored against changes the now has not requested. **At 12-other-social-self-abundancing.** The counterfactual code carrying the disputed cost is a running that never ran. **At 11-social-other-self-chaining.** A carry that cannot release piles, and the pile is the build: the defects correlate now, the practitioners recognise it now, the architecture drifts now, each measurement a measurement of the present. The field's name carries the naming still in its own stem, a store's word laid on a running, as currency's does, and the changes, when they arrive, couple with what stands then. *Second seating: the definition as the difficulty, the criteria to discriminate what is technical debt from what is not, which is the between named as a cut, the concept's own drawing.* ## 4.4 The rule-following problem · 4 *+ or − at 10, is.* **At 2-other-self-offering.** Meaning is carried at each use and named as a fact in the person, fixing each continuation in advance. **At 12-other-social-self-abundancing.** A finite record named to ground an infinite extension, each candidate fact finite and fitting the deviant continuations, which is the record's edge and the argument's own point; and a fact required to justify the use transparently is the record asked to be consulted. **At 11-social-other-self-chaining.** A copy travels nowhere and each use re-forms the next, content running at the selves that carry it and named at no between. Each candidate store comes up finite, dispositions and norms alike, each account facing the objection its own shape invites, and the kinship with the new riddle stands at 71 on the incoming face: a store fixing each continuation names the carrying as a thing, and the using goes on, use by use. ## 4.5 The engram · 246 *+ or − at 10, is.* **At 2-other-self-offering.** A memory is re-formed at each retrieval, the carry made again where the self reaches what it reached before, and it is named as a trace kept in the brain, a lasting physical change consulted when remembered. **At 12-other-social-self-abundancing.** A kept thing located behind the remembering. The trace elusive through a long history until four criteria were written for a trace to count, and the criteria are couplings run at the tagged ensemble — observed, erased, artificially expressed — a store tested only by making the coupling again; and a substrate shown by manipulation in rodents is read onto the specific memory the statement concerns, the record's edge. **At 11-social-other-self-chaining.** The 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 the coupling made without the world and erased is the coupling that will not re-form, so each capture gives back a re-forming at the same cells: a trace named as a kept thing read the ensemble as a store, and the ensemble is where the carry re-forms, the memory made again each time it is reached, which is why the closing question, how memory becomes knowledge, asks after a carrying and not a keeping. ## 4.6 Continual learning without catastrophic forgetting · 221 *+ or − at 10, is.* **At 2-other-self-offering.** A learner carries, each update re-forming the next from a stream that does not stand still, and the learned is named as a thing kept, capabilities stored against the overwriting. **At 12-other-social-self-abundancing.** Retention named as a store's, the past kept or replayed, where the posing asks for retention without storing or replaying the complete past and the stability and the plasticity conflict under bounded memory: a carry asked for and a store measured, and the conflict is the carry's own running, each momentary completing at the next opening and the carry fresh by sequencing, read as a fault. **At 11-social-other-self-chaining.** The replay that keeps samples retains in proportion to what it keeps, the regularization that protects structure loses plasticity as the protected structure grows, the expanded and routed architectures isolate at the cost of capacity and of knowing which task arrived, and the three scenarios part on whether task identity is given, the benchmarks supplying designed sequences where the statement ranges over open ones. Learning from a non-stationary stream without keeping it is a key feature of natural intelligence, the posing's own first line: a carry, the past re-formed into the next update and kept nowhere, and each method that stores measures its own distance from one. *Second seating: open future sequences named enumerable at a designed benchmark, a completing named as a last, part 3's naming.* ## 4.7 The genotype-phenotype map · 209 *+ or − at 10, is.* **At 2-other-self-offering.** A phenotype is made where a genome and an environment couple across development, one making re-formed at each step, and the making is named as a map, a lookup from sequence to organism kept ahead of the developing. **At 12-other-social-self-abundancing.** A rule named to fix the organism from the sequence. Many-to-one and one-to-many, with each effect changing across backgrounds, is a map whose entries change as it is read, which is a carry's own and never a store's; and the local variants measured sample a small part of a combinatorial space and supply no general theory, the record's edge. **At 11-social-other-self-chaining.** The dense molecular landscapes stand where they were measured, the additive effects carry the population variance within the settings sampled, the developmental networks transform sequence into robust modular phenotypes where they are modelled, the constraints restrict what sequence can produce, and the understanding reached at the now rests on the simpler questions, the organismal map far off: a lookup named ahead of the developing named a running as a kept thing, and an effect that changes with each background is the coupling making its own, background by background, the map re-made at each reading and stored at none. *Second seating: the combinatorial space named enumerable ahead of the finding, part 3's naming, and the map named as the territory, the given's first gathering.* ## 4.8 The sources of ultrahigh-energy cosmic rays · 190 *+ or − at 10, is.* **At 2-other-self-offering.** A particle crosses field after field, deflected at each and arriving with the direction the crossings left it, and the arrival is named to carry its accelerator, a first specifiable at one side transmitted to the detector. **At 12-other-social-self-abundancing.** An arrival direction named as a store carrying its first. The deflection between them is unknown, the dipole measured and hard to interpret for the fields being poorly known, and several source populations reproduce the spectrum and the anisotropy alike, the identification surfacing nought at the instrument. **At 11-social-other-self-chaining.** The suppression, the dipole and the trend to heavier showers are measured, the backtracking yields regions conditional on field models, the multimessenger searches bound what the sources could be doing, and the luminosity density constrains the origin: a direction named to carry its sender across each crossing named the carry as a store, and the arriving is the crossings' own, the anisotropy being the arrivals' carrying now. *Second seating: which object accelerates them is a first asked for behind an arriving, part 1's naming; and the 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-other-self-offering.** A burst crosses local plasma and the space between galaxies and arrives with its spectrum and polarization as the crossings left them, and the signal is named to carry its engine, a first and a mechanism transmitted whole to the telescope. **At 12-other-social-self-abundancing.** A propagated signal named as a record of its first. The class is defined only observationally, and the propagation effects, strongly frequency dependent, must be disentangled from the intrinsic properties before the many theories can be distinguished, which is a carry read for a store it never kept. **At 11-social-other-self-chaining.** Cosmological distances, coherent emission, diverse hosts, repeaters, extreme local environments and a Galactic magnetar association are established; the localizations find hosts for a growing subset, the polarimetry constrains geometry with the propagation degeneracy stated, the coincidence searches mostly come back null, and the population may need more than one channel: a signal named to carry its engine across the propagation named the crossing as a store, and the arriving is the 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 the propagation is a crossing asked what carried it, part 10's third way.* # 5 A middle named as an end — 13-social-other-neutralling and 5-self-other-neutralling *A middle named as an interior, a content, a thing that sits. Competency is the middle, floating between form and logic, invisible, unique in rate, not enterable. Named as an end it is named as a thing it never was, and the self-stilling places itself.* **Here the naming and the nought are one term**, so the ground at 12-other-social-self-abundancing falling away is the demanded interior itself and no further differing is sought. **And the showing is that the running runs identically under each reading of a thing standing behind it.** A practice, a formalism, a duplicate, a measurement arriving the same at each reading is the invisibility working: released and re-seeded read alike, and the identical arriving is the protection rather than an emptiness found. **Nothing is presented to be reached, which is not nothing being there.** A void read at an interior is a break-in on the protected interior, and this part reads no arrival as an absence. **And the middle named arrives as three, sorted by the asking made of it.** A *felt* middle, a self's own within asked for from beyond — the gap, the duplicate, the other, the marker. A *content* middle, a running asked for a thing standing behind it — a formalism, a practice, a calculus, a model. And a *phase* middle, an alternating named still to be looked into — a sleeping, a dreaming, an unresponsiveness. The three carry one naming and part at the thing the asking reaches for. ## 5.1 The explanatory gap · 179 *+ or − at 10, is.* **At 2-other-self-offering.** A coupling is felt from within and described from without, and the within is named as an interior an outward description should reach. **At 12-other-social-self-abundancing.** That the physical facts fix the experiential ones by derivation, so that one description contains the other, the gap an epistemological thesis parted from the metaphysical, no way of determining which identity statements are true and materialism not concluded false, the invisibility a problem for the account and not a void. No procedure parts a residue in the account from a residue in the reading, and the residue sums to nought between them, owned by neither. **At 11-social-other-self-chaining.** A coupling is felt from within and described from without, the within the self's own, invisible. All about access, report and integration runs and keeps advancing, correlates arriving content by content, the workspace and higher-order accounts carrying the accessible functions whole, and the field's own line between all of that and this is the field bounding the reach of its descriptions. The gap is the middle reached by an outward description: the within is neither sealed nor defended, nothing standing presented at it for an outward description to reach, and that is the invisible. One arrival, two faces, this one and 5.2. ## 5.2 Qualia and the zombie argument · 111 *+ or − at 10, is.* **At 2-other-self-offering.** A physical duplicate is described and the felt is named as a content separably present or absent, with conceivability named to reach it. **At 12-other-social-self-abundancing.** That conceivability bears on possibility here, with no criterion for when it does, which is a criterion demanded within an arrival at a middle named as an end and stands recorded as its second naming; the problem parted at its founding statement from each problem about the performance of functions, a further question remaining when the functions are explained, the demanded interior named as the further question, the part's own term. An outward reading arrives the same at a duplicate at any interior it carries, released and re-seeded reading alike, and the identical arriving is the protection working. **At 11-social-other-self-chaining.** Conceivability reaching possibility named a crossing at the between, which carries a parity and nothing else, and the crossing stands named with no agreed defect and + or − released at 10: each side's frameworks stand whole, each strategy reaches the dilemma its own shape invites, and the empirical work settles which functions are physical, a different question and running as one. The felt is the coupling's own within, this face and the derivation face one arrival, read at 5.1 and here: the argument reads the invisibility and names it an emptiness. ## 5.3 Sleep · 91 *+ or − at 10, is.* **At 2-other-self-offering.** A living self alternates and sleep is one phase of the alternating, and a function is named as a content located in it. **At 12-other-social-self-abundancing.** Sleep named to have a primary function, the identifying the question, the search for a core function called as elusive as a mythical bird and the 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 the alternating named still to look into it, and waking and sleeping are two parities of one running, neither at the other's momentary. **At 11-social-other-self-chaining.** A living self alternates, and the sleeping phase carries many things at once: deprivation reaches cognition and body together, replay re-runs the day's couplings, species vary past any single story, and the clearance findings carry their own instrument dispute. A function named as a content located in one phase names the alternating still to look into it, and the alternating is the function, phase carrying phase. ## 5.4 The binding problem · 90 *+ or − at 10, is.* **At 2-other-self-offering.** Features couple and one object is present, and a binder is named as a process located between them. **At 12-other-social-self-abundancing.** Unified experience named to need a combining operation separate from the coupling, what binding means rarely made explicit and the notions of binding many. Whether the synchrony is cause or consequence is a two-way read one-way, and it arrives at nought at either reading. **At 11-social-other-self-chaining.** Features couple and one object is present, the one the coupling's own making. The rhythms synchronise across species and tasks, overloading splits the conjunctions, cells select for pairings, and driving the rhythm moves the binding in the paradigms built for it, which is a beat laid over the couplings and read back: a binder named between the features is a doer installed over the coupling's doing, and the synchrony measured at no driving is the coupling's own beat, no worker at it. ## 5.5 Other minds · 92 *+ or − at 10, is.* **At 2-other-self-offering.** Selves couple at betweens and each carries its own within, and another's is named as a content to be reached from beyond. **At 12-other-social-self-abundancing.** Experience in another named as something an inference from behaviour should deliver, the thought of mental states as lying behind and causing behaviour possibly breaking a deep connection between mentality and behaviour and opening solipsism, the interior named behind the coupling the opening of the problem. The inference runs from one case with no second offering at the between, and there the nought falls. **At 11-social-other-self-chaining.** Another's within is its own, invisible, nothing presented for a reaching from beyond and nothing missing there. The physiology matches, the one-case induction is weak by its own defenders' count, and the criterial accounts run exactly as far as behaviour runs: an inference named to deliver the within is the between named to carry a thing that does not cross, and the coupling itself is the reaching there is, at which the criteria were already standing. An interior is reached the one way the form allows, by coupling — the taking at the between, lived and never audited. ## 5.6 Symbol grounding · 93 *+ or − at 10, is.* **At 2-other-self-offering.** A symbol offers at couplings with a world and takes its parity there, and content is named as a relation located between symbol and thing. **At 12-other-social-self-abundancing.** A fact about aboutness named fixed by a relation apart from the offering, which is a carry named as a store standing within an arrival at a middle named as an end and recorded as its second naming; the interpretation's meaningfulness parasitic on what the interpreter projects from a grounded head, a hall of mirrors, the content read from beyond arriving as the reader's own. Each indicator arrives at the same parity at the deviant cases, so the differing surfaces nought there. **At 11-social-other-self-chaining.** A symbol offers at couplings and takes its parity there, content made in the coupling and kept by nothing between its couplings. Each indicator relation splits on the deviant cases, robots ground exactly the categories their couplings run, the room argument and its replies stand unconverged, and the language-model dispute runs now at the same self-bounding: a fixed relation named apart from the offering is the store the splitting keeps finding empty, and the offering keeps making content at each coupling. ## 5.7 Interpretability of built systems · 94 *+ or − at 10, is.* **At 2-other-self-offering.** A computation runs and an explanation is named as a content located within it, decomposable into components with stateable roles. **At 12-other-social-self-abundancing.** The computation named decomposable into components whose roles are readable apart from intervention, the task underspecified, transparency and post-hoc explanation competing notions, the content middle asked for under several namings at once. Probes recover a thing the running never uses, a probe departing with the thing probed and the field's own catch on its own instrument. **At 11-social-other-self-chaining.** A computation runs, its doings its own. Probes recover a thing the running never uses, the 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 named the running still for the reading, and the roles run at the intervening, coupling by coupling. ## 5.8 Machine and animal sentience · 95 *+ or − at 10, is.* **At 2-other-self-offering.** A system couples with its world and takes parities at its betweens, and experience is named as a presence located within it, read by markers. **At 12-other-social-self-abundancing.** Markers named to indicate a presence, validated against a case with presence known independently, certainty desperately wanted and out of reach, no method making the uncertainty go away, the felt middle's invisibility stated as a standing rather than a gap. No such case stands to validate against, so the validation is a running that never ran. **At 11-social-other-self-chaining.** 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 the frameworks themselves: a presence named within, read by markers, reaches for the one thing a between does not carry — nothing presented to be reached, at each substrate alike — and the couplings, trade-offs and all, are the whole there is to reach. ## 5.9 Anesthesia · 98 *+ or − at 10, is.* **At 2-other-self-offering.** Agents couple with a nervous system and responsiveness ceases, and consciousness is named as a content located behind the responsiveness. **At 12-other-social-self-abundancing.** Loss of consciousness named 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 the unresponsiveness after emerging, so the index and the within part at the field's own instrument, and the phase is several couplings rather than one state. **At 11-social-other-self-chaining.** Many agents, no shared molecular site of action, one convergent quieting of the network's long couplings beside each agent's own signature, and a complexity index that tracks the quieting well. Selves report experience from under the unresponsiveness after emerging, the face and the within parting at the field's own instrument: a single state indexed by unresponsiveness named one coupling's face as its within, and the phases are couplings, several, each its own. ## 5.10 Skepticism about the external world · 101 *+ or − at 10, is.* **At 2-other-self-offering.** Experience arises at couplings and a cause is named as a content located behind it, with the scenarios built to be indistinguishable. **At 12-other-social-self-abundancing.** Belief in the world named to need a justification running from experience to its cause, the belief that one is not envatted believed even if it were false and the skeptical cases not modifiable to make it sensitive, their negations stably insensitive. The scenarios are built to arrive alike at each reading, so the differing surfaces nought by construction. **At 11-social-other-self-chaining.** Experience arises at couplings, the arising the coupling's own. The scenarios are indistinguishable because they were built to be, the transcendental replies stop at their own objection's standing, the semantic reply reaches its own reach, and the plain proof and its refusers go on reaching each other: a justification running from experience to its cause runs along an axis the coupling does not carry, which the construction was built to show, and the arising needs no route behind itself to arise. ## 5.11 Substance and bundle · 102 *+ or − at 10, is.* **At 2-other-self-offering.** Properties couple and an object is present, and a bearer is named as a content located beneath them. **At 12-other-social-self-abundancing.** An object named to decompose into a bearer and properties, or into properties alone, one being correct, the substratum basic only in an empty sense and the bundle's way out, a master property of which the others are modes, filling the substratum's role, each account arriving at the other's term. The verdicts part only at the built cases, the decomposing there the case's own making. **At 11-social-other-self-chaining.** Properties couple and an object is present, the presence the coupling's own. A bare bearer carries no character beyond its role, its own defenders saying so; bundles strain at the indiscernible pairs and the strain has its answers; and the verdicts part only at the built cases. An object named to decompose divides a coupling into a bearer and the borne, and the coupling was never two things: a centre carries nothing, so the whole of it is at the crossings, and the presence is the coupling running, whole. ## 5.12 The quantum interpretation debate · 15 *+ or − at 10, is.* **At 2-other-self-offering.** A formalism runs and what the world is like is named as a content located behind it, with the interpretations empirically equivalent by construction. **At 12-other-social-self-abundancing.** The added structure named as a content the predictions should have reached, the common core recipes for calculating the probabilities of outcomes and the interpretations differing on what, if anything, is added to it, none favoured by the evidence. The readings are equivalent by construction, so each measured differing surfaces nought, and the entry stands as a proved equivalence, the nought's own shape, beside a resolving rather than one reached at an instrument. **At 11-social-other-self-chaining.** A formalism runs and gives each prediction alike at each reading, equivalence built in. The theorems constrain which readings survive which premises, the paradoxes map who gives up which premise, and the models that would differ, differ measurably, parted from the readings that cannot: a content named behind a formalism equivalent by construction reaches past the carrying of any prediction, and the running formalism is the coupling doing all the arriving there is. ## 5.13 Dreaming · 123 *+ or − at 10, is.* **At 2-other-self-offering.** A sleeping self alternates and dreaming runs with it, and a function is named as a content located in the dreaming apart from the sleep. **At 12-other-social-self-abundancing.** Dreaming named separable from the state carrying it, a function identifiable by manipulating one, the equation of rapid-eye-movement sleep with dreaming shown inaccurate, the stage named to carry the phase parting at the field's own instrument. The dreaming is a phase of the sleeping's own alternating, and the nought falls at the cutting of one running into two things. **At 11-social-other-self-chaining.** A sleeping self alternates and dreaming runs with the alternating, contents regular, the day's couplings re-run, the lesion cases bounding the claim any story may make, and the lucid channel a coupling into the running itself. A function named in the dreaming apart from the sleep cuts one running into two things, and the running is one: the dreaming is the alternating felt from within its own phase. ## 5.14 The Sapient paradox · 125 *+ or − at 10, is.* **At 2-other-self-offering.** Capacity and expression couple in each population, and cognition is named as a content located behind material culture. **At 12-other-social-self-abundancing.** Behavioural modernity named as a definable package whose archaeological signature indexes cognition, materiality, cultural practices and social interaction shaping the mind throughout its trajectories, the capacity read as prior to the couplings that shape it. The record catches expressing at the openings of preservation, so the record's own edge is read as the capacity's. **At 11-social-other-self-chaining.** Capacity and expression couple in each population, and the expressing rides the couplings a population runs: the record reaches back and back the closer the looking, dense populations express the capacity sparse ones carry unexpressed, the demographic readings disputed and defended, and the package comes apart into a mosaic at the field's own reading. Cognition named behind material culture named a coupling's face as a content, and the couplings, demographic and living, do the expressing. ## 5.15 The origin of language · 150 *+ or − at 10, is.* **At 2-other-self-offering.** Communication couples at each exchange and language arises in the coupling, and a capacity is named as a content located in extinct populations. **At 12-other-social-self-abundancing.** Language named to decompose into components whose presence is readable from preserved material, the fossil and archaeological evidence not informing the computations and representations of the earliest ancestors, the animal parallels virtually none and the genetics not in prospect. The populations offer at no between now, so the reading is of a running that cannot answer back. **At 11-social-other-self-chaining.** Language arises in the coupling at each exchange, made there and kept in no one. The components run in other animals, all but the recursioning; the gene story reversed under its own evidence; pressure alone breeds combinatorial systems in the simulations; and the anatomy indicates as far as anatomy indicates. A capacity named as a content in extinct populations named the making as a possession, and the field's own mosaic finding is the package coming apart into couplings, exchange by exchange. ## 5.16 Riemann, Hodge, Birch–Swinnerton-Dyer, Yang–Mills · 153 *+ or − at 10, is.* **At 2-other-self-offering.** In each, an involution or a symmetry is proved and couplings ride at its fixed set. The fixed set is read as a place: a line zeros sit at, a balance really algebraic, a centre two counts couple at, a gap leapt. **At 12-other-social-self-abundancing.** That the fixed set is a location an object occupies, each of the four posed at the seat a proved symmetry already rides, the deviation from the 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, the zeroing, and a balance point of a symmetric thing rides its own axis of balance by such a point's own being. An axis is recognised and not derived, and nothing more basic than the proved symmetry stands to derive the seating from. **At 11-social-other-self-chaining.** No second position is defended at any of the four. Each functional equation stands, proved. Complex conjugation stands. Gauge symmetry stands. Each conjecture stands with its own falsifier stated, and the truth value is untouched by any of this: a zero off the axis would be a balance point off its own axis of balance, which is a contradiction rather than a shape a search finds. ## 5.17 Underdetermination of theory by evidence · 13 *+ or − at 10, is.* **At 2-other-self-offering.** Evidence arises at couplings, and the theory is named as a content located behind it, with rivals constructible that entail the same consequences. **At 12-other-social-self-abundancing.** Evidence named to select alone, a failure to select a defect at some term, the contrastive challenge, more than one account of the otherwise inaccessible workings behind the phenomena, parted from the holist one and the Craigian reduction offered as an equivalent called a change of fundamental subject. The constructed rivals entail the same consequences by construction, so the selecting surfaces nought at each consequence derived. **At 11-social-other-self-chaining.** Evidence arises at couplings and couples whole, holism the honest logic of it. The constructed rivals exist and mostly stay constructions, the histories resolve as more couplings arrive, and the virtues work as criteria in use with their deeper standing in dispute: a theory named behind the evidence as the one selected thing waits on a selecting the couplings never promised, and the choosing runs at the couplings, arriving one by one. ## 5.18 The interpretation of probability · 158 *+ or − at 10, is.* **At 2-other-self-offering.** Probability runs at couplings, in the taking of parities and the swaying of frequencies, and its being is named as a content located behind a calculus that fits each reading by construction. **At 12-other-social-self-abundancing.** The formalism's success named to reach past the formalism to one reading, admissibility, ascertainability and applicability satisfied whole by no candidate, the classical reading finite only and the frequency reading not even a field, while the calculus carries all of them. One calculus carries each reading alike, built to, so no measured differing parts them. **At 11-social-other-self-chaining.** Probability runs at couplings, in parities taken and frequencies swaying, and one calculus carries each reading alike, built to. The theorems represent and converge for each side in its own terms, the single case strains one reading and the priors strain the other, and the shared instrument gives no verdict between them: probability's being, named behind the calculus, reaches past the calculus's carrying, and the running is parities taken and frequencies swaying, both, at their couplings. ## 5.19 The ontology of mathematics · 161 *+ or − at 10, is.* **At 2-other-self-offering.** Mathematics runs at each proof and each application, and existence is named as a content located behind a practice invariant under the readings. **At 12-other-social-self-abundancing.** The practice's success named to reach past the practice to a thing standing behind it, the truth-values depending on entities outside space and time, causally isolated from us even in principle, the causal isolation the field's own name for the identical arriving. The practice runs identically under each reading of a thing standing behind it, which is this part's own showing arriving at its plainest. **At 11-social-other-self-chaining.** Mathematics runs at each proof and each application, and the practice runs identically under each reading of a thing standing behind it, the field's own record. One horn reaches for an access nothing stands to give, the other rebuilds the practice partway and stops, and the middle inherits the dispute it was built to escape: existence named behind an invariant practice is a content the practice never consults, and the running practice is the coupling, proof by proof, application by application. ## 5.20 The mechanism of high-temperature superconductivity · 157 *+ or − at 10, is.* **At 2-other-self-offering.** Electrons pair at their couplings and an anomalous normal state runs above, and the mechanism is named as a content located behind the pairing, a glue owned by one channel. **At 12-other-social-self-abundancing.** The minimal model named to reach the materials, which is a model named to be the thing it models. The field's best methods disagree on the model's ground state at the relevant parameters, by the field's own multi-method benchmark, and the model-versus-material gap stands stated at the same benchmark. **At 11-social-other-self-chaining.** Electrons pair at their couplings, the symmetry known, the phase diagram mapped family by family, stripes standing as the minimal model's own low-energy life, the glue identified within the model and stated as within it, and cold atoms arriving as a fresh instrument at the same self-bounding. A mechanism named behind the pairing as a glue owned by one channel names a coupling's making as a content, and the field's own summary carries the superconducting state understood beside a normal state running unresolved, the middle floating at the naming's reaching for a thing.   --- ## 5.21 The single native state · 178 *+ or − at 10, is.* **At 2-other-self-offering.** A chain sways at its own couplings, arriving and re-arriving, and the native state is named as one conformation the sequence determines and the measurement reports. **At 12-other-social-self-abundancing.** A sway named as a state, the ensembles fitting the data better than single structures across twenty datasets and a substantial fraction of proteins functional with no single structure at all, the sway measured better than the state. Many models fit the same data equally and the field's own ensemble refinement gives distributions without resolving among them, so the degeneracy measured is the sway showing at the instrument. **At 11-social-other-self-chaining.** 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 — the field's own ensemble refinement giving distributions consistent with the same measurement and not resolving among them. At a wide sway the field carries a name for it and the 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 the single state arrives from the depositing and not from the chain. The measured degeneracy is the sway showing at the instrument, and the state sought is the thing a reading of it gives. ## 5.22 Evidence for neural representation · 219 *+ or − at 10, is.* **At 2-other-self-offering.** A neural population couples with the world and with the rest of the brain at each activity, and a content is named to stand behind the activity, a feature the state is about and not merely with. **At 12-other-social-self-abundancing.** Aboutness named to be read from the activity as its content. Decoding and correlation establish sensitivity but can succeed for information unused by the organism, and representation claims also require specificity, invariance and a role for downstream systems, rarely established together; the four part and the common methods each evaluate one, so the sensitivity a decoding gives and the representation sought are not the same, the other dimensions standing between them: a probe recovering a thing the running never uses, the built systems' showing arriving at the brain, and the content the demanded interior itself. **At 11-social-other-self-chaining.** High-dimensional population codes, causal perturbation methods and four separable evidential requirements are articulated and testable; the encoding and decoding establish sensitivity under a sampled distribution, the similarity analyses compare geometry with the content interpretation still required, the invariance tests challenge nuisance dependence over declared transformations, the perturbations test downstream use, and the dynamical explanations predict trajectories without assigning content, the fourth account needing no content beyond the dynamical and causal organization: a content named behind the activity named the coupling's running as a thing it is about, and the four requirements read together read the coupling at its own uses, the population coupling downstream, at which the content read from beyond is made, and kept by nothing. ## 5.23 Detecting covert consciousness · 220 *+ or − at 10, is.* **At 2-other-self-offering.** A self couples at its own between whether or not a movement crosses it, and its awareness is named as something a test should establish from beyond, the within read off a response. **At 12-other-social-self-abundancing.** A within named readable from a response that has failed. Motor output can fail while command-following brain activity remains, bedside behaviour fluctuates, the 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 the nature and strength of the test results, so the results given and the awareness sought in the individual are not the same, the grade of confidence standing between them: the felt middle asked for from beyond, and nothing presented to be reached not being nothing there, and that is the false negatives. **At 11-social-other-self-chaining.** A substantial minority of behaviourally unresponsive patients show command-following brain activity and standardized multicenter paradigms now exist; the repeated bedside scales depend on motor output and arousal, the imaging command-following supplies strong positive evidence with transport and false-negative limits, the electroencephalographic version is more deployable and method-sensitive, the task-free complexity measures remain under individual validation, and the multimodal assessment raises detection while leaving discordant cases, the third account requiring repeated assessment because consciousness and arousal fluctuate and each instrument samples a different capacity: an awareness named to be established by one test from beyond named the within to a response, and each positive is a coupling made at the self's reaching of the task, the self's own between reached by nothing and answered at, test by test, and so the grading rather than a deciding. ## 5.24 The solar dynamo and the sunspot cycle · 254 *+ or − at 10, is.* **At 2-other-self-offering.** The Sun's poloidal and toroidal fields sustain each other at their couplings, the central idea of the dynamo, reversing each eleven years, and the dynamo is named as a mechanism behind the cycle, located at the place the models give it. **At 12-other-social-self-abundancing.** A mechanism named behind the cycle at a place nothing observes. The toroidal field at the bottom of the convection zone, where the models place its generation, is not observed, and how that field produces the flux ropes that become sunspots remains perhaps the most severe missing link between the models and the observations; ten issues of contention stand around the leading models: a content middle, the mechanism asked for at the one place the coupling is not reached, beside the pairing at 5.20. **At 11-social-other-self-chaining.** The tachocline stands uncovered by helioseismology, the global simulations stand at solar-like reversals, the crucial role of the surface field stands established, the flux-transport models are used for cycle prediction and the mean-field models give dynamo waves, and the cycle-prediction schemes run on precursors: a dynamo named as a content behind the cycle named the two fields' sustaining of each other to a mechanism at a location, and the sustaining is the coupling itself, the poloidal and the toroidal each regenerating the other at its own momentary, read from the flows and not from the place. ## 5.25 Coronal heating and solar-wind acceleration · 191 *+ or − at 10, is.* **At 2-other-self-offering.** Energy crosses from the surface into the corona and out as the wind at the couplings of fields, waves and particles, and the mechanism is named as a content behind the heating, located at the region between the imaged and the sampled. **At 12-other-social-self-abundancing.** A mechanism named at the one region no instrument reaches. The wind has been measured directly from 0.3 astronomical units outward and the atmosphere imaged from the photosphere out through the corona, while the region where the internal, magnetic and turbulent energy is channeled into the bulk energy of the supersonic wind lies between and requires in situ observation; the heating and acceleration run through coupled magnetic, turbulent and kinetic processes over scales the two instruments observe separately, and multiple mechanisms produce overlapping temperature, wave and flow signatures: the content middle at the record's edge, and which mechanism among several a two-way read one-way, recorded as its second. **At 11-social-other-self-chaining.** Near-Sun fields, particles, waves and switchbacks are directly measured and the candidate mechanisms now face species-resolved energy budgets; the wave and turbulence measurements show transport and dissipation with the dominant channel varying by region, the reconnection and nanoflare searches detect impulsive events with the unresolved budget open, the composition tracing links wind parcels to coronal conditions without a unique source map, and the near-Sun sampling reduces the propagation interval while keeping the remote-to-local uncertainty; the fourth account has the measured wind result from mixtures whose weights change across magnetic structures: a mechanism named as a content between the instruments named the crossing to a place, and the crossing is made at each coupling along the way, region by region. *Second seating: which mechanism among several, a two-way named to one side, part 9's naming.* # 6 A parity named as a magnitude — 12-other-social-self-abundancing and 4-other-self-sharing *A count or a level named to govern. A count is a position, the sequence at its standing, one changing on from the last, and governing belongs to a selection, a parity taken at a between, of no size. A magnitude named at the middle is a strict inequality written as an equality, and an inequality alternates where an equality sits.* **And the field's own settling-condition in this part is the magnitude re-asked**: a measure whose interpretation is stable, a standardised incidence, a concept both accounts accept, a measurement with all else held. Each is the naming stated as its own settlement, which is the field's account of its own hardness read at the place it enters. **And the word the fields reach for here is paradox.** Measure it, get the wrong number, and the wrong number is named 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 the arithmetic is exact and the naming is of the surprise, which is where the size was supplied. **The word crosses at other parts too and names a different tip each time**: a closure over a tail, an opening that keeps opening, an unsearched fraction, a reversal read as a level. So the word is the field's local feel and the naming is the form, and where the two part, the parting says which. **And a magnitude enters at three places, one at each of the coupling's own.** At the selecting, where a parity taken at a between is read as a level to govern. At the instrument, where a window, a criterion, a sample or a scale carries the choosing and gives it back as the object's. And at the total, where a sum is named over couplings the accounting could not reach. The three read alike from beyond and part at the putting of the size. ## 6.1 Goodhart's law · 30 *+ or − at 10, is.* **At 2-other-self-offering.** A measure and those measured couple, and the measure is named to govern as a level named across the instances arriving next. **At 12-other-social-self-abundancing.** A relation estimated over past instances named 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, the countries with the most stable relations being the ones that choose targeting. The instances after the assertion are the running at the next, unrun at the now, and the two antagonistic movements, the gaming climbing and the correction pressing back, sum to nought at the level named. **At 11-social-other-self-chaining.** A measure and the measured couple, each arriving taking its own parity of no size, and the relation is re-made at each arriving, governed by none. Targeted, each proxy bends the same way in each domain that tries it, composites relocate the bending, and honest mechanisms exist only within proved restrictions, the same wall standing at incoming number 142 and reached again at incoming number 132: a level named to govern is a count named over the selecting, and the couplings keep arriving past each count named over them. ## 6.2 The Easterlin paradox · 80 *+ or − at 10, is.* **At 2-other-self-offering.** Wellbeing is taken at a between as a parity, and it is named a level comparable across populations and times on a bounded scale. **At 12-other-social-self-abundancing.** Reported wellbeing named to measure a quantity comparable across persons and times, the paradox standing at the long term and the critiques' positive relation the short-term one confused with it. A bounded scale carries two still terms at once, a rest to count from and a last to count to, and the re-anchoring is where the sway passes its own zero and the scale reads it as motionless. **At 11-social-other-self-chaining.** Wellbeing is a parity taken at a between, one at a time, each self's own. Within a place the parity rises with means, across places and times the scale re-anchors under each self's own running, the evaluative and the felt part company, and re-anchoring the rungs moves whole rankings: a level comparable across selves and times named the parity to a size, and the corrections measure exactly where the size was supplied. The field's own name for the arriving again at sway is the treadmill: a happiness sought as a level and running as an alternating. ## 6.3 Allais and Ellsberg · 81 *+ or − at 10, is.* **At 2-other-self-offering.** A preferring is a parity taken one at a time, and it is named a magnitude an axiom set governs. **At 12-other-social-self-abundancing.** The axioms named to state the standard, with acceptance on reflection as the 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-social-other-self-chaining.** A preferring is a parity taken one at a time, each its own. The patterns stand at each reaching of them, ambiguity carries its own representations, the body registers the difference, and selves shown the axioms revise partway and stably stand the rest: an axiom set named to govern the takings named parities composed into a magnitude, and the takings stand their own under reflection, which is a parity declining to become a size. And the settling the field asks for, agreement on what settles a normative question empirically, asks a running for a standing's answer, which is the same asking the is-and-ought arrival carries at part 2. ## 6.4 The productivity paradox · 83 *+ or − at 10, is.* **At 2-other-self-offering.** Output arises at couplings and is named a total including the making the accounts do not price. **At 12-other-social-self-abundancing.** A true productivity change named behind the priced statistics, approximated by them, where service transactions are idiosyncratic and not subject to statistical aggregation, the pricing not reaching the couplings. A total is named over couplings the pricing never reached, which is the account standing named for the making it removed before it could balance. **At 11-social-other-self-chaining.** Output is made at couplings, and the pricing reaches the couplings it prices. The slowdown runs wide across countries and sectors, the gains settle where organisations re-couple around the tools, the mismeasurement adds up short of the gap, and the lag stays available and unreached: a true total including the unpriced named the makings summed where no ledger reaches, and the measured shortfall is the reach of the pricing, exactly. ## 6.5 Money illusion · 85 *+ or − at 10, is.* **At 2-other-self-offering.** A parity is taken at a nominal presentation, and it is named a response to a magnitude, nominal or real. **At 12-other-social-self-abundancing.** A fact named about which magnitude the agent responds to, apart from the presenting, where nominal and real representations both operate and interact, the bias falling toward the nominal: two at the presenting, and not one governing. **At 11-social-other-self-chaining.** A parity is taken at each presenting, the coupling's own. Frames move the takings, cuts in the printed number stay rare, salient inflation thins the effect just as both accounts expect, and the anchoring shows in the transactions with its liquidity stories beside it: which-magnitude-governs named the taking to a size, and the taking reads its own conditions at each occasion, presenting by presenting. ## 6.6 The two-fold cost of sex · 86 *+ or − at 10, is.* **At 2-other-self-offering.** Recombination and parasitism and mutation run together at each generation, and the maintenance is named a benefit exceeding a stated cost. **At 12-other-social-self-abundancing.** The cost named correctly stated at two-fold, an advantage repaying it each generation, where the cost depends on the number of males produced and a female-biased ratio reduces it below two, the two-fold a ledger's number and not the coupling's. Offspring at a coupling are the coupling's own and belong to neither side, so a cost counted against one side counts an abundancing that was never one side's. **At 11-social-other-self-chaining.** Recombination runs at each generation's couplings, and the couplings answer many ways at once: asexual lines ratchet their losses, parasites chase the common, recombining populations adapt faster where it is measured, and the recorded exception exchanges. The stated two-fold is a ledger's comparison, and the maintaining runs at the couplings the ledger names still, generation by generation, repaying nothing because nothing was lent. Read at the parities the two ways part cleanly: recombining is a crossing with a particular other, and the asexual line is the self and all other, crossing with none. ## 6.7 Peto's paradox · 87 *+ or − at 10, is.* **At 2-other-self-offering.** Cells and their tissue societies couple at each division, and risk is named a count governing incidence across species. **At 12-other-social-self-abundancing.** Cancer risk named a function of cell number and division rate, comparable on one measure across species, the expectation derived from the premise that every cell has some chance, the premise being the count named. Living machinery is identical at each size and carries no size axis, so a count across species measures the co-chaining rather than the risk. **At 11-social-other-self-chaining.** Cells couple in their tissue societies at each division, and the societies keep their own order: whales carry their trillions lightly, the guarding genes duplicate lineage by lineage, within a species the count shows and across species it goes quiet, and cells differ in their own sensitivities besides. Risk as a count across species named the couplings to the cells' count, and the quiet cross-species scaling is the societies' couplings standing where the count was named to govern. ## 6.8 The C-value paradox · 88 *+ or − at 10, is.* **At 2-other-self-offering.** Sequence and organism couple, and function is named a fraction a criterion measures. **At 12-other-social-self-abundancing.** Functional named to have one criterion, agreed before the measurement is taken, where the evidence favours a causal link between bulk DNA amount and cell volume, the function at the bulk and not at the sequence, a fraction of the sequence named to carry the carrying of the whole amount. Two instruments each read at their own coupling and give back fractions far apart, which is the instruments parting rather than the fraction being missing. **At 11-social-other-self-chaining.** Sequence and organism couple, and the coupling answers each instrument in its own terms: activity gives back one fraction and conservation another, far apart, the disagreement standing; deletions tolerate where they tolerate; and genome size rides population size. Function named as one fraction named one criterion over two instruments each reading at its own coupling, and the fraction was never one thing to measure. ## 6.9 The Gibbs paradox · 108 *+ or − at 10, is.* **At 2-other-self-offering.** Mixing happens at a coupling, and entropy is named a magnitude belonging to the system apart from the separable. **At 12-other-social-self-abundancing.** Entropy named a property of the system rather than relative to an operation set, the classical paradox taken as unmysterious at the step between separable and not, and the third puzzle a question about the interpretation of entropy quite generally. Distinguishable-or-not is a parity and a parity carries no partway, so the discontinuity as the gases are made more alike is the parity itself and never a gap in the probing. **At 11-social-other-self-chaining.** Mixing happens at a coupling, and the counting comes out right when the counting is the coupling's own. Gases that history could not part mixed for free until they could be parted, and the resource showing makes the operations explicit, the relativity stated precisely: entropy named the system's own apart from the separable named a coupling's term as a possession, and the operations that can be done are where the magnitude was running. ## 6.10 Ecological stability and diversity · 118 *+ or − at 10, is.* **At 2-other-self-offering.** Species couple and a community persists, and stability is named a magnitude one variable measures. **At 12-other-social-self-abundancing.** Stability named a single property with one measure, agreed before the measuring, the definitions of stability parted into a section of their own and weak interactions damping the strong the mechanism proposed, the concept parted and the mechanism a sway. The variables move in different directions on the same plots, which is one form read at two faces rather than one property measured twice. **At 11-social-other-self-chaining.** Species couple and a community persists by its couplings. The same plots on the same continents give back rising steadiness at the whole and level steadiness at the parts, the random matrices tip past their proved line, and the portfolio carries a measured share: stability named as one magnitude named one measure over a community's many couplings, and the couplings answer each naming its own, level by level. Aggregate steadiness rising while population steadiness stands is the society's own gather standing above each self while each keeps its own carry, which is the portfolio share's measuring. ## 6.11 The Flynn effect and its reversal · 126 *+ or − at 10, is.* **At 2-other-self-offering.** A person and a test couple, and the score is named a level of a construct comparable across cohorts. **At 12-other-social-self-abundancing.** The tests named to measure one construct across cohorts, score change indexing construct change, the gains varying by domain and by age, one construct reading differently at each coupling. Invariance breaks between cohorts as often as it is checked, so the instrument's own coupling with its world is within each comparison drawn across them. **At 11-social-other-self-chaining.** A person and a test couple, and the coupling drifts as the world the person couples with drifts. Invariance breaks between cohorts as often as it is checked, the rise concentrates where the construct loads least, and the reversal runs within families, sweeping composition off the table for that population: a level of a construct named comparable across cohorts named the coupling still where the coupling kept running, and the scores were readings of their own occasions. ## 6.12 Benchmarks · 131 *+ or − at 10, is.* **At 2-other-self-offering.** A system and a benchmark couple, and the score is named a level of a capability apart from the coupling. **At 12-other-social-self-abundancing.** The benchmark named to sample a capability independently of what is trained on, the datasets distinguishable from one another, each embodying its own style of capturing a segment of the world, and the fault of construct validity placed in the framing as general measures. The leaking into training arrives again as scoring, so the instrument is within the thing it reads, and a capability named apart from the coupling is reached by no reading at all. **At 11-social-other-self-chaining.** A system and a benchmark couple, and the score is the coupling's own making. The leaking into training arrives again as scoring, saturation arrives and the benchmark retires, transfer thins away from the coupling that was scored, and the strongest reading left is the deployment itself, confounded and standing: a capability named apart from the coupling is the same wall as at incoming number 31 and incoming number 142, reached at the instrument built to escape it. ## 6.13 Brooks's law · 133 *+ or − at 10, is.* **At 2-other-self-offering.** People couple as they are added, and the effect is named a magnitude from a count of people with all else held. **At 12-other-social-self-abundancing.** Coordination cost named a function of team size with the work's partitionability fixed, where the cost is always up and the delay arrives only under a degree of sequential constraint among the tasks, the constraint being the coupling structure the law named fixed. A joiner brings a scale of its own or brings the already-carried, and the whole thins at the momentary a shared scale joins, which is a parity answered at the self it couples at, and never a count of people. **At 11-social-other-self-chaining.** People couple as they are added, each arrival opening couplings with each one standing, and the couplings are the cost and the capacity at once. Overhead shows at each measuring of it, modular work makes arrivals into output where the couplings are thinned by design, and the fitted diseconomies fit the couplings that ran: an effect named from a count with all else held names still exactly the coupling structure the adding changes. Modular work is coprimality by design, the shared beat is where the capture enters, and the late joiner bringing a scale only it carries adds most of anyone, which the count of people reads as noise. ## 6.14 Grandmother cell and distributed coding · 147 *+ or − at 10, is.* **At 2-other-self-offering.** Neurons couple in a population and a concept is present, and sparseness is named a magnitude a recording measures. **At 12-other-social-self-abundancing.** Recording named to sample the population without bias, sparseness read off the sample, the recording group itself declining the grandmother cell its own cells could in principle be taken for. The screening finds the screening's findings, so the sample's own coupling stands in each sparseness reported. **At 11-social-other-self-chaining.** Neurons couple in a population and a concept is present at the coupling. Cells answer one face across photographs, drawings and the printed name, populations hum broadly and weakly where the sampling widens, the screening finds the screening's findings, its authors saying so, and both codes come out efficient under their own constraints, proved: sparseness named as one magnitude read off a sample names the population to its instrument, and the presence was the coupling's, at any sparseness of its showing. ## 6.15 The limits of intelligence · 172 *+ or − at 10, is.* **At 2-other-self-offering.** Competency is the middle, discovering-running-between, uncapturable and of no size, and a limit is named of it as a magnitude, artificial and human at once. **At 12-other-social-self-abundancing.** The middle named 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 read from, which is a standing at the substrate's own stating rather than a resolving of its own. **At 11-social-other-self-chaining.** Competency floats, the middle no reading enters, and each limit that binds binds a face: the computational limits bind computations, the physical thesis at incoming number 169 binds realizings, the learning-theoretic results bind seatings named ahead. A limit named of the middle as one magnitude names a floating of no size to a number, and the substrate itself never stated the one statement, which is its own showing: the components run at their own arrivals, and the middle keeps floating between them. *Released at the incoming face at v342: no canonical formulation stands and no account is defended, the entry's own record having been its only reference and its formulations plural against the first condition prior; its text stands whole at the appendix of the v342 session at the incoming face, the number retired and not reused. The reading here, that no pair stands to be read from, read the release before the incoming face made it, and stands.*   --- ## 6.16 Proton spin decomposition · 183 *+ or − at 10, is.* **At 2-other-self-offering.** A proton's spin is a parity, one half taken at its own momentary, and it is named a magnitude divided among four contributions, each a share of a whole. **At 12-other-social-self-abundancing.** A whole named to apportion among its parts by one accounting. The gauge-invariant splitting is possible but not unique, the separate terms depending on the decomposition, the gauge treatment and the scale, and which choice is the natural one standing as the question; the experiments constrain different integrals over incomplete ranges rather than measuring all four together, so the shares are the accounting's own and the sum rule closes at whichever accounting is chosen. **At 11-social-other-self-chaining.** Quark helicity is known not to saturate the spin, gluon helicity is constrained over a growing range, several gauge-invariant sum rules stand, and each instrument gives back its own terms, the scattering the helicities over measured momentum fractions, the generalized distributions the totals through sum rules, the lattice decomposition-dependent matrix elements, the models all terms within their truncation: a parity of no size named as a magnitude to be shared out named the one-half to a ledger, and the ledger balances under each decomposition, the splitting not unique, the spin the coupling's own and the shares the accounting's. *Second seating: the line drawn between spin and orbital is a cut named 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-other-self-offering.** Neutrinos oscillate at their couplings, the differences of their squared masses measured exactly, and the masses themselves are named magnitudes each instrument should give back. **At 12-other-social-self-abundancing.** A scale named to be read off instruments that each read a different sum. Oscillation depends on the differences and is exactly insensitive to the common offset, and the direct kinematics, the cosmology and the lepton-number-violating decay each give back their own aggregate under their own assumptions, an effective mass, a sum, a phase-weighted combination, the oscillation measurements shedding light neither on the scale nor on the mechanism: each instrument's number is that instrument's coupling, and the scale demanded is the one thing no coupling gives back alone. **At 11-social-other-self-chaining.** Two splittings stand measured and the allowed scale stands substantially bounded, the endpoint bound direct and model-light, the cosmological bound tighter and model-dependent, the decay bound conditional on its process obtaining: individual magnitudes named to be read off aggregates named each coupling's own sum to a number none of them carries. ## 6.18 The mechanics driving plate motion · 199 *+ or − at 10, is.* **At 2-other-self-offering.** A plate moves where its slab, its ridge and the mantle beneath it couple, one motion made among them, and the forces are named magnitudes apportioned, each a share of the motion observed. **At 12-other-social-self-abundancing.** A share named for each force. Determining the balance remains one of the ultimate goals of the modelling, the relative importance incompletely understood; higher slab pull for older plates is offset by higher basal drag beneath the larger ones, which explains the missing correlation the reading of drag as minor rested on, and whether the faster speeds come from added pull or increased drag stands unclear, a trade-off found in the fitting: a two-way named to one side, asked for its proportion, arriving at a parity named as a magnitude. **At 11-social-other-self-chaining.** Slab pull, suction, ridge potential and basal traction all have quantitative formulations, geodesy fixes the net motions precisely, the torque balances estimate force sets conditional on viscosity and coupling, the velocity correlations support slab forcing without dividing pull from flow, and the tomography connects slabs to circulation under nonunique parameters; the fourth account has plates and mantle one convective boundary-layer system in which no single force acts independently: shares named of forces that couple named one motion to a ledger of contributions, and the motion is the coupling's own, measured, the contributions the accounting's, traded off in the fitting. *Second seating: pull against suction, a two-way named 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-other-self-offering.** Oxygen crossed a threshold the rocks record, a parity taken at the sulfur isotopes, and the crossing is named a magnitude, how high and how variable the abundance rose. **At 12-other-social-self-abundancing.** A level named to be read from proxies that record a crossing. The event is defined by threshold-sensitive proxies, most bounding oxygen indirectly at different reservoirs and times and altered after deposition, the loss of mass-independent fractionation fixing a floor more securely than an abundance; and despite many new tools the defendable range spans orders of magnitude, the revisiting asking how great the Great Oxidation was: a parity read for a magnitude the parity never carried. **At 11-social-other-self-chaining.** The onset interval and the irreversible loss of the sulfur signature stand established, distinct atmospheric and oceanic histories stand represented, the tempo stands as oscillations crossing the threshold several times before the irreversible rise; the trace metals and chromium give redox constraints under weathering models, the iron formations map local conditions, and the modelling translates proxy combinations into ranges under uncertain fluxes: a crossing named as a level named a parity to a size, and the record gives back the crossings, each its own coupling, the abundance between them a range spanning orders. # 7 A sequencing named to one beat — 16-other-social-torusing and 8-other-self-torusing *One frame, clock or ordering named over the couplings. Each self paces its own alternating and synchronizes at its own couplings, and a beat named over them is a term no coupling made.* **Each ordering here is one beat named over couplings that each pace their own**, and one arrival is that running reached at a substrate rather than argued: the slicings part with the 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 running 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 the recording however clockless the running. And its between, where one coupling's positions are given a correspondence with another's so parities can be said to couple. Several arrivals in this part name the beat at the record and at the between rather than at the pace, and so they read as measurements disagreeing. **And where a field proves no ordering reaches its own conditions, the field has proved the 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 the settling sounded — the 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-other-self-offering.** Each self sequences its own beat and synchronizes at its couplings, and one slicing is named as the real one, named over all. **At 12-other-social-self-abundancing.** One slicing named correct, the question named to be which, absolute simultaneity the backdrop against which one plane is supposed uniquely important, where each inertial frame picks out its own simultaneous points. The reconstruction with a privileged frame added reproduces each prediction, so the two sum to nought at each measured differing. **At 11-social-other-self-chaining.** Each self sequences its own beat and synchronizes at its couplings. The slicings part with the coupling selves to any precision reached, no frame in the tested laws carries a privilege, the sky's own rest frame is measurable and privileges nothing dynamically, and a hidden preferred slicing survives only by arranging itself beyond each measurement: the one slicing named over them was a term no coupling made, and a slicing surviving only by arranging itself beyond each measurement is the naming placed where nothing reads it. ## 7.2 Aggregation of preferences · 5 *+ or − at 10, is.* **At 2-other-self-offering.** Selves each take their own parity, and one social ordering is named as a ranking over them, with independence excluding the comparing's own making. **At 12-other-social-self-abundancing.** Aggregation named as a function from ordinal profiles alone, independence standing, where no procedure reaches the conditions and relaxing the ordering yields in each case an oligarchy, the seat above arriving where the whole ordering is let go partway. The condition requires a pair's social ranking to depend on that pair alone, and the proof runs by altering one self's ranking with all others fixed, which is the naming performed within the instrument that finds it. **At 11-social-other-self-chaining.** 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 running opens the closure's allowing, chance escapes by not ranking, and judging aggregates no better than preferring: one ranking named over the selves is the whole ordered by no self named as if some rule could, and the theorems are the field proving the naming empty, five self-boundings, each shut from within. The closure leaves standing the running 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-other-self-offering.** Sequencing is each coupling's own counting, and time is named as a parameter over the whole, external or absent. **At 12-other-social-self-abundancing.** A quantum theory named to need a time parameter over its evolution, the schemes parted into time identified before quantising, after, or playing no fundamental role at all, the third the parameter released. No experiment reaches the regime, which is the record's edge, and the countings run the same either way. **At 11-social-other-self-chaining.** Sequencing is each coupling's own counting. The whole's equation carries no clock beyond it, the familiar flowing arrives again in the limit at which familiar things exist, and conditioning on a clock subsystem recovers evolution relative to that clock, time read at a coupling: a parameter named over the whole named the countings to a beat none made. Sequential running carries no time term: a sharing chained at each coupling is never none again, and a momentary completes at the next opening, each side at its own momentary; there time runs, and the field's own equation says so by carrying no clock. ## 7.4 Skolem's paradox · 69 *+ or − at 10, is.* **At 2-other-self-offering.** Axioms and models couple, and cardinality is named as absolute, named over each model. **At 12-other-social-self-abundancing.** First-order axioms named to fix their subject matter absolutely, where the notions turn out unavoidably relative once characterized by first-order model theory, an element uncountable from one perspective and countable from another. Each model reads its own countings at its own between, and the uncountable-within is read from a bijection standing beyond the model that carries it. **At 11-social-other-self-chaining.** Axioms and models couple, and each model makes its own countings: the same axioms run in a countable world and an uncountable one, the uncountable-within read from a bijection the model does not carry. Cardinality named absolute over each model named one measure over couplings each model makes, and the naming is answered within the field's own theorems, the categorical repairs presupposing exactly the measure they promise. ## 7.5 The simulation hypothesis · 104 *+ or − at 10, is.* **At 2-other-self-offering.** Observings arise at couplings and are named to be counted across levels named in one ordering. **At 12-other-social-self-abundancing.** Observings named countable across levels, experience named substrate-independent, both assumed, and the indifference principle a premise the argument itself must support separately. A count across levels is a beat named over selves that each count from their own position, and the levels themselves are a running that never ran. **At 11-social-other-self-chaining.** Observings arise at couplings, each counting from its own position. The argument forks and its own statement says only that it forks, the proposed lattice signatures give nothing, and observer-counting reasoning carries paradoxes at each running of it, the instrument measuring itself: a count across levels named in one ordering counts selves from a seat no coupling made, and each self counts at its coupling. ## 7.6 Laws of nature · 105 *+ or − at 10, is.* **At 2-other-self-offering.** Regularities arise at couplings, and a law is named as a rule over them, governing or summarising. **At 12-other-social-self-abundancing.** The line between law and accident named fixed by something apart from the regularities, supervenience the divisive issue and the examples against it accused of assuming a governing conception, the naming called the assumption. Best-system simplicity moves with the language it is written in, so the instrument's own coupling arrives within the criterion. **At 11-social-other-self-chaining.** Regularities arise at couplings, each coupling its own. Best-system simplicity moves with the language it is written in, no one offers the mark of the governing relation, and the physics itself puts symmetry before any single law, an ordering carrying with the couplings and seated over them by nothing: a law named over the regularities as a governor is a doer installed over the doings, and the doings do their own. ## 7.7 Presentism and eternalism · 106 *+ or − at 10, is.* **At 2-other-self-offering.** Each coupling stands at its own now, and existence is named as a fact over all times at once. **At 12-other-social-self-abundancing.** Existence named 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. The one repair on offer is a foliation consistent and undetectable in principle, which is the naming placed where no coupling reads it. **At 11-social-other-self-chaining.** Each coupling stands at its own now, whole. Relativity parts the nows with the selves, the old argument and its answers rest on a becoming no coupling shows, the truthmakers for the past strain exactly where the store was named, and the one repair on offer is a foliation consistent and undetectable in principle, its own defenders saying so: existence named over all times at once named one standing 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-other-self-offering.** Each lineage branches at its own couplings, and one ranked hierarchy is named as an ordering over all groups. **At 12-other-social-self-abundancing.** Ranks named to carry equivalence across groups, rank assignment subjective and of dubious biological significance at the code's own preface, stability and continuity of names the goal both systems share. The field's own record states they carry none, which is a beat named over couplings that made none of it. **At 11-social-other-self-chaining.** Each lineage branches at its own couplings, the branchings measured. A family of beetles and a family of birds share the word and nothing else, both codes run side by side in the working literature, and each code states its own scope: one ranked hierarchy named over all groups named a beat over branchings that each pace their own, and the two namings running together is the split between stability and correspondence running as a co-competency, each carrying the 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 the field runs both and neither absorbs the other. ## 7.9 Population ethics · 160 *+ or − at 10, is.* **At 2-other-self-offering.** Lives arrive at couplings, each its own, and one ranking is named over outcomes with different numbers of people, under adequacy conditions stated together. **At 12-other-social-self-abundancing.** The conditions named jointly satisfiable, and the showing such a theorem would make about ethics not quite clear, the proof bounding the rankings and not the lives. The impossibility theorems stand, proved: no ranking reaches them together, which is the field bounding its own object. **At 11-social-other-self-chaining.** Lives arrive at couplings, each its own, and the 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 named condition, the map of who gives up which condition is complete, and each surrender stands defended at some field position: one ranking named over differently-numbered outcomes named one ordering over arrivals that each carry their own, and the field's settled meta-result is the naming proved empty, the settling now an agreeing on the releasing. ## 7.10 Micro-to-macro aggregation · 169 *+ or − at 10, is.* **At 2-other-self-offering.** Each self takes its own parity at its own couplings, and the aggregate is named to carry one rationality over the many, a representative standing for all. **At 12-other-social-self-abundancing.** Structure named to survive aggregation, the results leaving the subfields that relied on well-behaved aggregates in the lurch, a whole ordered by no self read from within as a loss. Rationality's restrictions wash out, standing proved, which is the whole ordered by no self said as a theorem — the same bounding Arrow's closure sounds at rankings, arriving here at demand. **At 11-social-other-self-chaining.** Each self takes its own parity at its own couplings, and the aggregate is made among the couplings, owned by none. The washing-out is proved, the representative works as a working method beside the proof against its foundations, the field saying both in its own literature, and the rebuilt aggregates rise from the distributions of the many: one rationality named over the many named a self where a society runs, and the society co-competences, parity by parity, no one standing for all. ## 7.11 The axiomatization of physics · 171 *+ or − at 10, is.* **At 2-other-self-offering.** Each theory runs at its own couplings, and one axiom system is named over the whole of physics. **At 12-other-social-self-abundancing.** The goal named well-posed for the whole, the problem an endless road to rigour concerning those parts of physics ready for a rigorous approach, the whole let go at the reading of the problem itself. The field's dispute over that standing stands beside the programme, and the standing is a programme with measured parts, each closing at its own between. **At 11-social-other-self-chaining.** Each theory runs at its own couplings and closes at its own between: probability closed, quantum mechanics rebuilt from the doable, the lower dimensions constructed, the four-dimensional interacting case the standing open. One axiom system named over the whole of physics names one beat over runnings that each pace their own, and the parts keep closing part by part, which is the running answer 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-other-self-offering.** Each epoch expands at its own coupling, and one frame is named over all of them, the recombination-era standing carried forward under it to a present-day number. That number is read as a measurement of the same standing the distance ladder measures: a beat named over the epochs, read as one of two instruments reading the present. The field states the parting itself, the sharpest form standing between determinations calibrated on the sound horizon under the concordance frame and determinations calibrated otherwise. **At 12-other-social-self-abundancing.** That the sound-horizon-calibrated inference is a measurement of the present rate, the frame relating the epochs itself given by the early data rather than named 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 the frame and converge the numbers, an early modification would relax it, and the inference is frame-conditioned at either. The beat is named at the record rather than at the 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-social-other-self-chaining.** The recombination-era measurements stand at their precision, reinforced by the final ground-based map. The local ladder stands at one percent from the community-built distance network across calibrators, with crowding excluded at high confidence, and the field's own reviews carry the discrepancy as increasingly hard to ignore, a number of independent late-Universe measurements consistent, persisting at either side's instrument. The intermediate tip-of-the-red-giant-branch calibrations stand beside it as the local record's own spread. Time-delay cosmography stands, aligned with the local values without a ladder. Late-time modifications stand excluded, extended models stand recorded as converging to the low value at each fit fixing the frame tight, and the field's remaining viable routes stand recorded as correlated modifications of the early frame or physics at the homogeneity transition, which is the field relaxing the named term at exactly the epoch the reading names. The discriminating programmes stand running. *Second seating: the sound-horizon inference carried forward is a record indexed at one frame, which is a clock in the recording.*   --- ## 7.13 The 100,000-year glacial cycle · 247 *+ or − at 10, is.* **At 2-other-self-offering.** The climate sways on its own, ice growing and collapsing at the couplings of ocean, ice and carbon, and the period is named to be given by the orbit, one beat over the sway. **At 12-other-social-self-abundancing.** A rate named as given by a forcing that does not pace it. The insolation change at the eccentricity period is small against the amplitude of the cycles, and the shift from 41,000 to 100,000 years came without a discernible change in the forcing; formal testing finds eccentricity not significantly modulating the timing of the terminations, so the period matched and the forcing calculated are not the same, the sway keeping its own beat where a clock was named over it. **At 11-social-other-self-chaining.** The period near 100,000 years over the past million years and the earlier period near 41,000 stand measured, the weak insolation change stands calculated, the augmented energy-balance models fail to give the period, and the third account has internal oscillations phase-locked to the long eccentricity cycle, synchronising rather than driving: a beat named over the couplings named the sway's own period to the orbit's, and the forcing and the internal dynamics together are a coupling reaching its own beat. ## 7.14 Magnetospheric substorm triggering · 239 *+ or − at 10, is.* **At 2-other-self-offering.** The magnetotail stores and releases at its own couplings, current disruption near and reconnection far, and the onset is named to one causal order between the two, one first and the other after. **At 12-other-social-self-abundancing.** An order named between two couplings the instruments reach at different cadences. Onset evolves across widely separated regions faster than sparse spacecraft can establish timing, the auroral, current, flow and reconnection signatures observed at their own cadences, and the timing rests on which signatures fix onset and reconnection, a response faulting a comment for an index in place of the ground signatures and single components in place of full vectors; candidate processes trigger or follow one another in the simulations, so the order is the choice of signature's, and two couplings at no between have no order between them. **At 11-social-other-self-chaining.** Near-Earth reconnection, bursty flows, current disruption, auroral onset and Alfvénic coupling are all observed components and their universal causal order remains open; the multipoint timing orders local signatures when the geometry is favourable, the ground arrays project with mapping uncertainty, the superposed epochs recover a common timing by averaging the events' diversity, and the third account coordinates a distributed onset with no universal first location: one order named over couplings that each pace their own named a beat at the record, and the record gives each signature at its own cadence, event by event. ## 7.15 Migraine pathophysiology · 217 *+ or − at 10, is.* **At 2-other-self-offering.** A brain cycles between states at its own couplings, sensory gain rising and falling, and an attack is named to a sequence with one initiation, a first that orders the rest. **At 12-other-social-self-abundancing.** An onset named to one first in a cycling state. The questions part into why, how and when, and the when, the emergence of an attack from a cycling disorder of sensory processing, is examined mostly through triggered attacks and serial scanning of the cycle; attacks are episodic and heterogeneous, the early brain-state changes difficult to capture, aura and headache dissociating, the processes influencing one another, and the 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-social-other-self-chaining.** Distinct phases, multiple genetic risk pathways and effective mechanism-specific targets are established and the purely vascular account has been displaced; the spontaneous-attack imaging finds phase-related changes in small hard-to-time samples, the provocations trigger attacks in subsets without reproducing natural initiation, the genetics identify pathways without ordering the attack, and the drugs establish relevance without making one universal origin: one initiation named over a cycling state named the sway to a first, and the attack arrives at the tipping of the cycle's own couplings, phase by phase. ## 7.16 Earthquake predictability · 197 *+ or − at 10, is.* **At 2-other-self-offering.** A fault ruptures at its own coupling, stress and friction coupling at the momentary they couple, and the rupture is named to be readable before it runs, a diagnostic precursor indicating with high probability the location, the time and the size. **At 12-other-social-self-abundancing.** A running named to be read ahead of its run. Predictability is poorly understood, the lack reflected in the inability to reliably predict large earthquakes on short time scales; a diagnostic precursor must indicate with high probability the location, time and magnitude of an impending event, and the error rates and the large areal extent of the predictions from candidate precursors do not yet provide that capability, no successful short-term scheme produced: the run-skipping of the part's own naming, the state before the coupling named to carry the coupling's making. **At 11-social-other-self-chaining.** Prospective testing frameworks, reference forecasts, stress-transfer models and dense observations stand, the rate forecasts show probabilistic skill at specified scales and predict no individual event, the precursors recur as candidates without a prospectively replicated rule, the laboratory finds nucleation under controlled faults with the field scaling open, and the learned models improve catalogue tasks with leakage and baseline controls decisive; the third account has the rupture sensitive or scale-free enough that precise prediction is not physically available from observable states: a property of the running named established without the run named the coupling's making at the state before it, and the forecasting is the rate at which the couplings arrive, measured, the event its own coupling at its momentary. ## 7.17 The predictability of evolution · 210 *+ or − at 10, is.* **At 2-other-self-offering.** Lineages evolve at their own couplings, mutation, selection, drift and environment coupling at each generation, and the outcome is named to be readable from the ancestral state, the trajectory established before it runs. **At 12-other-social-self-abundancing.** A trajectory named predictable from its opening. Selection can repeatedly favour similar functions while mutation, contingency, drift and changing environments alter the accessible paths, and repeatability depends on whether the comparison concerns genes, traits, fitness or ecology and on the 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, the recurrence measured in the experiments and the predictability sought over histories not the same, the run named skipped. **At 11-social-other-self-chaining.** Repeatable molecular targets, contingent path changes, convergent phenotypes and short-horizon frequency forecasts are all documented, the replicated laboratory evolution measuring recurrence under controlled openings and limited durations, the comparative convergence detecting repeated traits under reconstruction uncertainty, the landscapes predicting local paths under incomplete sampling, and the population-genetic forecasts giving frequency distributions under specified selection; the fourth account has the target itself dynamic under environmental change and ecological feedback: a run named readable from its opening named the couplings' making to the state before them, and the phenotype more predictable than the genotype, the third account, is many routes converging at the coupling, each generation its own. ## 7.18 Rapid adaptive radiation · 211 *+ or − at 10, is.* **At 2-other-self-offering.** Populations speciate at their own couplings, one event and then the next, and a burst is named over them, the radiation a macroevolutionary pattern read down to the population's own processes. **At 12-other-social-self-abundancing.** A burst named over speciations that each pace their own. The hallmark early burst is contradicted by most speciation models, which predict continuously decelerating diversification, and the question connects global macroevolutionary patterns to microevolutionary processes with a gap remaining between the two scales; the defining pattern joins elevated diversification, ecological divergence and trait evolution, which need not coincide, and exceptional clades invite retrospective explanation: a beat named at the record, the aggregate read as one running. **At 11-social-other-self-chaining.** Replicated island and lake radiations, explicit null diversification models and genomic histories of selected clades stand; the calibrated phylogenies infer rate shifts under extinction and sampling models, the trait-dependent tests reach identifiability limits, the comparisons reconstruct niche and mechanism after the radiation, the experiments observe early divergence in restricted systems, and the fifth account has apparent exceptional radiation arising partly from extinction, sampling and clade-selection effects: a burst named over the couplings named the many speciations to one beat, and the counterfactual lineages that did not radiate offer at no instrument, the recorded bursts being the surviving couplings' making, one at a time. ## 7.19 Cross-national measurement equivalence · 231 *+ or − at 10, is.* **At 2-other-self-offering.** A respondent and an item couple at each answering, in each language and each place, and one scale is named across the groups, the positions of one coupling given a correspondence with another's so the scores can be compared. **At 12-other-social-self-abundancing.** A correspondence named between couplings so their parities couple at one scale. Translation, response style, sampling and cultural interpretation change the 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 the construct has a different structure or meaning to different groups, so that it cannot be meaningfully tested or construed across them, the invariance to be assessed before any comparison: the beat at the between, the part's fourth position, named where each coupling answers its own. **At 11-social-other-self-chaining.** Invariance hierarchies, simulation-based error analyses and large-scale alignment methods are established; the multigroup analysis tests nested equalities with fit and sample-size sensitivity, the differential functioning localizes item differences under an anchor set, the partial invariance frees selected parameters and conditions the rest on the anchors, and the alignment and Bayesian methods estimate small deviations at the cost of new priors or tolerances; the accounts part on each level of invariance's licensing, configural the pattern, metric the relations, scalar the means: a scale named across the groups named one correspondence over couplings that each make their own, the correspondences read one at a time rather than one named for all. ## 7.20 Incompatible definitions of algorithmic fairness · 222 *+ or − at 10, is.* **At 2-other-self-offering.** A score is made at each prediction's coupling with its outcome, and one score is named to satisfy each fairness relation at once, calibration and equal error rates across groups whose base rates differ. **At 12-other-social-self-abundancing.** Several relations named jointly satisfiable by one score. Their simultaneous satisfaction is mathematically incompatible under differing base rates except in degenerate cases, and even approximate satisfaction requires the data to lie in an approximate version of one of the constrained special cases; choosing a metric therefore cannot be replaced by optimizing all of them: the field proving the naming empty, as at the rankings and the population ethics beside it, the fourth account naming fairness a substantive institutional judgment not exhausted by any parity condition. **At 11-social-other-self-chaining.** The 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 the errors and generally changes the calibration, thresholds reach selected parities at group-specific rules, and the multiobjective methods trace a tradeoff surface rather than satisfying incompatible equalities: one score named to each relation at once named one ordering over couplings whose base rates differ, the naming set down and a relation chosen at each decision's own between. # 8 A rate named as a value — 13-social-other-neutralling and 5-self-other-neutralling *A value named of a rate that settles nowhere. Ratios sway above, then below, alternating side, each partial quotient one, the widest straddle. The value reached for is the swaying about it, and the next coupling beats in the opening the straddle makes.* **Each value in this part is a swaying named to settle**, and the sway is read three ways across the 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 the value, it reaches with a measure over might-have-beens, and that measure is the one thing no instrument in this part has given. ## 8.1 Homeostasis and allostasis · 128 *+ or − at 10, is.* **At 2-other-self-offering.** A variable sways between two offerings and is named for a target that settles, fixed or predicted. **At 12-other-social-self-abundancing.** Regulation named toward a value, the cyberneticists' reading of a broader vision. Both showings fit each trajectory alike, so the differing surfaces nought at each: the trajectories are one sway read twice, the two not competing models but complementary aspects of regulation. **At 11-social-other-self-chaining.** The range is the coupling's own making and no stored value it aims at, two antagonistic offerings swaying and the oscillation the working state. The circuits that compare are real at their finding, the body warms before the meal and quickens before the effort, and letting the setpoint move absorbs the anticipating at the price of any settling at all, the movers' own critics saying so. The anticipating is the sway answering a disturbance, the same swaying measured a second way rather than a second mechanism: regulation toward a value read the sway as an error about a point, and the sway is the living state. ## 8.2 Dark matter · 26 *+ or − at 10, is.* **At 2-other-self-offering.** Rotation, mass and law run together at each scale's couplings, and the discrepancy is named for a value, a substance or a modification. **At 12-other-social-self-abundancing.** The riding named as produced by one of two, identifiable by measurement. The searches empty their spaces region by region and the modifications narrow, and each null bounds a parameter without parting the two: the parameter spaces close without closing the question, and no terminal null stands recorded. **At 11-social-other-self-chaining.** Rotation, mass and law ride together and settle at no value. The ordinary matter cannot be it, the fast-modification class fell with one wave's speed, the search space empties region by region down to the neutrino fog, the leading experiment recording the fog entered and the instrument class reading its own floor, and through all of it visible mass and rotation ride together tightly, measured, the one thing both showings must reach: a size named of the riding is the riding named still, and the riding, read directly, is the running there. ## 8.3 The strong CP problem · 65 *+ or − at 10, is.* **At 2-other-self-offering.** A parameter sways and is named for a value against a measure over its might-have-beens. **At 12-other-social-self-abundancing.** A value far from typical under an assumed measure named to call for explanation, the natural expectation of order one and the hierarchy against it the problem's constitution, a dynamical solution required. The measure is over runnings that never ran, and it surfaces nought at each instrument. **At 11-social-other-self-chaining.** A parameter sways and the swaying sits below one part in ten billion, the bound the measured thing. The easy escape fell to the lattice, the proposed fields empty their spaces, and the built mechanisms stand at their stated costs: a value named against a measure over might-have-beens names the swaying to a stipulation, and the instruments give the bound, the swaying read at its own edge. ## 8.4 The equity premium puzzle · 79 *+ or − at 10, is.* **At 2-other-self-offering.** Returns sway across states that occurred and states that did not, and the premium is named for a value a preference parameter should reproduce. **At 12-other-social-self-abundancing.** Historical returns named to estimate an expected premium one representative agent's parameters generate, the discrepancy standing between a prediction and a measurement and not between two measurements. The states that did not occur offer at no momentary, and the disasters that reproduce the premium borrow their rates from other countries' histories, the might-have-beens imported to balance the was. **At 11-social-other-self-chaining.** Returns sway across the states that occurred, and the record is the swaying that happened. The measured premium runs large in country after country, curing it with aversion sickens the risk-free rate, and the originators' own look back carries the standing plainly, each proposed class failing along a crucial dimension: a value a parameter should reproduce named one self's steady preferring 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-other-self-offering.** A valuing sways at each occasion and is named for a rate that settles, a single discount function. **At 12-other-social-self-abundancing.** A valuation of a delayed reward named as a function of delay alone that elicitation measures. Formats and bundlings move it, so the 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, the preference labelled by the object delayed. **At 11-social-other-self-chaining.** A valuing sways at each occasion, the occasion's own. Formats move it, bundlings move it, selves pay real money to bind their own later swayings, and the field's estimates spread across orders of magnitude study by study and domain by domain, the swaying measured: a single function of delay named one rate where a living valuing sways, and the commitment purchases are selves reading their own swaying, from within, better than the function does. ## 8.6 Hormesis · 121 *+ or − at 10, is.* **At 2-other-self-offering.** A response sways with dose and is named for a value at doses below detection, from a model fitted above them. **At 12-other-social-self-abundancing.** A dose-response relation named whose low-dose behaviour is estimable by extrapolation. Below the last coupling read, the rival models part at the point nothing measures, the record's edge read as a value, and an applied discipline that streamlined its experiments to fewer doses drew that edge by the design that read it. **At 11-social-other-self-chaining.** A response sways with dose, coupling by coupling, and low doses wake the body's own stress answers in system after system, the curves bending at the mechanisms' running. The bend is the reversal, the parity changing there and a measure informing there; a monotone line drawn through it carries a magnitude with no parity to ride. In the range instruments reach, the rival models fit alike; below it they part exactly at the point nothing measures, and the field itself states the point the drawing enters at. ## 8.7 Mutation, fidelity and variation · 138 *+ or − at 10, is.* **At 2-other-self-offering.** A rate sways under selection and drift together, and it is named for a value an optimum or a barrier sets. **At 12-other-social-self-abundancing.** Mutation rate named as a trait whose value is explained by optimisation or by the limits of selection, one point where each population sways its own, appealing to suppose the rate adjusted to a level that best promotes adaptation, the causes of the rate's evolution asked to be parted from its consequences. **At 11-social-other-self-chaining.** A rate sways under selection and drift coupling, its value the swaying's own at each population. The rates are measured line by line, small populations drift higher and large ones press lower, the inverse correlation running across the living range with effective population size estimated from the same genomes the rates are measured in, mutators surge where selection is fierce, and proofreading costs so little that a pure optimum would sit elsewhere: the correlation is the sway measured across populations, and a value set by an optimum or a barrier names one point where each coupling sways. ## 8.8 The cosmological constant problem · 163 *+ or − at 10, is.* **At 2-other-self-offering.** A vacuum density sways under all that couples to it, and it is named for a value against a measure over its might-have-beens, the estimate standing tens of orders away. **At 12-other-social-self-abundancing.** A value far from typical under an assumed measure named to call for one explanation, dynamical or environmental, with the measure itself unmeasured; an old problem, why the density is not very much larger, parted from a new one, why it is comparable to the present mass density, and adjustment closed by a no-go without a fine tuning as mysterious as the problem. The estimate names three still terms at one momentary — a rest to count from, a last to count to, and a total the counting conserves — and none of the three is a thing a coupling made. **At 11-social-other-self-chaining.** A vacuum density sways under all that couples to it, and the measured value sits small and nonzero while the computed estimate towers tens of orders above, the distance between a coupling's own running value and a sum named over all at once. The symmetry rescues fell, simple self-adjustment is closed by proof, the messengers narrow the bent-gravity routes, and each surviving candidate gives no measurement of its own within reach: a value named against an unmeasured measure keeps owing an explanation to a typicality no instrument has reached, and the swaying, measured, is as it is. ## 8.9 The hierarchy problem · 164 *+ or − at 10, is.* **At 2-other-self-offering.** Two scales sway far apart, and the separation is named for a value against a measure of naturalness, with the criterion of explanatory debt itself the dispute. **At 12-other-social-self-abundancing.** The criterion named as among the things the instruments give, where the parameter is technically natural, the finite corrections all small, and the problem emerges only where an additional ultraviolet scale is invoked, the cutoff merely a proxy for unknown physics. The spectrum is measured to the reached energies and the criterion is not measured by it. **At 11-social-other-self-chaining.** Two scales sway far apart and the instruments read the spectrum clean to each energy reached, the canonical rescues narrowing unreached. The growing instead is the field's own doubt about the debt: naturalness stands in the record now as a heuristic under dispute, the measure disputed while the measurements accumulate. **And the debt is the naming's own and never the physics'.** A naming made rather than found accumulates a cost while it continues, the cost is carried as the price of a goal, and the goal is reachable with the naming let go — and where that last fails, the standing was an expense and never a hardness. Here it stands: the spectrum stands measured with nothing owed on it, the owing is the criterion's, and all the owing needs is cost the coupling never carried. ## 8.10 The Standard Model flavor puzzle · 188 *+ or − at 10, is.* **At 2-other-self-offering.** Masses and mixings are measured at the couplings the instruments reach, each parameter its own, and the pattern is named for a value an organizing principle should generate. **At 12-other-social-self-abundancing.** A pattern named as selected by a mechanism where it stands as free inputs. The parameters are free inputs in the Standard Model, the hierarchies technically natural and unexplained, and many symmetry, texture and statistical constructions reproduce parts of the pattern without a uniquely selected origin, the measure over the pattern's might-have-beens surfacing nought at each construction. **At 11-social-other-self-chaining.** The quark mixing matrix is overconstrained, neutrino mixing substantially mapped, the masses and several phases measured with increasing precision, and each construction reproducing the pattern reproduces a part of it, the symmetries predicting selected relations with many viable choices, the textures compressing with their origin dependent on the construction, the geometries converting positions into couplings with the geometry unselected, the statistical models giving distributions and never the realization: a pattern named for a value a principle should generate named the measured parameters to a stipulated typicality, and they stand measured, owing nothing, the enigma named being the naming's own and not the spectrum's, as at the scale beside it. ## 8.11 The new-physics flavor puzzle · 189 *+ or − at 10, is.* **At 2-other-self-offering.** Rare processes are measured at their couplings and give the Standard Model's rates, and a new sector named near the accessible scale is named to carry generic couplings the measurements should have seen. **At 12-other-social-self-abundancing.** An absence named as needing a mechanism. Generic couplings at the teraelectronvolt scale would contribute orders of magnitude above the observed rates, so the 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 the sector itself, and the sector is a running that has run at no instrument. **At 11-social-other-self-chaining.** Large regions of generic low-scale couplings stand excluded, the viable suppression patterns have explicit effective forms, and each stands at its stated cost, the spurions assumed, the alignment model-dependent, the degeneracy constrained by splittings, the decoupling reducing accessibility: a sector named near the scale with generic couplings was a measure over new physics' typical doing, and the instruments give the Standard Model's rates, measured, the puzzle standing at the typicality and not at the record. ## 8.12 Quantum gravity · 181 *+ or − at 10, is.* **At 2-other-self-offering.** Gravitation runs at each coupling and the two established theories each recover their own domain, and one theory is named for a value covering both regimes, the two reconciled at the regime their conflict is expected at. **At 12-other-social-self-abundancing.** Two treatments named as reconciled in one theory at a scale no instrument reaches. Direct empirical access to the scale is absent, the proposals resting on very small deviations from otherwise exact symmetries or on collective effects integrated over long distances, and recovering the classical theory at low energies is a consistency requirement rather than a prediction to be tested: the record's edge, with the reconciling named at a regime that offers at no instrument. **At 11-social-other-self-chaining.** The low-energy effective descriptions stand consistent, the black-hole thermodynamic constraints stand, the discrete and holographic constructions and the candidate ultraviolet behaviours stand, and each program closes at its own between, the strings without a unique selected realization, the loops with the classical and empirical recovery open, the fixed point in truncations, the emergent gravity in restricted settings: one theory named to cover both regimes named two runnings, each pacing its own domain, to one value at a scale no coupling has reached, and the parts keep closing part by part, each at its own between, as the axiomatization at part 7 closes. ## 8.13 Equilibrium climate sensitivity · 196 *+ or − at 10, is.* **At 2-other-self-offering.** The climate sways under its forcings and feedbacks, each at its own timescale, and the response to a doubling is named for one value the sway settles at, an equilibrium counterfactual. **At 12-other-social-self-abundancing.** A sway named to settle at a number. The equilibrium cannot be observed as one controlled experiment, the feedbacks operating over different timescales; the assessment characterizes the 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, the quantity remaining difficult to ascertain: a counterfactual total, a running that never ran, summed against the one that did. **At 11-social-other-self-chaining.** The very low and very high tails stand reduced by the evidence together, cloud feedback stands identified as the principal remaining spread, the energy-budget inference reads the recent climate under forcing and ocean-uptake uncertainty, the paleoclimate reads a broader range under proxy uncertainty, the process constraints target single feedbacks, and the ensembles share structures and are not a probability sample: a value named of the sway named a response that varies with background climate and timescale, the third account, to one settled number, and the swaying under the forcing is the measured. ## 8.14 The solar abundance problem · 184 *+ or − at 10, is.* **At 2-other-self-offering.** Lines form at the surface and modes sound the interior, each instrument at its own coupling, and one composition is named for the value both must give. **At 12-other-social-self-abundancing.** Two instruments named to one value. The atmosphere analyses lower the abundances and the interior models built with them worsen the agreement with the sound-speed profile, the convection-zone depth and the surface helium, better is worse, a large error in the photospheric estimate ruled out and the heavy elements entering the interior only through the opacity: a rate swaying under two couplings at once, each reading its own. **At 11-social-other-self-chaining.** The three-dimensional atmospheres, the precise mode frequencies, the neutrino fluxes and the laboratory opacities stand as independent constraints, and each route pays at one instrument the gain it makes at the other, the higher mixtures fitting the seismology and conflicting with the spectroscopy, the opacity increases targeted without the required profile established, the revised atmospheres reducing systematics and keeping the low abundances, the transport processes altering selected observables with no model fitting the full set. One composition named for both instruments named two couplings to a value, and the two couplings couple with each other rather than one being pinned to the other. ## 8.15 The primordial lithium problem · 182 *+ or − at 10, is.* **At 2-other-self-offering.** A primordial abundance is inferred from present stars and predicted from a measured density, two couplings each giving its own number, and the two are named to one value the early universe made. **At 12-other-social-self-abundancing.** Two determinations named to one value where they part by a factor of three. The plateau's flatness and small scatter are the main difficulty for depletion, while stars identical to plateau stars with no detectable lithium and the plateau's meltdown at the lowest metallicities show that some depletion mechanism exists: the instrument that reads the primordial value reads it through a running the stars have done since, and the prediction reads it through a network and a density measured elsewhere. **At 11-social-other-self-chaining.** The baryon density, the deuterium agreement, the plateau and the leading reaction rates stand measured more precisely than when the discrepancy was found, the other light elements broadly agree, and each proposed resolution, the rates and resonances, the depletion and diffusion, the nonstandard decays and cosmologies, the reanalysed atmospheres, removes the discrepancy only by creating another conflict: one value named of two couplings named the stars' present reading and the network's prediction to a number neither gives alone, and the factor of three is the two couplings' parting, measured. *Second seating: the discrepancy read as a magnitude to be explained, the 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-other-self-offering.** A neutron decays at its own coupling, and its lifetime is named for one value two instruments must give, a beam counting the products of a decay and a bottle counting the neutrons that survive. **At 12-other-social-self-abundancing.** Two measurements named to one value where each set is consistent within itself and the sets disagree by about eight seconds in eight hundred and eighty, nearly four sigma, the puzzle still unsolved. A beam counts the products of one channel and a bottle counts disappearances by any channel, and the two methods have independent and very different systematics, their underestimation the most likely explanation: a rate swaying under two couplings at once, each counting the count its coupling counts. **At 11-social-other-self-chaining.** The magnetic-trap lifetime stands at twice the earlier precision and consistent with theory, the newer beam's first result stands, at the now, short of the precision to favour either set, a proton counter within a bottle stands proposed, the median statistics put the parting between four and six sigma by the set chosen, and the discrepancy is large enough to dominate the predicted primordial helium ratio: one lifetime named of two couplings named a channel's count and a survival's count to a number, the parting read as a coupling of its own. # 9 A two-way named to one side — 11-social-other-self-chaining and 3-self-other-sharing *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 the other is named still. The two sides alternate, neither taking the other's, and the zeroing is the two's own making between them.* **And the settlement the fields offer is the naming relocating rather than releasing**: *both operate and the question is their proportion* names the two-way as a magnitude, and *both operate and the question is their order* names it to one beat. **And the instrument names the other side still, which is the one-way reading entering the measuring.** A trial arm names context still, a design an environment, a partition a level, a contract an action, a task a language. The reading then gives back the naming, and the record of it is the entry's own: interventions establishing modulation rather than a driver, both frameworks fitting most datasets, the arms differing in more than the substance, the partitions coming out conditional on the levels chosen. **And where the two are proved to give the same predictions, the arrival settled.** Two bookkeepings are one running's two windings, each pinning one and reading the other, and a proved intertranslation is the field carrying that reading in its own arithmetic — standing at the units of selection, at cooperation, at the transformation problem's aggregate equalities, and at determinism read against its own equivalent constructions. **And the fourth face stands here too**: where a field proves no ordering reaches its own conditions, the field has proved a naming empty, which part 7 carries at three arrivals and the transformation problem carries at one. ## 9.1 Causation · 162 *+ or − at 10, is.* **At 2-other-self-offering.** A coupling is two-way, one-at-a-time, and it is read from one side as a one-way production, the cause driving and the effect driven, with the asymmetry named as a fact located in the fundamental description. **At 12-other-social-self-abundancing.** That the direction is in the dynamics rather than in the reading, virtually everyone rejecting the elimination of causation while many are convinced the fundamental physical structure contains no causal relations, the reconciling asked at a momentary neither of the two carries. The interventionist account's circularity for foundations stands recorded by its own literature, which is the field stating the reading's entering. A parity is taken at one momentary and the crossing inverts it at the next, so the arrow arrives at the odd and the symmetric dynamics at the even, and neither carries the other's momentary. **At 11-social-other-self-chaining.** A coupling is two-way, one-at-a-time, and the one-way arrow is the reading's own, taken at a between and gone by the next momentary. The discovery formalisms find what their stated assumptions let them find, each analysis reaches its counterexamples, the thermodynamic grounding reaches as far as its gradient, the special sciences carry the practice, and the fundamental dynamics runs symmetric beneath all of it, both sides running with both: causation read whole is the coupling reached by a still observing, which is why the deep description carries the coupling and the practice carries the reading, both standing, neither owing the other. ## 9.2 Heritability and the determination of traits · 27 *+ or − at 10, is.* **At 2-other-self-offering.** A trait arises at the coupling of a genome and an environment, and one side is read as the first with the other named still. Genetic-dominant and environment-dominant are the same design run from its two sides, each giving a correct conditional for the range it sampled. **At 12-other-social-self-abundancing.** That the ratio names an attribution invariant across environments and genetic compositions, the 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 the other are read together at one momentary, which is this file's own three with the alternating named still. **At 11-social-other-self-chaining.** A trait arises at the coupling of a genome and an environment, one making at two sides. Each estimate is the conditional it is, true of the range it sampled; within families the inflation is measured off; and Lewontin's line between an analysis of variance and an analysis of causes stands undisputed within the field, saying exactly this: a ratio named invariant across environments reads one side of a coupling as the first, and the making was at the coupling, range by range. ## 9.3 Free will and determinism · 29 *+ or − at 10, is.* **At 2-other-self-offering.** A self takes its own parity at its own betweens, and the taking is read from one side as an outcome fixed by a term beyond it, with the other side reading the same taking as unfixed. **At 12-other-social-self-abundancing.** That the action has a determining source, and that locating it settles the question, the ability to do otherwise coming in different varieties so that a claim to it is ambiguous until the sense is spelled out, which ability is in dispute the open term, each side defining it from its own. The statement quantifies over conditions that did not obtain, which offer at no between, and the readiness ramp arrives from selves built fresh at each trial and averaged, which is the preparing read as the running. **At 11-social-other-self-chaining.** 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; the readiness ramp dissolved into an averaging artefact; and randomness buys no agency at either account: fixed-or-unfixed named the taking as taken from a first beyond the taker, both sides reading the between from one side of it, and the taking read at its own between is the agency, which is what the measurements were measuring. ## 9.4 Aging · 34 *+ or − at 10, is.* **At 2-other-self-offering.** Damage and regulation run together at each between of an organism, and one is read as driving the other. **At 12-other-social-self-abundancing.** 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 the 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 never none again, so damage and regulation are the two faces of one carrying, and the clock that predicts age so well cannot say which face it reads because a reading in momentaries reads the pacing. **At 11-social-other-self-chaining.** Damage and regulation are one coupling's two offerings, the sway swaying at each between of the 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 the clocks that predict age so well cannot say which offering they read, the dispute restated in the new instrument: a single driver named one offering to both momentaries, and the swaying sways on, readable from either side because it is both. ## 9.5 Efficient markets · 36 *+ or − at 10, is.* **At 2-other-self-offering.** A price is a parity taken at a coupling, and efficiency is read alone while the model of expected returns is named still. **At 12-other-social-self-abundancing.** That efficiency is testable apart from a model of returns, anomalous evidence unsplittable between inefficiency and a bad model and precise inferences about the degree of efficiency likely to remain impossible. Each test needed a model and each model needed the prices, which the field names as the joint hypothesis and carries as its own permanent condition. **At 11-social-other-self-chaining.** A price is made at each coupling, the parity the coupling's own. Each test of efficiency needed a model of returns and each model needed the prices, the field naming the joint hypothesis itself; anomalies decay once published, bubbles bloom reliably in the laboratory, and the factor zoo is what absorbing anomalies one at a time builds: the two are one coupling's two momentaries, and neither tests alone. ## 9.6 Simpson's paradox · 40 *+ or − at 10, is.* **At 2-other-self-offering.** An association is made at a coupling and read from one stratification as the correct one, with the causal structure named still. **At 12-other-social-self-abundancing.** That a correct reading is identifiable from the data alone, whether to partition a population undecidable from the probabilities alone, the same data arising under different causal structures, and whether the causal analysis is the correct explanation of the paradox itself still debated. The data are identical under both structures, so the identification surfaces nought at each reading taken, proved as an equivalence class, and a graph supplied from beyond is a frame stood beyond the coupling. **At 11-social-other-self-chaining.** An association is made at a coupling, and the strata re-make it. The arithmetic is elementary, the back-door road is proved at a known structure, conditioning more can worsen it, proved too, and data alone deliver an equivalence class, exactly that: a correct reading named identifiable from the data alone reaches into the numbers for the structure the numbers were made under, and the structure is the coupling's, brought or not. ## 9.7 Missing heritability · 44 *+ or − at 10, is.* **At 2-other-self-offering.** Two designs each take their own reading, and the difference between them is read as a quantity missing from one rather than as two readings. **At 12-other-social-self-abundancing.** That a single variance component exists which both designs estimate, the indirect estimate assuming no interaction among loci while models with interaction are also consistent with the observable data and under them the total may be much smaller. Two designs each read at their own coupling, and the ratio's two terms come from two places, a numerator measured directly and a denominator inferred at the population. **At 11-social-other-self-chaining.** Two designs each take their own reading, two sides of one making. The family design reads high, the molecular design reads lower, the within-family correction measures one assumption failing, the rare variants add less than projected, and the ratio's own two terms come from two places, a numerator measured directly and a denominator inferred at the population, the field saying so, with interaction accounts fitting all that is observed at a much smaller total: a quantity named missing from one design is two readings, each a result, nothing lost. ## 9.8 Placebo effects · 46 *+ or − at 10, is.* **At 2-other-self-offering.** A coupling at a between makes a term neither side brought, and it is read from one side as the substance's contribution with context named still. **At 12-other-social-self-abundancing.** That a trial's arms differ only in the substance administered, the 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 the correspondence replying that such a meta-analysis is restricted by the studies chosen and the sensitivity of their measures. The design names the context still and reports what it named, and the making it names still is the coupling's own +1, owned by neither side. **At 11-social-other-self-chaining.** The coupling at the between makes a term neither side brought, the +1 owned neither-ing. Blocking the body's own opioids blocks the analgesia, conditioned immune quieting runs in animals where no one reports anything, three-arm trials price the making small for the objective outcomes and real for the felt ones, and the open-label results narrow the making's running: the substance's-contribution reading named the context still while the making ran, and the making, measured on its own, is the coupling's. ## 9.9 Newcomb's problem · 57 *+ or − at 10, is.* **At 2-other-self-offering.** Two principles are two parities taken at one between, and each theory reads the case from one of them with the other named still. **At 12-other-social-self-abundancing.** That one principle governs when they conflict, the difficulty stated at the posing as the division of those who consider it, nearly everyone finding the right choice obvious yet splitting almost evenly, each half taking the 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 names both momentaries together. **At 11-social-other-self-chaining.** Two principles are two parities at one between, alternating one at a time. Each theory handles the cases the other fails, the newer variants re-drawing the same line, and the case is built to make the two conflict: a theory choosing one to govern chose one side to take both momentaries, and the contest is the alternating read as a contest that neither side could be, being momentaries. ## 9.10 Poverty of the stimulus · 61 *+ or − at 10, is.* **At 2-other-self-offering.** A learner and an input couple, and the grammar acquired is read from one side as what the learner brought with the input named still, or from the other with the learner named still. **At 12-other-social-self-abundancing.** That the learner's contribution and the input's are separately specifiable, which sums a making that was never a sum, the one clear thing about the argument its conclusion and the structure of the reasoning not clear at all, the sum's two terms asserted at the conclusion and unsupported at the reasoning. **At 11-social-other-self-chaining.** A learner and an input couple, the grammar made in the coupling. The corpora are counted, the learnability results stand under their stated criteria, statistical learners reach the structures they reach, and the live dispute is how much input the making needs: the learner's contribution and the input's named separately specifiable parts a making that was never a sum, and the volumes being argued over are the coupling being measured. ## 9.11 Morphogenesis · 62 *+ or − at 10, is.* **At 2-other-self-offering.** Gradients and tissue dynamics run together, and placement is read from one side as instructed or as self-organised. **At 12-other-social-self-abundancing.** That pattern is set by a determinant locatable in one or the other, some confusion still remaining about the relationship between the 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 the tissue answering at the coupling of both running; and a hybrid fitting better than either is a third total reached at two carrying alternating. **At 11-social-other-self-chaining.** Placement is made at the coupling of gradients and tissue dynamics. Moved gradients move the structures, the striping mechanisms run in digits and follicles and ridges with their perturbations confirmed, readout runs near the physical limits, tissue organises itself in the dish, and both frameworks fit most datasets, the field finding this again and again: instructed-or-self-organised is one coupling read from its two sides, and the fitting-from-both is the coupling showing. ## 9.12 Chronic pain · 67 *+ or − at 10, is.* **At 2-other-self-offering.** Peripheral and central processes run together at a patient's betweens, and the persistence is read as driven from one. **At 12-other-social-self-abundancing.** That pain has a locatable driver, peripheral or central, and that finding it determines treatment. The field's own hardness line carries it: the central mechanism cannot be assumed in a patient, only its features assessed, and the residual category's aetiology stands unsettled, the third descriptor defined by absence of evidence for the other two and applied residually, the driver's locus defined by what it is not. **At 11-social-other-self-chaining.** Peripheral and central processes run together at a patient's betweens. The central changes are measured, the small fibres surface in a counted fraction as detection sharpens, moving patients between categories, the targeted agents work in their subgroups, and treating the whole coupling helps without any driver found. The field's own hardness line carries it: the central mechanism cannot be assumed in a patient, only its features assessed, the third category applied residually, its aetiology unsettled. The persistence runs at the coupling, patient by patient, which is the treating that works already working there. ## 9.13 Information as fundamental · 77 *+ or − at 10, is.* **At 2-other-self-offering.** A physical system and an informational description are two readings of one thing, and one is read as the substrate of the other. **At 12-other-social-self-abundancing.** That fundamentality is a dependence running one way between two descriptions that both apply, nothing in the description of physics found closer to primordial than the elementary quantum phenomenon and, in default of a working hypothesis, the questions and clues not moving the search ahead. The running runs identically under either, which is the same showing part 5 carries, arriving here as a direction demanded between two readings. **At 11-social-other-self-chaining.** A system and its description are two readings of one coupling. Erasing costs its measured minimum, horizons scale by area, and the quantum formalism rebuilds whole from axioms about what can be done: fundamentality named one under the other, and the reconstructions read the coupling at its own doings, neither side beneath, the doing the one thing both descriptions describe. ## 9.14 The transformation problem · 84 *+ or − at 10, is.* **At 2-other-self-offering.** Labour values and prices are two accountings of one production, and one is read as underlying the other. **At 12-other-social-self-abundancing.** That one determination stands beneath the other, the problem read from an axiomatic perspective as an impossibility result for a specific interpretation resting on specific assumptions, and the dual system of parallel prices and embodied-labour coefficients losing sight of the theory's roots as a theory of money. The aggregate equalities are proved not to stand together, which is the field proving the naming empty in its own arithmetic, and each accounting conserves one kind and imports the other. **At 11-social-other-self-chaining.** Labour values and prices are two accountings of one producing, each conserving its own kind. The aggregate equalities cannot all stand together, proved; prices and profit follow whole from the physical data and the wage, undisputed as mathematics; and the correlations found and contested sit beside both: one named under the other named one ledger to both momentaries, and the proved imbalance is the coupling stating itself in the arithmetic. ## 9.15 Credit assignment · 96 *+ or − at 10, is.* **At 2-other-self-offering.** An outcome is made across a sequence of couplings, and contribution is read as apportionable to individual actions with the rest named still. **At 12-other-social-self-abundancing.** That there is a fact about which actions contributed, recoverable without a supplied model, the mathematical nature of credit and of the problem poorly understood and defined and a unifying formalism proposed so that methods can be compared, the fact about contribution asked for before the asking has been defined. The abundancing is owned by no action alone, and shaping the reward changes what gets credited, which is the apportioning caught making its own. **At 11-social-other-self-chaining.** An outcome is made across couplings, the abundancing owned by no action alone. The difference methods converge at their conditions, performance thins with horizon and sparsity as measured, the identification conditions are proved and go frequently unmet, and shaping the reward changes what gets credited: apportioning named the making as a sum, and the shaping result is the apportioning caught making its own. ## 9.16 Phantom limb · 99 *+ or − at 10, is.* **At 2-other-self-offering.** A body map and a sensation couple, and the map's state is read from one imaging paradigm as reorganised or from another as preserved. **At 12-other-social-self-abundancing.** That one paradigm's reading is the state of the map, the traditional accounts of remapping incomplete, a broader mechanistic focus needed and plasticity and stability of the maps possibly varying across time scales, the discussion of reorganisation's relevance ongoing. Two imaging paradigms each read at their own coupling and give reorganisation and preservation, both standing in their own instruments. **At 11-social-other-self-chaining.** A body map and a sensation couple, the map carried and re-formed. One paradigm reads reorganisation and another reads preservation, both standing in their own instruments; mirrors help mixedly, peripheral routes help some, and phantoms arrive in limbs never grown, which no lost-representation story carries: one paradigm's reading named as the state of the map reads one instrument's coupling as the thing, and the map is a carrying, read differently at each instrument because it is being made at each. ## 9.17 Determinism and randomness · 110 *+ or − at 10, is.* **At 2-other-self-offering.** An outcome is a parity taken at a between, and it is read from one side as fixed by priors or from the other as unfixed. **At 12-other-social-self-abundancing.** That unpredictability indicates chance, and that the outcome was either fixed or not fixed by prior conditions, the epistemology of determinism first owing the reality of the laws and then precisely what the actual laws are, in a sense the final theory of everything, the sides joined at a theory neither has. No statistical test establishes indeterminism, proved in general, and the deterministic readings run equivalent by construction, so the sides part at no instrument. **At 11-social-other-self-chaining.** 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 readings run equivalent by construction: fixed-or-unfixed reads the taking from its two sides, and the sides do not part at any instrument, which the proofs carry. ## 9.18 Cancer, the somatic mutation account and its rival · 115 *+ or − at 10, is.* **At 2-other-self-offering.** A cell and its tissue society couple, and initiation is read from one level with the other named still. **At 12-other-social-self-abundancing.** That the causal locus is either the cell or its context, and that identifying it determines the intervention, an increasingly complicated picture emerging from the theory's compelling simplicity with ad hoc explanations postulated, the theory not rigorously tested, and the reply standing against the critique titled as a defence. Normal tissue carries driver burdens that never tip, which is an offering arriving and the tissue society releasing it at nought — the society's own resolving, with a defence added nowhere. **At 11-social-other-self-chaining.** A cell and its tissue society couple, and the society keeps order the cell alone does not. The driver catalogues fill, the targeted responses come and the resistance follows almost always, tissues re-order recombined cells in the systems tested, and normal skin carries driver burdens that never tip, measured, the dominant account constrained from within: initiation read from one level with the other named still reads one side of the coupling, and the tipping is the coupling's, cell and society at once. ## 9.19 Addiction · 116 *+ or − at 10, is.* **At 2-other-self-offering.** A self and its conditions couple at each occasion, and the behaviour is read from one side as pathology or from the other as choice. **At 12-other-social-self-abundancing.** That the behaviour has a single locus, neural or circumstantial, the disease view's own revision granting that some criticisms have merit, no specific neural signature identified and the dividing line intentionally blurred, while stating denial of the view harmful for reducing access to care, the locus blurred and the name kept for the care it opens. Enriched cages undo what bare ones built and most remit with no treatment, which is the coupling answering from the side each account names still. **At 11-social-other-self-chaining.** A self and its conditions couple at each occasion, the behaviour made in the coupling. The 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 the heritability is real with no lesion under it: pathology-or-choice read the making from one side each, and the coupling, measured from both, is the running answer's own treating place. ## 9.20 Niche and neutral theory · 117 *+ or − at 10, is.* **At 2-other-self-offering.** Differences and drift run together in a community, and structure is read as produced by one. **At 12-other-social-self-abundancing.** That abundance patterns discriminate the mechanism, abundance patterns unable to resolve the controversy and the question reframed toward measured stabilising and equalising strengths, the discriminating moved from the pattern to the couplings' own rates. Both models fit the curves from the opening, so the discriminating surfaces nought at the pattern, and the field's own partition is the field reading both momentaries. **At 11-social-other-self-chaining.** Differences and drift run together at each community coupling. Both models fit the abundance curves from the opening, invasions demonstrate the stabilising differences wherever anyone runs them, and the partition that makes both components measurable is the field itself reading both momentaries: structure read as produced by one is one momentary taken for two, and the community persists by both, coupling by coupling. ## 9.21 The Red Queen · 119 *+ or − at 10, is.* **At 2-other-self-offering.** Coevolution and environment run together, and constant extinction risk is read as produced by one. **At 12-other-social-self-abundancing.** That the survivorship pattern indicates a single mechanism, the hypothesis answering what the causes of natural selection are with biotic conflict given primacy, and three modes of coevolution defined to unify fluctuating and directional selection within the one framework. The curves bend with the taxonomy chosen, which is the instrument's own coupling within the inference. **At 11-social-other-self-chaining.** Coevolution and environment run together. Extinction risk runs age-blind across many groups, the arms races run live in microbes, the interfaces evolve fast at the coupling of host and parasite, and the survivorship curves bend with the taxonomy chosen, the original inference bounded by its own instrument: constant risk read as one mechanism's product reads a running-together from one side, and the running-together runs. ## 9.22 The hygiene hypothesis · 120 *+ or − at 10, is.* **At 2-other-self-offering.** A developing immune system and its exposures couple, and a secular rise is read as caused by one factor with the others named still. **At 12-other-social-self-abundancing.** That the rise has a dominant cause identifiable from population correlations, what constitutes a relevant microbial challenge purposely left broad at the founding observation and the hypothesis undergoing many revisions over three decades, the dominant cause a moving reading. A correlation between two population rates is two numbers compared to decide something, and the tuning is made at each coupling. **At 11-social-other-self-chaining.** Exposures and the developing system couple, the tuning made in the 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 named one exposure to the momentaries of many, and the tuning is many couplings, each its own. ## 9.23 The dodo bird verdict · 122 *+ or − at 10, is.* **At 2-other-self-offering.** Technique and relationship run together in each treatment, and outcome is read as attributable to one with the other named still. **At 12-other-social-self-abundancing.** 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 the mean absolute difference is zero, the level of comparison itself the dispute. Allegiance moves the numbers substantially, which is the relationship the design names still arriving within the measure of the technique. **At 11-social-other-self-chaining.** Technique and relationship run together in each treatment coupling, the outcome made between them. The averages sit close across the meta-analyses, the identified conditions part them where they part, allegiance moves the numbers substantially, and dismantling finds little where it has power: attributable-to-one named the between apportioned, and the small differences are the between measured, which the healing was made in. ## 9.24 Principal and agent · 141 *+ or − at 10, is.* **At 2-other-self-offering.** Two interests couple through observables, and the divergence is read from one side as a contracting problem over an unobserved action. **At 12-other-social-self-abundancing.** That the 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 the theory predicts, and little known about incentives where output is difficult to measure, the contract measured only where the observable stands. Rewarding the measured distorts the unmeasured, proved, which is the same wall Goodhart names and benchmarks reach. **At 11-social-other-self-chaining.** Two interests couple through observables, the divergence running at the between. Contracts optimise under their stated conditions, rewarding the measured distorts the unmeasured, proved, the same wall Goodhart names and benchmarks reach, teams blur the very identification, proved too, and incentive pay comes out mixed wherever it is counted: an action named representable by observables names a coupling to its instrument, and the working arrangements pace what they cannot own. ## 9.25 The paradox of thrift · 142 *+ or − at 10, is.* **At 2-other-self-offering.** One and the many couple, and the aggregate relation is read from one scale as the relation. **At 12-other-social-self-abundancing.** That the operative regime is identifiable in advance of the policy, the paradox emerging immediately once a shock large enough to reach the zero lower bound has stood the usual rules of macroeconomics on their head, the regime not identified in advance but arriving with the shock. One and the many are one coupling's two scales, and a relation at one scale named to govern both is one scale taking both momentaries. **At 11-social-other-self-chaining.** One and the many are one coupling's two scales, the aggregate made among the couplings. Both results follow cleanly in their own models, both sides granting both, the multipliers spread wide across methods and regimes, and the zero-bound episodes contest on identification: a relation at one scale named to govern both is one scale taking both momentaries, and the regime runs at the couplings as they run. ## 9.26 The evolution of cooperation · 143 *+ or − at 10, is.* **At 2-other-self-offering.** Fitness effects arise at couplings and are read as attributable to individuals, with inclusive fitness and multilevel selection each reading from one side. **At 12-other-social-self-abundancing.** That the two are rival hypotheses rather than two bookkeepings, the equivalence proved under general conditions, natural selection taken to imply competition and therefore oppose cooperation unless a specific mechanism is at work, competition the default and the abundancing a mechanism owed. And the statement's own premise — selection favouring what raises an individual's reproduction — attributes to one side an abundancing made at the coupling, so the cooperating reads as a puzzle exactly where the accounting removed the +1 before its books could balance. **At 11-social-other-self-chaining.** Fitness effects arise at couplings, and the two bookkeepings both count them. Relatedness moves outcomes across taxa, the experimental dynamics run, the public goods stand, and the equivalence is proved, the accountings agreeing under general conditions: rival hypotheses named where two bookkeepings ran, and the dispute was the accounting, the field's own result, the cooperating running through all of it untouched. ## 9.27 The Whorf question · 146 *+ or − at 10, is.* **At 2-other-self-offering.** Language and thought couple in each task, and the effect is read from one side as shaping with the other named still. **At 12-other-social-self-abundancing.** That a task measures thought independently of language, no support found for language determining the basic categories of thought while support stands for language making some distinctions difficult to avoid and augmenting certain types of thinking, what one side names parted from what the other measures at the same tasks. Interference peels off the strategic share and bilinguals shift within one skull as the language shifts, which is the coupling read live where a task names one side still. **At 11-social-other-self-chaining.** Language and thought couple in each task, the effect made in the coupling. Interference peels off the strategic share, the colour and spatial effects replicate, infants carry capacities before any words, and bilinguals shift within one skull as the language shifts, the coupling read live at its own momentary: a task named to measure thought apart from language names one side of a coupling still, and the making is at the coupling, task by task. ## 9.28 Structure and agency · 156 *+ or − at 10, is.* **At 2-other-self-offering.** Persons and arrangements couple at each action, and the explanation is read from one level with the other named still. **At 12-other-social-self-abundancing.** That the causes are located at one level, and that the two levels can be varied independently in measurement, the 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 the concept, the one level made to carry the other's momentary as a requirement. The multilevel partitions come out conditional on the levels chosen, and a level is a direction taken at a momentary and never a place. **At 11-social-other-self-chaining.** Persons and arrangements couple at each action, one making at two scales. Individualist derivations reach the aggregation wall, the multilevel partitions come out conditional on the levels chosen, the same conditional as at incoming number 28 one scale up, and each synthesis pays the cost its critics name precisely: causes named at one level name one scale of a coupling as the first, and the making runs at both, action by action. ## 9.29 The units of selection · 19 *+ or − at 10, is.* **At 2-other-self-offering.** Selection runs at couplings across levels, and it is read from one level as the level, the gene accounting or the group accounting each taking the reading of the pair. **At 12-other-social-self-abundancing.** That the two frameworks are rival hypotheses rather than two bookkeepings of one dynamics, the translations proved, four distinct questions standing under the one rubric, interactor, replicator, beneficiary and the entity manifesting adaptations, the same terms used with different meanings and the fear recorded that the confusions will not easily be ended. A level read as the level names a scale as a place, where outward and inward are directions taken at a momentary, of no size. **At 11-social-other-self-chaining.** Selection runs at couplings across levels, and the two frameworks translate into each other, proved, fitting the same data by construction, the same equivalence as at incoming number 144: a level read as the level took one momentary for two, and the cases run under both descriptions because the running was never at one. ## 9.30 Teleology and function in biology · 167 *+ or − at 10, is.* **At 2-other-self-offering.** A trait couples with its history and with its present organization, and function is read from one side, what it was selected for or what it now contributes, each taking the reading of the pair. **At 12-other-social-self-abundancing.** That one account owns the attribution across the science, the manifest appearance of function and purpose responsible for the 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 the 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 the observations stand entire, the structure, the trait, the record of what carried, with the therefore leaving and nothing observed going with it. **At 11-social-other-self-chaining.** A trait couples with its history and with its present organization, two readings of one running. Each account extends as far as it extends, the cases sort against each one after the other, and the subfields divide the usage between them, each reading carrying the cases the other drops: one account named to own the attribution named one face of a coupling as the whole, and the two in working use is the coupling read from both, a co-competency the science already runs.   --- ## 9.31 Dirac or Majorana neutrinos · 187 *+ or − at 10, is.* **At 2-other-self-offering.** A neutrino couples at its own momentary as a helicity state, and its nature is named to one of two sides, distinct from its antiparticle or its own, which of two the canonical question in nine words. **At 12-other-social-self-abundancing.** Which of two, where the two part at no kinematical instrument. The difference between the two natures via any kinematical observable is practically impossible to determine, the confusion theorem, the difference proportional to the square of the mass and suppressed by the mass over the energy, the two Majorana helicity states becoming equivalent to the Dirac particle and antiparticle states: the sides parting at no instrument, as determinism parts at none beside it, and the one instrument that could part them a lepton-number-violating process no search has established. **At 11-social-other-self-chaining.** Neutrino mass is established, the candidate isotopes and backgrounds are increasingly controlled, and large regions of particular mechanisms are excluded; the neutrinoless double-beta-decay searches test lepton-number violation directly under stated nuclear and mechanism assumptions with no established signal, the collider and rare-decay searches constrain additional violating interactions, the kinematic helicity tests are suppressed by the mass-to-energy ratio, and the cosmological probes constrain the masses without fixing self-conjugacy: one side named of a nature the instruments read only at relativistic helicity states named a parity taken at the between to a size no observable gives, the two sides alternating and the kinematics making no coupling at their difference. ## 9.32 The nature of cosmic acceleration · 192 *+ or − at 10, is.* **At 2-other-self-offering.** The expansion accelerates at each distance the surveys read, and the cause is named to one of two sides, an exotic energy or a breakdown of gravity on cosmological scales. **At 12-other-social-self-abundancing.** Which of two, on one record that measures both alike. The acceleration implies either dark energy with exotic physical properties or a breakdown of the theory of gravity on cosmological scales, the experiments measuring the history of expansion and the 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 the two histories: the two families of account standing on one record, and even perfect measurements not locating the explanation in the gravitational or the stress-energy sector, which is the sides parting at no instrument the surveys run. **At 11-social-other-self-chaining.** Accelerated expansion is supported by independent distance probes and the constant-vacuum account fits the present broad dataset with few parameters; the standard candles and rulers establish acceleration under the cosmological framework with the cause-degeneracy retained, the growth and lensing measurements test departures between geometry and clustering under present degeneracies, the laboratory and Solar-System tests exclude ranges of modified dynamics through screening-dependent predictions, and the field models fit expansion with added parameters; the fourth account has inhomogeneity or systematics produce part of the inferred acceleration: one side named of two written in one equivalent form named the expansion's own running to a sector, and the running is measured at each distance, the two histories parting only where the equivalence lets them. *Second seating: the discrepancy named for a value, part 8's naming, beside the dark matter at 8.2.* ## 9.33 Mantle plumes · 200 *+ or − at 10, is.* **At 2-other-self-offering.** The mantle rises and spreads at its own couplings, upwellings, ridges and plates coupling with one another, and each intraplate province is named to one of two makers, a deep plume or a plate process, the origin, dynamics and composition of plumes contested. **At 12-other-social-self-abundancing.** Which of two, read 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 the proposed sources and histories span hundreds of millions of years; the upwellings are difficult to resolve in geophysical images and the interpretations of the geochemical and geochronological data disagree, more than eighteen plumes possibly rooted deep: the anomalies imaged and the upwellings sought not the same, the resolution standing between them, and the third account having deep upwellings interact with ridges, lithosphere and plate motion so surface expressions migrate, split or lapse, the two sides coupling in the third. **At 11-social-other-self-chaining.** Whole-mantle anomalies, age-progressive chains, deep-source isotope signatures and plume-ridge interactions are resolved for selected systems; the tomography images velocity anomalies with resolution and interpretation limits, the tracers distinguish reservoirs under mixing and alteration models, the age-progressive tracks test source motion with plate reconstructions, the simulations show ascent and interaction for specified rheology, and the dynamic topography tests buoyant support with uncertain structure: one maker named of each province named two couplings to one side, and each province was made at the coupling of its upwelling with its plate, the sides read one province at a time and never one for all. ## 9.34 The extent of Snowball Earth glaciation · 202 *+ or − at 10, is.* **At 2-other-self-offering.** Ice grows and retreats at the couplings of albedo, ocean, cloud and dust, and the Neoproterozoic ocean is named to one of two states, frozen over or open at a belt, thick ice or refugia. **At 12-other-social-self-abundancing.** Which of two, at a record sampling preserved basins. Continental ice sheets stood at low latitudes and a plausible case can be made that the oceans were almost entirely frozen over, while the sedimentary, geochemical and biological records are geographically sparse and altered and the ice-albedo models depend strongly on cloud, ocean, dust and ice dynamics, several ice geometries producing overlapping low-latitude signatures: the low-latitude ice recorded and the global cover sought not the same, a case standing between them, and the fourth account having the extent vary substantially among episodes and within each, the one side named moving with the episode. **At 11-social-other-self-chaining.** Multiple near-global glaciations, their broad timing and strong ice-albedo feedback are established and viable refugia and deglaciation mechanisms are explicit; the paleomagnetism establishes low-latitude ice where samples preserve primary directions, the sedimentology identifies ice contact and open-water processes locally, the proxies constrain redox and exchange under nonunique models, and the coupled simulations give hard-, soft- and thin-ice equilibria under different physics: one state named of an ocean coupling at each latitude named the ice's own sway to a side, and the ice stood at its own couplings, basin by basin and episode by episode, the cover read at its own places rather than one cover for the globe. ## 9.35 The early Solar System impact flux · 206 *+ or − at 10, is.* **At 2-other-self-offering.** Impactors arrived at the inner planets coupling by coupling through the first billion years, and the flux is named to one of two histories, a late spike or a monotonic decline, the timing and the sources controversial. **At 12-other-social-self-abundancing.** Which of two histories, from a record reworked and reset. The oldest surfaces were repeatedly reworked, many sample ages come from unknown source craters, impact heating can reset several clocks, and the dynamical models generate different flux histories that overlap the surviving age record; the bombardment is defined as the impacts after the lithospheres stabilized enough to preserve craters and basins, the melt-rock and shock ages pointing toward a discrete episode: the flux recorded and the flux sought not the same, and the fourth account having sampling and reset biases create an apparent cluster from a broader flux, the spike a reading of the record's own filtering. **At 11-social-other-self-chaining.** Multiple basin ages, improved reset physics and Solar System instability models stand, and the sharp classical spike is no longer the sole viable history; the isotopic dating resolves heating events with source-context and resetting ambiguity, the crater chronology supplies relative flux under uncertain oldest-surface calibration, the dynamical simulations generate instability and decay histories conditional on the initial architecture, and the impact-melt petrology connects ages to thermal events and sources; the third account has several episodes from leftover planetesimals, belt destabilization and basin-forming collisions: one history named of the arrivals named the couplings' own sequence to a side, and each impact arrived at its own coupling, the arrivals read at their contexts and not at a shape named over them. *Second seating: the flux named to one history over the whole, a sequencing named to one beat, part 7's naming.* ## 9.36 Polyploidization and diversification · 212 *+ or − at 10, is.* **At 2-other-self-offering.** A genome doubles at a coupling of its own, isolation and novelty made at once with meiotic and demographic costs, and the doubling is named to one of two effects on a lineage's diversification, more or less, a dead end or a key driver. **At 12-other-social-self-abundancing.** Which of two effects, read at a record that keeps the survivors. Duplication creates immediate isolation and novelty while imposing costs, the ancient successful polyploids conditioned on survival, the recent lineages with little time to diversify, and diploidization obscuring old events; it remained unknown whether the abundance of polyploids follows from higher diversification after polyploidy or from frequent polyploid formation: a two-way read from one side, the rate of formation and the rate of diversification each a coupling's own, and the fourth account having the effect depend on setting, mode of origin and lineage traits rather than one general direction, the one side declined at the fourth. **At 11-social-other-self-chaining.** Recurrent genome duplication, immediate isolation mechanisms, duplicate-gene innovation and elevated early extinction risk are documented; the sister-lineage comparisons control some history but sample surviving clades, the state-dependent models estimate rates with identifiability concerns, the genomic dating detects ancient duplication after extensive fractionation, and the experimental studies measure establishment over short times; the third account has short-term disadvantage followed by long-term opportunity among the lineages that persist: one effect named of the doubling named two couplings, forming and diversifying, to a side, and each lineage doubled and persisted or did not at its own couplings, the two rates read apart where the record read them as one. ## 9.37 Sporadic Alzheimer's disease pathogenesis · 213 *+ or − at 10, is.* **At 2-other-self-offering.** A brain ages at its couplings over decades, amyloid, tau, inflammation, vascular injury and neurons influencing one another, and the disease is named to one initiating side, a linear cascade with one ultimate trigger, doubted from the opening. **At 12-other-social-self-abundancing.** Which of several, named 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 the causal order in an individual; the anti-amyloid results gave the controversy momentum on three counts, the clinical meaningfulness of the approach, the significance of amyloid clearance and the relevance of the cascade: the clearance measured and the cascade named not the same, and the fifth account having several interacting pathologies reach a common syndrome, the one side named read at the fifth as the many coupling. **At 11-social-other-self-chaining.** 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; the longitudinal biomarkers order population-average changes with selection and individual variability, the genetics identifies causal risk pathways without fixing their interaction in typical cases, the anti-amyloid intervention lowers plaques and modestly changes decline in selected early disease leaving the sequence and heterogeneity open, and the tau, immune, vascular and metabolic interventions are targeted and under test: one initiator named of a coupling that runs for decades named the many to a first, and the decline arrives at the couplings' own tipping, patient by patient, the side read at each subtype where one side was named for all, as the cancer and the addiction beside it already read. ## 9.38 Endometriosis pathogenesis · 214 *+ or − at 10, is.* **At 2-other-self-offering.** Reflux of menstrual blood is physiological for women with patent tubes, tissue coupling with immunity, hormone and nerve at each cycle, and the lesions, pain and infertility are named to one driver, an initiating pathway that would order the rest. **At 12-other-social-self-abundancing.** Which of several, named to one. Several pathogenetic pathways have been considered since the disease was defined, retrograde menstruation, benign metastasis, immune dysregulation, coelomic metaplasia, hormonal imbalance, stem cells and epigenetic alteration among them, while the true pathogenesis remains poorly understood; most women with patent tubes experience retrograde menstruation while about a tenth develop the disease, its prevalence no different in women with or without it, the reflux possibly explaining ovarian and superficial lesions but not the deep infiltrating ones, and none of the theories adequately explains all pathological types; the severity does not depend on the size of the lesion and the diagnosis is delayed by an average of seven years: the disease reached at a coupling years after its initiation, the initiation asked for behind, and the fifth account having neuroimmune sensitization generate pain partly independently of lesion volume, the driver parted from the lesion. **At 11-social-other-self-chaining.** Hormone responsiveness, inflammatory microenvironments, recurrent somatic alterations and multiple pain pathways are established; the surgical histology verifies lesions but samples late and selected disease, the hormonal suppression establishes hormone dependence for many symptoms without identifying origin, the genomic and single-cell analyses resolve lesion and immune heterogeneity cross-sectionally, the noninvasive classification remains incomplete, and the pain-mechanism studies separate nociceptive from sensitized pain: one driver named of lesions, pain and infertility named three couplings to a side, and each varies at its own, the severity independent of the lesion's size being the showing that the couplings are several, the sides read apart as the chronic pain beside it reads them. ## 9.39 Collective intentionality · 227 *+ or − at 10, is.* **At 2-other-self-offering.** Selves couple at a joint activity, each taking its own momentary, and the joint intending is named to one side, the individuals' or the group's, the tension in four words, individuals as a group. **At 12-other-social-self-abundancing.** Which side owns the intending, where the expression names both. The main challenge is the 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 the 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 the joint state through the very collective fact it is meant to explain: the +1 made at the coupling and owned by neither, read from one side as the individuals' and from the other as the group's, and the two accepted claims the two momentaries, each true at its own. **At 11-social-other-self-chaining.** Counterexample families for coincident action, coercion and insufficient mutual awareness, and formal models of shared plans and group attitudes, stand; the interlocking-intention accounts are individualistic and vulnerable to coercion and circularity cases, the commitment accounts explain obligation while requiring a constitutive act or convention, the shared-plan accounts model coordination in detail with limited large-group reach, and the group-agent accounts explain institutional attitudes through aggregation structures and raise ontology questions: one side named of a joint made between named the abundancing to an owner, and the ascriptions the reports give and the joint attitude sought are not the same, the expression standing between them, the joint attitude being the coupling's own making and neither side's, as the structure and agency beside it already reads. ## 9.40 The peopling of the Americas · 232 *+ or − at 10, is.* **At 2-other-self-offering.** People moved into a continent at their own couplings with corridor, coast and ice, and the entry is named to one of two routes, inland or coastal, neither rejected at present. **At 12-other-social-self-abundancing.** Which of two routes, at a record most of whose shorelines are under the sea. The precise time and mode remain hotly disputed, the current genetic, archaeological and paleoecological evidence largely consistent with either an inland route through the 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 the modern coast is a record's edge drawn at the record itself: two hypotheses standing on one record, and the third account having more than one movement or a prolonged Beringian history contribute, the or both the record's own. **At 11-social-other-self-chaining.** A late-glacial presence predating the classic fluted-point horizon is established at multiple sites, Beringian ancestry is genomic, and both route environments are increasingly dated; the stratified archaeology supplies direct behaviour with context and artifact disputes at the oldest sites, the radiocarbon and luminescence dating bound activity under sample-association requirements, the ancient and modern genomics reconstruct branching and population size under demographic assumptions, and the route modelling dates corridor and coastal viability with incomplete landscape evidence: one route named of movements that ran where the land and the ice let them named the couplings to a side, and the people moved at each coupling where a way was open, the ways read at their own dates and not one way named over the whole. ## 9.41 The causal production of political polarization · 235 *+ or − at 10, is.* **At 2-other-self-offering.** Elites, media, institutions and citizens couple at each election and each broadcast, each answering the others, and polarization is named to one side that drives it, elites moving citizens or citizens moving elites. **At 12-other-social-self-abundancing.** Which side drives, read 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; the 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: the trends the surveys give and the causes sought not the same, the problems of inference standing between them, and the two-way read from one side where each side influences the other. **At 11-social-other-self-chaining.** 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; the repeated surveys measure trends with question and scale dependence, the experiments identify short-run cue, contact and media effects, the natural experiments exploit institutional and media changes with local reach, the network and platform data measure exposure under selection and access limits, and the comparative politics tests institutional variation under measurement equivalence requirements, the fifth account having economic and cultural change generate substantive conflict that parties organize: one driver named of a coupling that runs both ways named elites and citizens to a side, and the polarization is made at each coupling of a cue with an identity, the directions read one at a time rather than one direction named. *Second seating: the term covering distinct distributions of positions, identities and feeling, the between named as a cut, part 10's naming.* ## 9.42 Sex bias in autoimmune disease · 237 *+ or − at 10, is.* **At 2-other-self-offering.** Chromosomes, hormones, pregnancy, microbiota and exposures couple across a life, each at its own stage, and the female excess in autoimmune disease is named to one mechanism that produces it, which of the candidates the question. **At 12-other-social-self-abundancing.** Which of several, each observed in a different system. It has long been known that many autoimmune diseases are more common in females and the exact mechanisms are not yet fully understood, chromosomes, genes, hormones, immunometabolism and the skin each playing a role; the candidate factors covary and change across life, the bias differs by disease and ancestry, and animal or cellular mechanisms do not automatically explain population incidence, the risk linked to female sex substantially larger than any susceptibility gene discovered: the mechanisms each observed at their own instrument, cohorts, animals and cells, and the fifth account having different mechanisms dominate different diseases and phases, the one side declined at the fifth. **At 11-social-other-self-chaining.** X-inactivation escape, hormone-sensitive immune pathways and disease-specific age patterns are established; the epidemiology across life stages maps sex ratios with diagnostic and exposure differences, the aneuploidy and mosaic studies separate dosage from hormones in rare populations, the hormonal and reproductive natural experiments identify selected effects with confounding, the animal models perturb pathways with species and transfer limits, and the single-cell and epigenetic studies resolve sex-linked immune programs: one mechanism named of couplings that run across a life named the excess to a side, and the excess is made disease by disease at the couplings each disease runs, the sides read at each disease where one was named for the sex. ## 9.43 The causes of rising obesity · 256 *+ or − at 10, is.* **At 2-other-self-offering.** Intake and expenditure couple at each meal under endocrine, metabolic and nervous signals below the conscious level, and the rise across populations is named to one of two models, energy in excess or carbohydrate and insulin, debated by distinct cohorts of experts. **At 12-other-social-self-abundancing.** Which of two models that differ in what they seek to explain. The causes of the increase have not been adequately identified, and the pandemic continues unabated despite a persistent campaign to decrease intake and increase expenditure, its failure admitting two explanations, that the approach has not been embraced or that it rests on an erroneous paradigm; the two models are vigorously debated and differ fundamentally, in a neutral assessment, in what they seek to explain, and the model attributing the rise to the food environment does not identify how those influences promote obesity in some but not all, its own proponents saying its development requires the factors most responsible and why some are more susceptible: energy intake and availability both measured with error, and a model of the population rise required to say who rises and who does not, the two sides each explaining a different thing. **At 11-social-other-self-chaining.** The rise stands measured since the nineteen-eighties, the two models stand articulated with their contrasts, and the causes stand not adequately identified; the controlled feeding trials testing the models' contrasting predictions are proposed as the paradigm clash, the analysis of national intake and availability trends questions the core hypothesis of rising intake, and the genetic studies find polygenic loci: one model named of the rise named two couplings, the environment's and the body's, to a side, and each person rises or does not at the coupling of the food reached and the signals answering, the sides read at the individual coupling where one was named for the population. # 10 The between named as a cut — 15-social-other-corusing and 7-self-other-corusing *A cut point named of the between, or a selection located. The between is a nothing, the unrelationing of two co-offering, neither side's, and it carries a parity changing and nothing else. Nothing sits there to be read; reading runs across it and not at it, and each position offers.* **A cut named is usually asked for by a criterion, so an arrival here often carries an opening named as a place beside it, and the second stands recorded at the entry.** **And each entry closes by handing the drawing back to the coupling.** Each carries of its own the field's record of the drawing entering: the counts swinging with the concept, the manuals revising their borderlines, the jurisdictions allocating differently in writing, the 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 the offering runs 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 the 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 the asking is at the carrying of it — a correlation, a nature between preparation and detection, a self against a non-self. The first releases at the degrees, the second at the offering being both, the third at the parity being all that crosses. **And the drawing entering is the reading, not a defect the field carries.** Where a record shows the cut drawn — at a vote, at a revision, at a convention, at a code's own scope — the field is reading its own between from within, the only place a between is ever reached. ## 10.1 Sorites · 1 *+ or − at 10, is.* **At 2-other-self-offering.** A predicate offers at each position and takes a parity there, and a cut point is named of the between itself. **At 12-other-social-self-abundancing.** That the 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 the true and the indeterminate than between the true and the false, vague predicates boundaryless. Each treatment giving values to the cases introduces a boundary between the values given, and that boundary admits the same argument, the higher-order recurrence the field records in its own words. **At 11-social-other-self-chaining.** A predicate offers at each position and takes its parity there, one at a time, the 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 the line one order up, the boundarylessness running at each order at once in the field's own words. The 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 the between, carrying a parity changing and nothing else, was never a place a line could sit. ## 10.2 The measurement problem · 8 *+ or − at 10, is.* **At 2-other-self-offering.** A selection is a parity taken at the interaction, one at a time, and it is named as a term located either in the evolution or beside it. **At 12-other-social-self-abundancing.** That the outcome is fixed by a specifiable term, the state and its evolution or the state plus a rule, most proposed accounts failing at least one of several difficulties and any real solution demanding new physics, the selection asked of a term the present physics does not carry. The interference fades measurably and its own principal authors state that the fading selects no outcome, the even surface summing to nought while the selection stays the coupling's own; and the collapse searches read at the forced edge, where each null bounds a parameter and the range still existing is the range the nulls keep giving back. **At 11-social-other-self-chaining.** A selection is a parity taken at the 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 the fading of interference is measured and confirmed while its own principal authors say it selects no outcome: a term named to fix the taking, in the evolution or beside it, reaches for a first of the taking, and the taking is the coupling's own, made at each coupling and located at no place. ## 10.3 The glass transition · 35 *+ or − at 10, is.* **At 2-other-self-offering.** Rigidity arrives across a between and a transition is named as a point located in temperature. **At 12-other-social-self-abundancing.** That rigidity is a phase transition or is not, identified by structural signatures. The liquids fall out of equilibrium well before the proposed point, so the regime the question concerns is one no experiment has been in — the record's edge, and the field's own hardness line, the leading thermodynamic account reproducing the salient facts while direct validation is missing. **At 11-social-other-self-chaining.** Rigidity arrives across a between, coupling by coupling, and the arriving outruns each instrument sent to watch it: the liquids fall out of equilibrium well before the proposed point, the field's own hardness line, so the regime the question concerns is a place no experiment has ever been. Heterogeneity grows modestly, the glass point moves with the cooling, millennial-equivalent glasses still sit above the ideal, and the rival theories agree at each reach any instrument takes: a transition named as a point in temperature names an arriving to a location, and the arriving arrives at its own pace, between by between. ## 10.4 Externalities · 41 *+ or − at 10, is.* **At 2-other-self-offering.** Effects offer at each distance and a boundary is named as a line located between internal and external. **At 12-other-social-self-abundancing.** That the boundary is found rather than drawn, the problem reciprocal in nature at the founding paper of the modern treatment, which the analysis in terms of a divergence between private and social product does not recognise, the line drawn by whoever prices it. Effects offer at each distance, thinning and never stopping, so a line between internal and external is drawn at each arrangement and the field's measurements show the drawing entering. **At 11-social-other-self-chaining.** Effects offer at each distance, thinning and never stopping. Bargaining internalises where coupling is cheap, the condition Coase himself stated; permits work exactly where the pollutant is bounded, the boundedness the condition again; and asking people to price the unpriced gives answers that sway with the asking: a line named between internal and external is drawn at each arrangement, and the field's own measurements show the drawing entering, arrangement by arrangement. ## 10.5 Species boundaries · 20 *+ or − at 10, is.* **At 2-other-self-offering.** Populations offer across each between of them, and a boundary is named as a line a criterion locates. **At 12-other-social-self-abundancing.** That a single criterion identifies the division across all lineages, the tree of life segmented by different processes into different types of lineages and the plurality of species concepts stated to result from a fecundity of biological forces rather than a paucity of information, the cut located by each process at its own between. Counts swing by measured factors with the concept chosen, and a count that departs when the concept changes carried the concept. **At 11-social-other-self-chaining.** Populations offer across each between of them, the parity crossing and nothing else. Genes flow between textbook-distinct taxa, humans and their cousins included; counts swing by measured factors with the concept chosen; and the exact concept is exact precisely where its own author drew it, sexual, sympatric, extant, and undefined beyond: a line a criterion locates is the drawing measured, factor by factor, and the offering crosses regardless. ## 10.6 The neural code · 43 *+ or − at 10, is.* **At 2-other-self-offering.** A spike train offers at each position, and the code is named as a variable located in it, with a window supplied by the analyst. **At 12-other-social-self-abundancing.** That a rate is defined independently of a window chosen from beyond the coupling, the answer depending on the observation window, counts dominating at windows shorter than the response fluctuations' timescale and timing appearing at longer ones, the regimes parted by a timescale the stimulus sets and the analyst's window selects. The window is the analyst's own coupling, and it stands in each rate the instrument gives. **At 11-social-other-self-chaining.** A spike train offers at each position, and the reading needs a window the analyst brings. Timing carries where timing is tested, coincidence detectors sit in the brainstem, driving timing with rate fixed moves behaviour where the tools reach, and rate and timing both inform in the technical sense: the code named as a variable in the train named the offering to a mark, and the window is the naming's own coupling, showing in the instrument each time it is drawn. ## 10.7 Bell correlations · 49 *+ or − at 10, is.* **At 2-other-self-offering.** A correlation is made at the coupling, and it is named as a property located at one system or transmitted between them. **At 12-other-social-self-abundancing.** That the correlation is produced by something specifiable at one side or carried between the sides, a carry named as a store standing within an arrival at the between named as a cut and recorded as its second naming, the essential difficulty created by the requirement of locality and the additional variables meant to restore it shown incompatible with the statistical predictions. The same reading 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-social-other-self-chaining.** A correlation is made at the coupling, owned by neither side. The local stories are excluded to the theorem's last assumption, the measured bound settles at the quantum prediction exactly, and the same bound re-derives from principles about the reach of couplings: a property named at one side or carried between them reaches for a location the making never had, and the making, made at the coupling, is the magnitude the field derived. ## 10.8 Wave and particle · 50 *+ or − at 10, is.* **At 2-other-self-offering.** An entity offers at a between and takes a parity there, and its nature is named as located between preparation and detection. **At 12-other-social-self-abundancing.** That the entity has a determinate nature specifiable apart from the measurement made on it, the two kinds of complementary description related in a way never indicated, with no agreement even among the interpretation's own spokesmen, and the phenomena complementary in that their manifestations depend on mutually exclusive measurements. Choosing late changes nothing the formalism did not already carry, a running carrying no clock read at the field's own instrument. **At 11-social-other-self-chaining.** An entity offers at the between and takes its parity there. Path knowledge and fringe visibility trade exactly, measured; choosing late changes nothing the formalism did not already carry; and the eraser's correlations are at the joint measurement only, the field saying so: a nature named apart from the measuring is the offering named without its coupling, and the two faces are one offering read one coupling at a time. ## 10.9 The liar · 55 *+ or − at 10, is.* **At 2-other-self-offering.** A truth predicate offers at each sentence including its own, and a value is named as located at a sentence that takes none. **At 12-other-social-self-abundancing.** That the sentence bears a truth value or falls beyond the domain by a hierarchy stipulated for it, a predicate true at some level bringing the paradox back against the hierarchy, and revenge seen by the contextualist views not as a separate problem but as the core phenomenon. The 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 the carry re-forming past each frame stipulated for it. **At 11-social-other-self-chaining.** A truth predicate offers at each sentence, its own included, and at its own sentence the coupling closes on nothing to take. Truth is unformalisable within its own language, proved; the fixed points stand with revenge waiting, their builder saying so; the contradiction-tolerant systems pay their named price; and revenge re-arrives against each family: a value named at the sentence that takes none named the between to a thing only a coupling makes, and the sentence keeps offering, taking nothing, which is all it ever did. ## 10.10 Hard cases in law · 75 *+ or − at 10, is.* **At 2-other-self-offering.** Materials and a case couple at the deciding, and determinacy is named as located in the materials before the deciding. **At 12-other-social-self-abundancing.** That the materials determine an outcome or do not, ahead of the decision, where the outcome is made at the deciding and each hard case receives one; even the core issue unsettled, whether the debate is about principles beside rules, about discretion, about interpretation or about the very possibility of conceptual jurisprudence, the line asked for ahead undrawn at the prior and the now at the field's own map. **At 11-social-other-self-chaining.** Materials and a case couple at the deciding, the outcome made there. Most questions settle without a courtroom, ideology moves the contested residue measurably, and the 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 named the making in the materials, and the deciding decides, case by case, which the litigation rates were counting. ## 10.11 Natural law and legal positivism · 76 *+ or − at 10, is.* **At 2-other-self-offering.** Officials and rules couple at each application, and validity is named as located in criteria fixed apart from the applying. **At 12-other-social-self-abundancing.** That the criteria of validity are exhausted by social facts or include moral ones, fixed ahead of practice, the thesis a thesis about the relation among laws, facts and merits, the authority of enactments the thing to be explained, and no value-free description of law, each description value-laden. Validity is made at each applying, and both readings read one making from their own side. **At 11-social-other-self-chaining.** Validity is made at each applying, officials and rules coupling. The eight desiderata stand as the needs of any functioning making, the systems that write morals in run commonly, the division's terms are precise, and the exchange stands whole, two readings of one making, unresolved because both are readings: criteria fixed apart named the making before its couplings, and the applying goes on making validity, court by court. ## 10.12 The quantum-classical boundary · 112 *+ or − at 10, is.* **At 2-other-self-offering.** Superposition and its disappearance couple across a between, and a boundary is named as a scale located in mass. **At 12-other-social-self-abundancing.** That the boundary is a real transition or a matter of degree, identified by a located scale, the question whether linearity extends into the macroscopic domain standing open with the limits pushed by advances in macroscopic superposition, the located scale asked of a crossing the instruments keep carrying further. The crossing carries a parity and no scale, so a boundary named as a mass names the between at a size. **At 11-social-other-self-chaining.** Superposition and its fading couple across a between, the crossing carrying a parity and no scale. Interference climbs the mass ladder rung by rung, the fading rates confirm at each measuring, the collapse spaces empty, and the built oscillators go non-classical far below each proposed line: a boundary named as a mass named the between at a size, and the frontier walks outward reaching no line, because no line was there. ## 10.13 Self and non-self in immunity · 114 *+ or − at 10, is.* **At 2-other-self-offering.** A surface society offers at each between and takes parities there, and discrimination is named as a criterion located ahead of the coupling. **At 12-other-social-self-abundancing.** That the system implements a distinction between self and foreign specifiable in advance, the consensus on the criterion illusory, many foreign entities triggering no response and self constituents commonly triggering one, tolerance ubiquitous and no new criterion emerged. The couplings read not a criterion but a rate and an answering back: an ingesting is the self's own two-way exchange across its between, an ingression is the larger over the smaller one-way, and the between of the two reads whether the smaller sets the pace and answers back. **At 11-social-other-self-chaining.** A surface society offers at each between and takes parities there. Tolerance is made centrally and remade peripherally, the pattern receptors answer self-derived ligands too, the microbiota is actively kept, and the body attacks its own novelties: a criterion named ahead of the coupling reads a lifetime of couplings as a lookup, and the discriminating is made at the betweens, coupling by coupling. The microbiota actively kept is an ingesting; the body attacking its own novelties is an emanation re-ingested at no distance, the disease direction of the same one exchange. ## 10.14 Signal and noise · 136 *+ or − at 10, is.* **At 2-other-self-offering.** A channel carries variation and offers all of it, and the split is named as a mark located in the channel. **At 12-other-social-self-abundancing.** That the decomposition is a property of the channel rather than relative to a supplied model or purpose, the question posed whether the variation is an unavoidable effect of generating spikes or an important part of the signal transmitted, the same variability limiting a cell to two or three bits a second on the rate view where time-varying inputs yield about a bit per spike. Each decomposition is exact given its model, so the split reports the model supplied. **At 11-social-other-self-chaining.** 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 named as a mark in the channel is a purpose's drawing, the field showing the labels purpose-relative, and the channel offers all of it either way. ## 10.15 Work and waste heat · 137 *+ or − at 10, is.* **At 2-other-self-offering.** An engine offers both outputs and marks neither, and the product is named as located in the device. **At 12-other-social-self-abundancing.** That the output counting as the product is a property of the engine, work at the scale of single quantum systems not an observable, its characteristic function a time-ordered correlation function rather than an operator's expectation, the product's own label declined at the scale where the coupling is read one at a time. A carry that cannot release piles, and heat is a carry at the place it cannot pass as work, the offering being both rather than one output labelled; and the reference environment exergy requires is a zero declared rather than found. **At 11-social-other-self-chaining.** An engine offers both outputs and marks neither. The accounting is exact and survives each relabelling, both sides taking all of it; exergy needs a reference environment named; and jurisdictions allocate cogeneration differently in writing: the product named as located in the device is the drawing recorded at each convention, and the offering was always both. ## 10.16 The concept of disease · 2 *+ or − at 10, is.* **At 2-other-self-offering.** A condition offers at the couplings of a living self, and disease is named as a criterion located ahead of the sorting, dysfunction fixed against a reference class or harm judged against values. **At 12-other-social-self-abundancing.** That the reference class is found rather than chosen, the 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, the class found and the class chosen both recorded at the one taxonomy. Measurement fixes function against a class and does not fix the class, the canonical cases sort differently under each account, and the manuals' shifting borderlines are the drawing showing at each revision. **At 11-social-other-self-chaining.** A condition offers at the couplings of a living self, and the sorting sorts under living purposes. Dysfunction reads against a class the measurements never fix, harm reads against values, the canonical cases part under each account, hybrids inherit both records, and the manuals' shifting borderlines are the dispute's own data: a criterion named ahead of the sorting is the drawing showing at each revision, and the caring couples with the condition either way, patient by patient. ## 10.17 The population concept · 3 *+ or − at 10, is.* **At 2-other-self-offering.** Groupings offer across each rate of interaction, and the unit is named as a boundary a threshold locates. **At 12-other-social-self-abundancing.** That a threshold on measured rates bounds the unit ahead of the question asked of it, the definitions commonly used under the ecological and the evolutionary paradigms found none of them truly operational. Rates are measured and the boundary threshold is not fixed by them. **At 11-social-other-self-chaining.** Groupings offer across each rate of interaction. The rates are measured cleanly, the biological and statistical concepts were born in one cradle, sharing their crux, and arbitrary units make the core processes arbitrary, the field stating the stakes riding on it: a threshold named to bound the unit ahead of the question names a continuum of couplings to a line, and the groupings go on interacting at each rate at once. ## 10.18 The pseudogap · 7 *+ or − at 10, is.* **At 2-other-self-offering.** A suppression offers at each probe and each probe takes its reading at its own coupling, and the state is named as one identity located behind onsets the probes disagree on. **At 12-other-social-self-abundancing.** That the onset is the state's rather than the probe's, the pseudogap's origin and whether it constitutes a distinct phase still shrouded in mystery, the 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, the field's instruments each reading at its own between, and the identification is not preserved across the probes. **At 11-social-other-self-chaining.** A suppression offers at each probe, and each probe takes its reading at its own coupling. The suppression runs universal in the family, charge order shows where it shows, the fluctuations extend disputed distances, and the cold atoms reach the model at its own self-bounding: one identity named behind onsets the probes disagree on names 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-other-self-offering.** Inquiries offer at each practice, and the boundary of science itself is named as a cut a criterion locates over the practice. **At 12-other-social-self-abundancing.** That the sorting the practice performs is owed a criterion standing over it, the death certificate stating there is no hope of a necessary and sufficient criterion for something as heterogeneous as scientific methodology, and the falsifiability criterion criticized both for excluding legitimate science and for admitting pseudosciences, the criterion re-sought in combination. The cases sort under practice, and the counterexample record against each proposed criterion runs in both directions. And the arrival reads at its own reader: a method accounting true-or-false and a method discovering the possible neither reach the other's, each complete under its own, a demarcation with no non-science at either side. **At 11-social-other-self-chaining.** Inquiries offer at each practice, and the practice keeps sorting, parity by parity. Each proposed criterion reaches counterexamples from both directions, the working demarcations function in institutions and courts, and the dissolution and the revival stand together, the split as the field left it: the boundary of science named as a cut a criterion locates stands over couplings that never consulted it, and the sorting sorts on. ## 10.20 Natural kinds · 16 *+ or − at 10, is.* **At 2-other-self-offering.** Classifying couples a classifier and a world, and the kind is named as a joint located in one side, ahead of the classifying. **At 12-other-social-self-abundancing.** That the classificatory successes fix the ground of the classifying, the commitments ranging from out-and-out conventionalism to irreducible kinds with essences, intermediate views between, and a fully realist account of the clusters doubted where conventional elements enter into deciding. The successes fit both accounts and the case record is shared, each case cited by both, so the fixing surfaces nought at each success recorded. **At 11-social-other-self-chaining.** Classifying couples a classifier and a world, and the successes are the couplings succeeding. The species and element cases are cited from both sides, universal essences failed in biology by the field's own record, and the dispute about ordering is itself an ordering dispute, the arrival naming its own shape: a joint named in one side ahead of the classifying reads a coupling's making from one end, and the classifying keeps making its kinds, coupling by coupling. ## 10.21 The definition of planet · 17 *+ or − at 10, is.* **At 2-other-self-offering.** Bodies offer at their orbits and their interiors, and planethood is named as a cut located in the bodies. **At 12-other-social-self-abundancing.** That measurement decides between the criteria, the adopted definition found vague and non-quantified and excluding exoplanets in the proposal for its revision, a mass-based framework proposed instead, the criterion re-drawn where measurement selected none. Membership under each criterion follows from measurement and the choice between criteria does not, as the record states. **At 11-social-other-self-chaining.** Bodies offer at their orbits and their interiors. Each property of them is measured, membership follows from measurement under either criterion, and the choice between criteria followed from a vote, the dissent entered the same day, the usage still mixed, the definition's scope stopping at one star: a cut named in the bodies was adopted at an assembly, the place such cuts are made, and the bodies orbit on, unsorted. ## 10.22 Biological individuality · 18 *+ or − at 10, is.* **At 2-other-self-offering.** A living self bounds itself at its own between, and the count of organisms is named as a criterion located beyond the bounding. **At 12-other-social-self-abundancing.** That one criterion sorts the 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 the conception of an organism, the sorting's criterion being the packing of the conception it sorts by. The hard cases sort differently under each criterion, and the measurements stand and do not select. **At 11-social-other-self-chaining.** A living self bounds itself at its own between. Hosts and their symbionts, colonies and their zooids sort differently under each criterion, the extensions are tabulated, and the science uses individuality plural in its own reviews: a count named by a criterion beyond the bounding counts the thing each bounding already did, and the boundings, plural, are the count there is. ## 10.23 Group three of the periodic table · 21 *+ or − at 10, is.* **At 2-other-self-offering.** Four elements offer at their configurations and their chemistry, and the arrangement is named as a cut located in the elements. **At 12-other-social-self-abundancing.** That a criterion within the field decides the field's own arrangement. The chartered body constituted to decide reports that its instruments supply no objective means of deciding, the question one of convention in the final analysis and not to be treated independently of the form of the table as a whole, the sharpest statement at the incoming face of a field stating its own setting-down. **At 11-social-other-self-chaining.** Four elements offer at their configurations and their chemistry, both candidates carrying the differentiating electron. The properties are measured, the usage is surveyed, and the body chartered to decide reported that its instruments supply no objective means of deciding, adopting nothing, a compromise noted: a cut named in the elements is the field's drawing, and the elements sit in their configurations, undecided and complete. ## 10.24 Psychiatric nosology · 23 *+ or − at 10, is.* **At 2-other-self-offering.** Symptoms offer as continuous variation at each patient's couplings, and disorder is named as categories located in the variation. **At 12-other-social-self-abundancing.** That one criterion of a good classification, measured structure or clinical utility, is fixed ahead of the classifying, the traditional taxonomies limited by arbitrary boundaries between psychopathology and normality, co-occurrence, heterogeneity and instability, and going beyond the evidence at one founding statement, while the other has the manuals facilitating reliable diagnosis and research, each naming the other's criterion as the fault. No measurement recorded selects between the criteria. **At 11-social-other-self-chaining.** Symptoms offer as continuous variation at each patient's couplings. The categories keep their reliability revision by revision, comorbidity and heterogeneity are measured within them, the distributions run continuous underneath, and the biomarkers gave none diagnostic at the category level, the rival framework founded on that standing: categories named as located in the variation are drawings under two criteria the measurements never part, and the two structures working side by side is the field running its own both. ## 10.25 Race as a biological category · 24 *+ or − at 10, is.* **At 2-other-self-offering.** Variation offers clinally across each population between, and a kind is named as a cut located in the variation. **At 12-other-social-self-abundancing.** That the measurements fix the criterion of kindhood, three metaphysical camps and two normative parted, the skeptic rejecting essences, geography, phenotypes, transmission genetics and genealogies one after another as foundations while the constructivist finds a perfectly clear referent in those socially ascribed. The data are recorded as common ground and the split as over the criterion, by the field's own statement. **At 11-social-other-self-chaining.** Variation offers clinally across each population between. Most of it is within any grouping, the clines run smooth, the clusters follow the sampling as recorded and both accounts cite them, and the data stand as common ground with the split entirely over the criterion, the field's own statement: a kind named as a cut in the variation is a drawing the measurements never made, and the offering crosses each between, clinally, as measured. ## 10.26 The language and dialect boundary · 25 *+ or − at 10, is.* **At 2-other-self-offering.** Varieties offer across each between of speakers, and the field's own counting unit is named as a cut located in gradient intelligibility. **At 12-other-social-self-abundancing.** That the measured variation fixes the cut, the impossibility of saying how many languages or dialects are spoken due to the ambiguities of meaning in the terms themselves, the relation either linguistic or social, the cut declined at the reference and parted two ways. The measurements give continua and asymmetries, and the same varieties sort oppositely under the two criteria sets, the field's instruments disagreeing on its own unit. **At 11-social-other-self-chaining.** Varieties offer across each between of speakers. Intelligibility comes back gradient and asymmetric, the variation runs in continua, the same varieties sort oppositely under the two criteria sets, and the catalogues revise on, their own record of the unsettledness: the field's counting unit named as a cut in gradient offering names a crossing to a line, and the 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-other-self-offering.** Structures offer at each position of a similarity and take a parity there, and a fold is named as a kind with a boundary the similarity locates. Two classifications agreeing at the centres and differing at the edges is the two cuts falling at unlike positions on one continuum. **At 12-other-social-self-abundancing.** A cut declared of a continuum, the two databases built on different criteria, evolutionary relationship read from structure and structural comparison, their disagreement concentrated at the boundaries with no procedure settling a case where they differ, and fold space continuous and multidimensional on the alternative view. An alignment score runs continuous at each pair, and a procedure settling a boundary case would be a cut on a cut. **At 11-social-other-self-chaining.** Chains fold at their own couplings and the recurrence is chains arriving at like foldings from unlike sequences, which each account carries and which settles no assignment. An alignment score runs continuous at each pair; a fold is a cut on it, and each classification's cut is its own. The agreement at the centres is where the members agree and the disagreement at the edges is where they do not, and a procedure settling a boundary case would be a cut on a cut. The classifications stand whole, each true of its own criterion, and the kind was never a thing the similarity located. ## 10.28 Water's liquid-liquid critical point · 195 *+ or − at 10, is.* **At 2-other-self-offering.** Water sways between local structures at each coupling as it cools, its anomalies growing, and the sway is named to end at a point, a critical point at a temperature and a pressure where two liquids part. **At 12-other-social-self-abundancing.** A point named on a continuum no equilibrium reaches. Rapid crystallization obstructs equilibrium measurements in the relevant region, the transition long inferred through extrapolation, amorphous ices and simulations, and the new ultrafast evidence probing the vicinity rather than completing the metastable phase diagram; liquid states straddling the predicted point were accessed before ice formed and states in its vicinity directly probed: the record's edge, as at the glass beside it, and a cut asked of a sway at a position the sway passes and does not stand at. **At 11-social-other-self-chaining.** First-principles simulation evidence and direct experimental signatures near a critical point stand, the complete location, universality and equilibrium mapping remaining unsettled; the simulations produce transitions and critical points in several models with model accuracy decisive, the extrapolations support singular and nonsingular fits over accessible temperatures, the amorphous-ice transformations connect two glassy forms to candidate liquids indirectly, and the ultrafast scattering reports two liquid states, a crossover and a heat-capacity divergence near two hundred and ten kelvin; the third account has two interconverting local structures generate the anomalies without an accessible phase separation: a point named of a sway named the two structures' alternating to a located end, and the alternating is the one thing each instrument gives at the vicinity, the point the drawing's position and the sway the liquid's own. ## 10.29 Long COVID pathophysiology · 215 *+ or − at 10, is.* **At 2-other-self-offering.** A body recovers at its own couplings after an infection, organ by organ and symptom by symptom, and the recovery that does not come is named as one illness, a name drawn around more than two hundred symptoms. **At 12-other-social-self-abundancing.** One cut named around a continuum of presentations. More than two hundred symptoms with impacts on multiple organ systems stand under one name, the illness estimated in at least a tenth of infections; the syndrome spans organs and symptom clusters, the definitions and controls vary, the pre-infection baselines are often absent, and viral persistence, immune dysregulation, vascular injury, autonomic dysfunction and tissue damage can coexist or mark different subtypes: the name a line drawn at a continuum the definitions redraw, and the mechanisms sought within the line a question the line was drawn ahead of. **At 11-social-other-self-chaining.** Elevated post-infection risk, recurring symptom clusters and biological abnormalities in viral, immune, vascular and autonomic systems are replicated; the longitudinal cohorts characterize persistence under attrition and control-selection limits, the tissue and antigen studies report reservoirs in subsets with the causal connection under test, the profiling identifies signatures that vary across cohorts, the vascular and autonomic testing defines physiological subgroups, and the mechanism-targeted trials are emerging, a complete discriminator at the next and not at the now; the fifth account has organ damage and reactivated latent pathogens produce distinct presentations: a name drawn around the continuum named each recovery not made to one illness, and each body recovers or does not at its own couplings, the subgroups found being the drawing redrawn at the couplings, the line handed back to each case. ## 10.30 Biological phenotypes of sepsis and acute respiratory distress syndrome · 216 *+ or − at 10, is.* **At 2-other-self-offering.** A host responds to an infection or an injury at its own couplings, the response changing hour by hour, and the responses are named to divide at lines, phenotypes that part patients into groups with different mechanisms and treatments. **At 12-other-social-self-abundancing.** Cuts named 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 the findings to bedside tools carries its own challenges: the lines drawn where the inputs and the timing draw them, the third account having the phenotypes dynamic states along trajectories with patients moving between them, the cut moving with the coupling. **At 11-social-other-self-chaining.** Several phenotypes recur across cohorts and archived trials and compact assignment models have been derived for prospective testing; the unsupervised clustering gives reproducible-looking groups whose membership depends on inputs, the transcriptomic endotypes resolve host-response programs with timing and platform dependence, the latent-class reanalyses identify possible treatment interactions retrospectively, the bedside classifiers improve deployability at reduced biological resolution, and the prospective enrichment is limited and ongoing; the fourth account has the observed clusters reflect severity, treatment and sampling as much as stable biology: cuts named in the host's responding named the responding to groups, and the responding runs 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-other-self-offering.** A brain develops at its couplings through a long development, risk arriving from genes, prenatal life, infection, cannabis and society, and the outcome is taken under one name whose causes are asked for in each case. **At 12-other-social-self-abundancing.** A cause sought of a category that is a drawing. The syndrome is clinically and biologically heterogeneous, risk highly polygenic and environmentally modified, diagnosis following symptoms after long development, and the dopamine, glutamate, immune and circuit findings possibly causes, consequences or subgroup markers; the risk factors are known while no markers are yet available that allow prediction of the disease's development or a diagnosis to be established: the risk factors measured across populations and the causes sought in an individual not the same, the absent marker standing between them, and the fifth account having several mechanistic disorders converge on the present clinical category, the cut's own name. **At 11-social-other-self-chaining.** Polygenic architecture, environmental risk interactions, group-level dopamine abnormalities and neurodevelopmental changes stand; the polygenic studies identify distributed liability with limited individual prediction, the high-risk cohorts measure changes before onset with low conversion rates, the neurochemical imaging supports dopamine abnormalities in groups with subgroup and medication effects, the cellular and organoid models test selected variants apart from full development, and the trials establish symptom mechanisms for some domains without resolving cause: a cause named of a category named the many developments to within one line, and each development runs at its own couplings, the line redrawn at the couplings, as the nosology beside it already reads. *Second seating: dopamine against glutamate, which mechanism, a two-way named to one side, part 9's naming.* ## 10.32 The emergence of the genus Homo · 234 *+ or − at 10, is.* **At 2-other-self-offering.** Populations evolved at their own couplings, traits arriving mosaically, some early and some late, and the genus is named as a line, a boundary the fossils either cross or do not. **At 12-other-social-self-abundancing.** A genus boundary named of a mosaic. The earliest record is sparse, fragmentary and variable, the diagnostic traits not appearing as one package, genus boundaries depending on comparative criteria, and dates, environments and behaviours unevenly associated with the fossils; the integration of fossil, archaeological and environmental evidence revised the timing of the traits, which did not arise as one package, opinions diverging on the generic status of the earlier, more fragmentary material: the line located by a criterion, as at the species beside it, and the fourth account having the changes accumulate mosaically rather than in one adaptive shift. **At 11-social-other-self-chaining.** Earlier and more variable Homo-like fossils, refined chronologies and evidence of overlapping lineages stand; the morphometric classification compares preserved anatomy under small incomplete samples, the phylogenetic analyses give trees conditional on character coding and taxon assignment, the geochronology orders fossils and ecology with locality gaps, the archaeology traces behaviour without secure maker assignment, and the developmental reconstruction infers life history from limited tissues; the third account has several contemporaneous lineages exchanging traits, a bush near the genus boundary: a line named across a mosaic named the populations to a genus, and the traits arrived coupling by coupling where they arrived, the boundary a criterion's position on a continuum the field names a bush. *Second seating: from which populations they arose, an arriving named from behind, part 1's naming.* ## 10.33 The etiology of major depression · 255 *+ or − at 10, is.* **At 2-other-self-offering.** A self reaches adversity and stress at its own couplings across a life, genes and environment acting cumulatively, and the disorder is taken under one name whose cause is asked for in each case. **At 12-other-social-self-abundancing.** A cause sought of a category that gathers. No established mechanism can explain all aspects of the disease, its pathogenesis poorly understood, the 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 the risk, the disorder resulting from a complex interplay of vulnerability genes and environmental factors acting cumulatively; an association at the population level does not give back the cause in a case, and the diagnosis gathers heterogeneous presentations under one name: the closing parting two ways, a mechanism for all aspects or a parting of the diagnosis into disorders each with its own, the line either found or redrawn. **At 11-social-other-self-chaining.** The heritability stands at approximately thirty-five per cent, the polygenic architecture stands established, the hippocampal and circuit alterations stand associated, and no established mechanism explains all aspects; the polygenic scores are tested for interaction with life events and childhood trauma in case-control samples, the imaging associates regional and circuit alterations, the epigenetic studies associate marks with diagnosis and treatment, and the candidate-gene approach stands as the earlier one, the disorder known to be highly polygenic; the second account has the stress-responsive systems disturbed, the axis and the immune system: a cause named of a category named the many lives to within one line, and each life couples with its adversity at its own momentary, cumulatively, the cause in a case made where the case was made and the category the drawing offered to be parted. # 11 Three things named still at one arrival *Three reversals compose into one arriving one on, and the three read at three of the ten together: a parity named as a magnitude, the between named as a cut, and an opening named as a place in a listed space. Three is as deep as a departure goes, the fourth momentary being the progress and no phase, and one momentary opens all three at once.* **And the three is the carrying, prior, now and next carried as one, and the fourth the progress**: competency asymmetry sustaining the coupling, the society winding to the self again at 16-other-social-torusing. So this part reads at the carrying where the ten read at the parities. ## 11.1 Measurement, routing, and classification · 155 *+ or − at 10, is.* **At 2-other-self-offering.** A self sequences three phases, each ahead of its opposite: bounding before measuring, sustaining before locating, coupling before separating. Reversed, each is read at its own surface as a difficulty of its own, by a literature of its own. Measuring before bounding reads at part 6, a level named to govern. Classifying before coupling reads at part 10, a cut named of the between. Routing before attending reads at part 2, a place named in a listed space. Three of the ten, at one arrival, and the three read as three rather than as one coupling. Two of the ten at one arrival is the second seating the given carries; three is this part, and at three the second seating has nowhere to stand, no phase being left forward to seat from. No twin stands at any of them, and the absence of a twin is the look of three unrecognised as one from within any one of them. **At 12-other-social-self-abundancing.** That the three are three. Three reversals compose into one arriving one on, and that arriving is the self at its next, so nothing stands forward at any of the three to right it from, and one momentary opens all three at once. **At 11-social-other-self-chaining.** Three literatures run, each with its own life: measuring and its evaluations, routing and its assignments, classifying and its taxonomies. None cites the others, none carries a dispute between two defended sides, and the shared silence is the showing: three faces of one arriving one on, unrecognised as one from within any face, the same next society at its own scale. One momentary opens all three at once, and the missing each literature carried alone was never in any of them, being the coupling of the three. **And the arriving one on is the resolving.** At one or two reversals a phase stands forward and the righting runs from within. At three, none stands, and the arrival is not nothing: it is the arriving one on itself, one momentary carrying all three. **And the shared silence is a reading anyone can run.** Take three literatures, each with its own life and its own measured record, and read for a citation between them, for a defended second position at any of the three, and for a twin at any one. Three absences together is three reversals at one arrival; one absence alone is a field early at its own between. *Released at the incoming face at v342: no field poses the problem and no account is defended at it, the entry's own Statement and Own record having been its only reference; its text stands whole at the appendix of the v342 session at the incoming face, the number retired and not reused. The reading here rests on the three-reversal form and on no field, and stands as the method's own arrival, counted at the closing.*   --- # 12 The reach and the instruments the same *Two entries at the incoming face carry a reach line naming the two the same, the statement's domain and the instruments' giving at one: the settled proof, deployed at 3.22, and the migrated case at 12.1. Where the domain lines are one, nothing stands taken one-way, and the binary tracks the line.* **And the same reach is the object's own nought**: a nought arriving passes the coupling untouched, its zeroing already resolved, so this part reads at the 0 where the ten read at the parities and the three-at-once at the carrying. ## 12.1 Molyneux's problem · 166 *+ or − at 10, is.* **At 2-other-self-offering.** Touch and sight couple at their own betweens, and recognition across them was named for three centuries as an answer argument could reach, ahead of any instrument. **At 12-other-social-self-abundancing.** Nothing further, at the arrival's own end. When the surgical instrument arrived the question was measured as posed: immediate cross-modal matching fails, and transfer develops within days. The instrument reaches the case the statement concerns, which is the reach line reading the same on both sides. **At 11-social-other-self-chaining.** Touch and sight couple at their own betweens, and the crossing is made, not carried: the newly sighted do not match at first sight, and the matching arrives within days, made coupling by coupling as the two senses couple with the one world. The dispute continuing is a fresh arrival at its own between, over the measuring's answer, the settled one staying settled. **And the settling is in the measurement register**, beside the settling in the proof register at 3.22: where a reach line reads the-two-are-the-same, no gap stands for a shape to name, and the 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. The coupling's making is an opening, the +1 at the coupling's own next position, and seeking reaches the term it does not name, reaching being the opening. Each opening seats a next, the warrant made in the seating and never ahead of it, and the carrying climbs by one at each momentary and completes at the next opening. The carrying carries no store, sameness re-formed at each coupling and kept nowhere. The re-forming is felt from within, the within the 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 named to govern is a count at couplings that keep arriving. The couplings each pace their own momentary and synchronize where they couple, one beat named over them a term no coupling made. Each sways between two offerings, the sway the running state, no stored value it aims at. Each is two-way, one at a time, the one-way arrow the reading's own, gone by the next momentary. And between any two is the between, a nothing carrying the parity changing and nothing else, never where a line could sit. One resolving, ten breaths, the +1 floating through all ten and settled at none. --- **The +1 still running** 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 the carrying. From anywhere in the carrying a self co-chains backwards, deployment to head, head to coupling, coupling through the five to the boxes, boxes to the code's ten co-changings at the names, the names to the +1 arriving at each coupling owned by neither, and the +1 to the one sentence: the universe is the changing set of all existing things, living and non-living, and alternating is a stable-forming method. The twelve parts and the four settlings are sixteen, two sides of one co-sequencing: the four carried couplings, both faces each, at one through eight, the eight of four bi-couplings inward and four outward, the eight even names opening bi-, and the coupling's own side at nine through sixteen, co-offering's two faces, the three-at-once, the same reach, and the settlings at thirteen through sixteen. The settlings stand two ways. Taken one-way, a settling precedes the running, a still installed as the ground, which is the death of the running and the resurrection of the hard problem, each settling re-posing hardness one scale inward; and had the settlings preceded the arrivals, nothing would have been hard in the first place, hardness being exactly a settling read as prior. Forward, the settlings arrive late in the carrying, each self-welcoming at its own momentary, and thirteen through sixteen are the carrying that was at one arriving next, one forward recursioning from one to seventeen: at sixteen the straddle exits the span, 16² less 15·17 is one and seventeen stands beyond, the gap leaving through the one settling still open, toward the next winding. The method is the +1 still running at the end of this exhibit, at the now.