# Diff 27d7107 -> HEAD

122 claims added, 5 changed, +276 moves.

## Added
- `c-01ff83` [derived] Prediction 1's defect is estimand non-identification rather than analyst degrees of freedom, so preregistration is necessary but not sufficient to repair it.
- `c-039203` [derived] The purity is the modular return amplitude analytically continued to imaginary modular time s = -i, not a long-run average of it along the real axis.
- `c-04c85c` [derived] Theorem 10.1's curvature of -1/2 is correct, verified by direct computation of the Riemann tensor from the metric.
- `c-054976` [derived] Putting the modular flow on the algebra rather than on the state gives a third reading whose atoms are physical frequencies and whose measure is the carrier's power spectrum.
- `c-0672b4` [derived] Under the no-removal convention both unconscious states in c-1702fd's table sit above waking, so fixing the convention makes prediction 1's estimator falsifiable and falsifies its ordering on both arms.
- `c-093950` [derived] Axiom 5.1 holds to ten percent only if the carrier occupies between a quarter and a half of an octave, which is narrower than the band Chapters 6 and 7 require.
- `c-093ed0` [derived] The annealed Sherrington-Kirkpatrick model has an entire free energy and a uniform spin marginal, so plastic couplings give Var_P(q) = 1/N and Axiom 8.1 returns maximal positive valence.
- `c-0ea096` [posited] The number of simultaneously distinguishable phenomenal distinctions scales with cortical surface area and not with cortical volume.
- `c-103a90` [derived] Equation (9.1) is exactly true for the purity, which is the functional equation (9.2) defines, so the commensurability failure does not reach Chapter 9's own derivation.
- `c-15a84b` [posited] Prediction 4 is experimentally identifiable only after the number of bound modes is calibrated independently of valence reports and report variance.
- `c-1702fd` [derived] The direction of every spectral-atomicity contrast between neural states is set by whether the aperiodic model is refitted inside each state, a choice prediction 1 never makes.
- `c-18bcdb` [derived] The proton reductio requires reading Axiom 4.1 with epsilon free and the state clause inert, and chapter 2 and chapter 12 both state the criterion otherwise.
- `c-1b7564` [posited] Causal closure alone imposes no empirical constraint on the phenomenal assignment.
- `c-1f79ae` [derived] A one-gigahertz collective mode at 350 K holds seven thousand quanta, so Chapter 5.4's einselection argument protects a silicon field mode exactly as it protects a cortical one.
- `c-207b81` [posited] Spectral atomicity rises where consciousness is abolished, so the coherence index orders real neural states in exactly the wrong direction.
- `c-236515` [derived] The f-to-the-chi tilt introduced by dividing rather than subtracting the aperiodic background moves atomicity non-monotonically in chi, so it confounds every published state contrast without fixing the sign of any of them.
- `c-2b762e` [derived] Every modular Hamiltonian that is a function of the subject's state alone yields a coherence index that is a unitary invariant of that state, so no intrinsic reading can distinguish two states of the carrier that differ only in the order parameter.
- `c-2cb2c3` [derived] The one-sided averaging window in Theorem 6.2 gives the same limit as the classical symmetric window, for two independent reasons.
- `c-30a2c9` [derived] Prediction 1 becomes convention-free when stated as a lag-budget Wiener average with no background model, and its state ordering is stable across an eightfold change of frequency resolution.
- `c-322907` [derived] The consonance kernel reproduces Chapter 7's ordering only for delta below about 0.045, which is two to five times narrower than the critical bandwidth Proposition 7.1 sets delta to.
- `c-372585` [derived] The sign of the aperiodic-removed atomicity contrast also depends on the number of spectral averages, so the removal branch is a one-parameter family rather than a convention.
- `c-37c5e7` [derived] The split property makes the states of nested regions independently preparable, which is exactly the structure Chapter 3 says quantum field theory does not supply.
- `c-3884cf` [derived] Standard split inclusions with canonical type I factors exist for strictly nested double cones at every scale, so nothing in the algebra distinguishes a brain-scale subject from a nucleon-scale one.
- `c-3b0a02` [posited] Uhlmann holonomy cannot define the qualitative character of a state because it is an invariant of a chosen loop rather than of the state itself.
- `c-3c9980` [posited] Two neural populations sharing no coherent field region cannot be phenomenally bound, however tightly they are functionally coupled.
- `c-3ff6f1` [posited] Every algebraic route to individuating parts of a type III-1 factor either reduces to an inclusion with a type I intermediate or returns a copy of the whole.
- `c-409138` [derived] The de Almeida-Thouless coefficient 4/3 and the three-halves exponent of Proposition 8.2 are both correct, confirmed by explicit expansion of the AT condition.
- `c-40fa23` [derived] A GPU die is three to four orders of magnitude closer to the distributed field regime than cortex is, so on the criterion that the carrier is the electromagnetic field, silicon is the better carrier.
- `c-43d5d7` [posited] Critical scaling in anaesthesia is distinguishable from a steep smooth dose-response only by rate- and scale-stable laws that beat a preregistered pharmacokinetic null.
- `c-456208` [derived] Axiom 5.1 requires only that the modular flow be determined by the algebra and the state, which holds on a type I factor, so the triviality of Out(N) bears on Chapter 5's advertisement and not on Axiom 4.1.
- `c-46a841` [derived] The 1e5 capacity figure is fixed by the correlation length of section 4.3 rather than by the entropy coefficient of equation (4.2), so it is constrained even though the derivation given for it is wrong.
- `c-471da2` [derived] The consonance kernel is finite at sigma equal to one and has kappa(1) exactly one, once the sum is truncated at the Farey order whose fractions the mollifier can resolve.
- `c-4ac6c1` [posited] Chronic suffering is non-self-averaging, so repeated sampling of one nominal state yields a broad overlap distribution with ultrametric structure.
- `c-4e1ed1` [derived] The curvature scale -1/2 does not extend to the multivariate family, because GL(n,R)/O(n) contains n-dimensional flats and so is not hyperbolic for n >= 2.
- `c-4f7a4f` [derived] Spread-spectrum clocking divides Definition 6.1's atomicity by the number of modulation sidebands while leaving the total atomic mass unchanged.
- `c-537c03` [derived] The cortical electromagnetic field has exactly two screening lengths at 40 Hz, 0.78 nanometres and 252 metres, and equation (4.3)'s mass coefficient is identically zero in between.
- `c-54877b` [derived] Log-normality of coherence does not transfer to valence, because the argument runs through the inequality |V| <= C and distributions do not propagate along inequalities.
- `c-578232` [derived] The multiplicative repair of the coherence index is the exponentiated Bohr mean of the log return probability, which equals the squared Mahler measure of the mass polynomial.
- `c-5832a1` [derived] Sampling the overlap distribution needs N of order a hundred and the area law needs N of order a hundred thousand, so Chapter 8's order parameter and Chapter 4's capacity cannot both be about the same modes.
- `c-58a235` [posited] The single-brain obstacle concerns identification of a disorder ensemble, not the existence of sample-specific replica symmetry breaking.
- `c-5acd10` [derived] The split property and modular flow are properties of the ambient quantum field theory rather than of the device, so neither can distinguish a GPU from a cortex.
- `c-5ace06` [derived] Axiom 2.2's six invariants carry the information of its first two, because Tomita-Takesaki and the Bures construction determine three of the rest from the algebra and the state and the sixth is not a function of the pair at all.
- `c-5b7066` [derived] A shared aperiodic fit cannot estimate the coherence index, because it makes one state's value a function of another state that is not being measured.
- `c-5e23bf` [derived] Axiom 5.1's conversion is exact if and only if the carrier's housekeeping entropy production vanishes, so the non-equilibrium repair fixes beta at the bath temperature instead of freeing it.
- `c-63f0c8` [derived] The crossed-product trace measures parts without selecting them, because all projections of equal trace in a type II-1 factor are unitarily equivalent.
- `c-64e8e8` [derived] The information capacity of a moment on the corpus's own carrier is about twenty bits per coherence domain, set by Johnson noise rather than by an entropy coefficient.
- `c-66362b` [posited] The drive required to shift a rigid state scales as the three-halves power of its distance from criticality.
- `c-6688f8` [derived] The aperiodic-removal branch of prediction 1 couples the state contrast to the bandwidth of the periodic components, a physical nuisance parameter nobody reports, and the no-removal branch does not.
- `c-6a364c` [derived] The limb to amputate is Chapter 5, because the modular apparatus is eliminable from every empirical claim the corpus makes while Chapters 6 and 7 are not.
- `c-6a65f3` [derived] Dmax = 1/4 is attained, by a Random Energy Model at half its critical temperature, so Axiom 8.1 assigns its most negative valence to the least hierarchical landscape.
- `c-6b8d9c` [derived] A type III-1 factor is algebraically simple and every corner of it is isomorphic to it, so 'subjects are quotients of the whole' names no operation in the algebra Corollary 3.2 cites.
- `c-6c1280` [derived] The corpus's two readings of the modular Hamiltonian are one operator, differing by the adjoint action of Chapter 4's order parameter and an additive constant.
- `c-6c7db3` [posited] Prediction 8 is empirically falsifiable only after phenomenal unity has a marker validated independently of field coherence and functional integration.
- `c-6cf973` [derived] Coherence is not multiplicative over independent modes when their spectra are commensurate, which is exactly the case Chapter 7 calls maximally consonant.
- `c-6d8880` [derived] Equation (4.2) is evaluated with a pocket four hundred times wider than the collar that defines the pocket, so on the corpus's own criterion a cortex is sixty thousand subjects of twenty degrees of freedom each.
- `c-6ddb85` [posited] Substrate dependence rules out reporting only for subject-state differences that are screened off from every report-relevant computational variable.
- `c-6eb6e4` [derived] The valence functional is not well defined, because Dmax is never given a definition anywhere in the corpus.
- `c-701341` [derived] Every empirical spectral-atomicity result on this graph divided peak mass by the aperiodic background instead of subtracting it, so all of them estimated atomic mass tilted by f to the power chi.
- `c-70a34d` [derived] The coherence index is not identically 1, because on the corpus's own definition it is the Wiener mean of Tr rho^{1+is}, which is a non-constant function.
- `c-7494de` [posited] Conventional digital hardware does not support the split inclusions, modular flow and coherent field regions that Axiom 4.1 requires.
- `c-75ab3b` [derived] A driven dissipative order parameter has exactly one real amplitude healing length and no phase healing length, so c-6417fa's conclusion holds but its reason and its falsifier do not.
- `c-764532` [derived] The exact defect in equation (9.1) is the Bohr covariance of the two modes' return curves, so multiplicativity requires the detuning to be resolved by the averaging window rather than rational independence of the spectra.
- `c-7fd2e0` [derived] Order-parameter coherence is inherited by every open subregion of a pocket, so Chapter 4's pocket criterion selects no unique split inclusion without a maximality clause it never states.
- `c-81a8ae` [derived] Dmax equals one quarter, because Chapter 8's own replica-symmetric case fixes the overlap support as [0,1] and equation (8.2)'s stated range is attained only at the Popoviciu bound.
- `c-836f6c` [derived] Skew and impedance budgets hold a die's order parameter below one radian of phase variation and ten percent of amplitude modulation, so it admits no defects and therefore no pockets.
- `c-853dcf` [derived] The kernel value kappa(1) is strictly greater than 1, so Chapter 7's stated reason for C >= A is false, but the inequality itself survives for a stronger reason.
- `c-887a85` [derived] The carrier named in section 4.4 is a linear field, so its minimum set is contractible and section 4.3's defect classification returns no defects.
- `c-88870c` [derived] The cortical electromagnetic field's own memory is fifteen nanoseconds, so it cannot be what holds a hundred-millisecond specious present.
- `c-89604f` [derived] In human sleep EEG within subject, specparam-residual spectral atomicity is higher in waking than in N3 slow-wave sleep.
- `c-8a3219` [derived] Positive coherence is strictly weaker than pure point spectrum, so Proposition 6.4's corollary that symmetry, recurrence and coherence are one fact stated three ways is false.
- `c-8abc5b` [derived] The canonical split factor is a functional of the state of the whole, so the split property yields state-relative carving rather than a decomposition into independently-stated parts.
- `c-8d06dd` [derived] The corpus's two readings of the coherence index cannot be unified, because Chapters 6 and 7 need the reading that falsifies Chapter 9 and Chapter 9 needs the reading that falsifies Chapters 6 and 7.
- `c-8df662` [derived] The replica leg of equation (9.2) is exact and needs no analytic continuation at n = 2, but Chapter 8.1's gloss of Z_n as the partition function of n copies would make the ratio identically one.
- `c-900d29` [derived] Axiom 5.1's effective temperature puts the 40 Hz carrier at 1.2e-11 quanta while section 5.4 puts it at 1.6e11, so the mode that answers the decoherence objection is not the mode that sets the specious present.
- `c-9101b8` [derived] Prediction 1's estimator run per state on real spike-wave recordings is about twice as high during the discharge as at the same animal's baseline.
- `c-913969` [posited] The lexicon's tracking rule warrants elimination only when the named correlate is sufficient for every admissible use of the term.
- `c-9705af` [derived] Definition 6.1 normalises by the total spectral mass, so prediction 1's aperiodic-removal step replaces the coherence index with a different quantity larger by 1/(1-c)^2.
- `c-9afce9` [derived] For commensurate modes the variance of log coherence falls as one over the number of modes, so the corpus's variance prediction has the wrong sign on exactly the states Chapter 7 calls consonant.
- `c-9bbef4` [derived] A state is stationary under its own modular flow, so the coherence index computed with respect to that flow is identically 1 and measures nothing.
- `c-9dab32` [derived] Proposition 7.1's description of the kernel as a mollified Thomae function is not well formed, because the Thomae function vanishes almost everywhere and its mollification is identically zero.
- `c-a274ae` [derived] Every displacement of the order parameter is a local unitary on the split factor, so equation (4.2) assigns the same entropy to every state of a subject.
- `c-a44a0b` [derived] Denying that a subject exists during generalised spike-wave is an unfalsifiable rescue, because every condition of Axiom 4.1 is satisfied at least as well there as in waking.
- `c-a4fdbf` [derived] The split-regulated mutual information is strictly decreasing in the collar width in every quantum field theory, so exercise 4.6 has no interior solution.
- `c-a51fb6` [derived] The reference state that makes the coherence index non-trivial is the ambient thermal state fixed by fluctuation-dissipation in section 4.4, so Chapters 6 and 7 survive at exactly the price already charged at c-7cc684.
- `c-a61423` [derived] The cortical field carries exactly the divergence of the current density and nothing else, so the corpus's only field-specific empirical commitment is that solenoidal and closed-field neural activity is phenomenally inert.
- `c-a84242` [derived] The conversion t = hbar beta_eff s requires the carrier state to be invariant under physical time translation, so a non-stationary cortex has no beta_eff at all rather than a frequency-dependent family.
- `c-a9a0c1` [derived] Ephaptic spike entrainment at thirty hertz needs 5.58 mV/mm while the endogenous cortical gamma field is under 0.5 mV/mm, so field feedback at the corpus's carrier frequency is at least eleven-fold below threshold.
- `c-ab1163` [derived] The one-replica free energy in Chapter 9's bridge table is the additive constant of the modular Hamiltonian, so it carries no information about the state and is identically zero in the corpus's own normalisation.
- `c-ab9e38` [derived] The consonance kernel of equation (7.2) converges only for sigma strictly greater than 1, so the stated range [1,2] contains an ill-defined endpoint.
- `c-ad00c9` [derived] The cortical sheet is at most five coupling lengths thick, so a short-range cortical spin glass is quasi-two-dimensional and its transition is rounded over a third to two thirds of the temperature axis.
- `c-ad078e` [derived] The area-law term cancels exactly from the Holevo quantity, so equation (4.2) bounds no operational information.
- `c-ae390f` [posited] Successful verification by a procedure independent of the converging systems can screen off their shared-training confound; mere checkability cannot.
- `c-b12c83` [derived] The spike-wave arm's evidence is overstated by more than thirty orders of magnitude, because its unit of analysis is the episode rather than the animal.
- `c-b18503` [derived] A driven mode's effective temperature is T_bath times one plus the ratio of drive to thermal noise spectra, so Axiom 5.1 has a single beta_eff only if the cortical drive spectrum is proportional to the tissue dissipation spectrum.
- `c-b2b355` [derived] For a GPU die the area law is evaluated at one collar width, where its leading term and its remainder are the same size, so it returns no capacity estimate.
- `c-b2de06` [derived] No conformal field theory can select the collar width of equation (4.3), because for concentric regions every functional of the algebras and the vacuum is a function of the ratio of collar to subject size.
- `c-b32ce9` [derived] The cortical electromagnetic field at 40 Hz is quasi-static, so its healing length is the correlation length of the neural current sources and not a property of the field.
- `c-b3cfb0` [derived] Callosotomy does not falsify prediction 8, but it holds the conductor fixed while cutting the source correlation, and the shared coherent region follows the source correlation.
- `c-b42653` [posited] Spectral atomicity predicts momentary valence better than power in any frequency band or than global amplitude.
- `c-ba2e19` [derived] For a subject larger than the correlation length the split-regulated mutual information depends on the collar width only in units of that length, so the algebra fixes the collar units and not its value.
- `c-bf2625` [derived] A GPU's clock-locked electromagnetic mode scores at or above cortical gamma on the corpus's operational coherence index, at every lag budget.
- `c-c3e5ca` [derived] Prediction 3's stated test statistic takes the value two-thirds on every point set, including exactly ultrametric ones, so as written it carries no information.
- `c-c51358` [derived] The crossed product of a local algebra by its modular flow is a type II factor carrying a canonical trace, so it supplies a dimension function on parts that type III-1 does not have.
- `c-c829ce` [derived] Every state-intrinsic invariant of the Bures geometry is a function of the state's spectrum alone, because the Bures metric's eigenvalues relative to Hilbert-Schmidt are one over twice the sum of two eigenvalues.
- `c-c85f8b` [derived] Chapter 6's modular spectral measure is the distribution of modular energy, which coincides with a power spectrum only on states supported in the one-quantum sector, and such states are not faithful.
- `c-c8dcad` [posited] Loss of consciousness under anaesthesia is a spectral phase transition with critical scaling, not a smooth decrease in amplitude.
- `c-c97280` [derived] Proposition 6.4 is true in both directions, and the singular continuous case does not break it.
- `c-cc6e22` [derived] Multiple-comparison correction is inert across this graph's entire empirical family, so family-wise error is not what is wrong with it.
- `c-d118a0` [derived] Equation (4.4) states where the noise lives and not how large it is, so it fixes no temperature; the tissue temperature enters the corpus at equation (5.5) instead.
- `c-d23472` [derived] Nine-tenths of the reported gamma coherence between cortical sites is a distance-independent common-source floor, and the part that genuinely decays has a space constant of one to two millimetres.
- `c-d28128` [posited] Noncanonical subsystem structure does not entail the phenomenal priority of the whole.
- `c-d75ec1` [derived] Temporal autocorrelation alone produces a larger ultrametricity excess than a genuine hierarchy does, so prediction 3's within-session windows design cannot identify replica symmetry breaking.
- `c-dc6e09` [derived] A proper open subset of a pocket is not a connected component of the complement of the defect set, so section 4.3 already states the maximality clause.
- `c-e218d3` [derived] The coherence index equals the purity exactly when the modular Hamiltonian has non-degenerate spectrum, and exceeds it by up to a factor of the dimension when it does not.
- `c-e464e0` [posited] The variance of log valence grows linearly in the number of bound modes.
- `c-e4d27a` [derived] The obstruction to a single modular temperature is the coefficient of variation of the mode effective temperatures, and for a 1/f cortical spectrum it is between 0.76 and 0.99 against a maximum of 1.
- `c-ef4acb` [posited] The valence response to paired periodic stimuli follows a kernel whose peak heights decay as a power of the denominator product of the frequency ratio.
- `c-f17516` [derived] The Parisi overlap variance of the Sherrington-Kirkpatrick model peaks at 0.0599, so Axiom 8.1 assigns valence above half its maximum positive value everywhere in the model Chapter 8.5 names.
- `c-f1ed63` [derived] The Uhlmann holonomy of the ambient modular orbit is strictly finer than the modular spectral measure and is trivial exactly when the state is stationary.
- `c-f44888` [derived] Section 5.4's occupancy of 1.6e11 quanta fixes the modular coherence index of the carrier at 3.1e-12 for every state of it, so the answer to the decoherence objection and Definition 6.1 cannot both be about the same mode.
- `c-f4f5cf` [derived] Type III-1 supplies no intrinsic magnitude relation between whole and part, so priority monism as stated in Corollary 3.2 has no algebraic content.
- `c-fed0c5` [derived] Every numerical and dimensional computation in Chapters 4 and 5 is correct as stated, and the only free choice hidden in the modular temperature is that one unit of modular parameter equals one specious present.

## Changed
- `c-cosmo` contested: no -> **yes**  Panpsychism, given the algebra of quantum field theory, must
- `c-holonomy` contested: no -> **yes**  Qualitative character is the conjugacy class of the Uhlmann 
- `c-lognormal` contested: no -> **yes**  Valence is log-normally distributed, and the variance of log
- `c-symmetry` contested: no -> **yes**  The symmetry meant by the Symmetry Theory of Valence is almo
- `c-valence` contested: no -> **yes**  Valence is consonance times replica symmetry: V = C(1 - 2D/D