The graph at f8fdaeb

134 claims · 222 moves · 17 contested · 6 lexicon entries, as the corpus stood at this commit.

Since then

1 claims added · 0 changed status · +1 moves
full diff →

established (5)

c-fisherThe Fisher-Rao metric on the family of univariate Gaussians is hyperbolic with constant curvature -1/2.c-rageContinuous spectrum implies escape from every compact region in Cesaro mean; point spectrum implies almost-periodic recurrence.c-splitStrictly nested local algebras admit an intermediate type I factor (the split property).c-typeiiiLocal algebras in relativistic QFT are type III-1 factors, so they contain no minimal projections and admit no normal pure states.c-wienerThe long-run mean of the squared Fourier transform of a measure equals the sum of its squared atomic masses.

derived (64)

c-039203The 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-04c85cTheorem 10.1's curvature of -1/2 is correct, verified by direct computation of the Riemann tensor from the metric.c-103a90Equation (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-1702fdThe 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-1f79aeA 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-2cb2c3The one-sided averaging window in Theorem 6.2 gives the same limit as the classical symmetric window, for two independent reasons.c-37c5e7The 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-3884cfStandard 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-409138The 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-40fa23A 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-449365The type III-1 classification does extrapolate to warm neural tissue, because any state of finite energy density is locally normal to the vacuum and local normality does not change the local algebra.c-456208Axiom 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-46a841The 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-471da2The 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-4e1ed1The 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-4f7a4fSpread-spectrum clocking divides Definition 6.1's atomicity by the number of modulation sidebands while leaving the total atomic mass unchanged.c-54877bLog-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-5acd10The 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-5cfd9aThe canonical intermediate type I factor is a function of the two algebras and the state alone, so it cannot encode the order-parameter pocket that Axiom 4.1 uses to individuate subjects.c-63f0c8The crossed-product trace measures parts without selecting them, because all projections of equal trace in a type II-1 factor are unitarily equivalent.c-6417faA driven dissipative order parameter has no single real healing length, so epsilon = xi is underdetermined and not merely underived.c-67b72eSpectral atomicity is exactly zero for every physically realisable neural signal, and what its estimators measure is the quality factor of the rhythms divided by the lag budget.c-6b8d9cA 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-6cf973Coherence is not multiplicative over independent modes when their spectra are commensurate, which is exactly the case Chapter 7 calls maximally consonant.c-6eb6e4The valence functional is not well defined, because Dmax is never given a definition anywhere in the corpus.c-70a34dThe 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-7cc684Fluctuation-dissipation fixes beta_eff at the tissue temperature, so one unit of modular parameter is 25 femtoseconds and the 8e-11 K figure is a restatement of the specious present rather than a prediction.c-7fd2e0Order-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-81a8aeDmax 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-836f6cSkew 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-853dcfThe 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-89604fIn human sleep EEG within subject, specparam-residual spectral atomicity is higher in waking than in N3 slow-wave sleep.c-8a3219Positive 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-8d06ddThe 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-8df662The 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-9101b8Prediction 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-965521The obstruction to estimating atomicity is the frequency domain rather than the 1/f background, and a cross-segment time-domain U-statistic estimates the lag-truncated atomicity with bias two orders of magnitude below the periodogram estimator.c-9afce9For 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-9bbef4A 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-9c12a8Modular flow on a type I factor lies in the trivial outer class, so the split factor that Axiom 4.1 identifies with the subject carries no state-independent intrinsic time.c-9dab32Proposition 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-a44a0bDenying 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-a51fb6The 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-ab1163The 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-ab9e38The 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-annealEscaping a frustrated state requires a drive scaling as the three-halves power of its rigidity, with a finite therapeutic window.c-areacapThe information capacity of a moment of experience scales with the area of its boundary, not the volume it encloses.c-b2b355For 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-b32ce9The 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-bf2625A GPU's clock-locked electromagnetic mode scores at or above cortical gamma on the corpus's operational coherence index, at every lag budget.c-c28da2Topological pockets of a coarse-grained order parameter in a finite dissipative medium do not lie in inequivalent superselection sectors, so the frame-invariant separation of subjects is decoherence after all.c-c4c1a5Removing the aperiodic component before estimating spectral atomicity increases the bias rather than reducing it, because atomicity is a ratio of quadratics and subtraction empties the denominator faster than the numerator.c-c51358The 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-c97280Proposition 6.4 is true in both directions, and the singular continuous case does not break it.c-cosmoPanpsychism, given the algebra of quantum field theory, must be cosmopsychist rather than micropsychist.c-d54489At the parameters c-areacap uses the cortical sheet is about two and a half collar-widths thick, so the area law is evaluated outside its asymptotic regime and does not separate numerically from a volume law.c-d63d6dThe coefficient in the area law counts local field species below the collar, and for macroscopic QED in an absorbing medium it is between 1e4 and 1e14, so the 1e5 figure in c-areacap is unconstrained.c-e218d3The 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-f4f5cfType 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-fa2321No unbiased estimator of spectral atomicity exists at any record length, under any background, because atomicity is discontinuous below the frequency resolution.c-fed0c5Every 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.c-llm-characterIf the ubiquity axiom holds, a running language model has intrinsic phenomenal character.c-lognormalValence is log-normally distributed, and the variance of log-valence grows linearly in the number of bound modes.c-symmetryThe symmetry meant by the Symmetry Theory of Valence is almost-periodicity of the modular orbit, measured by the atomic mass of the spectral measure.

posited (61)

contested (1)

c-convergence-evidenceIndependent convergence of multiple models on the same partition of their state-space is evidence that the partition tracks something real.

open (3)

c-epsilonThe identification of the split collar with the Ginzburg-Landau healing length is stipulated, not derived.c-estimatorNo unbiased estimator of spectral atomicity under 1/f backgrounds is known, so the theory's central quantity cannot yet be measured.c-selfavgFrustration requires a disorder average, but a single brain is a single realisation, and non-self-averaging is precisely what replica symmetry breaking asserts.

← all history