CORRECTION NOTICE (v5, 2026-09-06). The central result of v1-v4 is WITHDRAWN. This record has not been peer reviewed. Issued 2026-09-06 by the author (v5 of this record). This notice was added to the archived record; the manuscript itself is unaltered. This record has not been peer reviewed. What is wrong The force exponent reported here as alpha = 3.92 +/- 0.16 is an artifact of the fitting procedure, not a property of the data. The fit was unweighted least squares in linear space applied to a steeply falling profile, which places 95.8 percent of its objective on the single point at the shortest retained separation. Re-fitting the same data with nothing discarded, changing only the error model, gives 2.82 (relative-error weighting) or 2.89 (log-space regression). Across fifteen combinations of standard estimator and fit window the exponent spans 2.53 to 3.92, and the value published here is the largest of them. What the data show instead, and how firmly The retraction is certain. The replacement is not. On the open 24-site chain the same data give alpha = 2.6 +/- 0.2, where the interval is the spread of a plateau in the local logarithmic slope over six consecutive separations, not a statistical error (the bootstrap error on the published fit to the same data is 0.63); the plateau value was reproduced at 2.5921 by a separately written implementation run on the same recorded state (SIM-2026-073). This is a single geometry at a single size. On a 24-site periodic ring, analysed with chord distance as pre-registered, two probes that are both energy-density-like (Delta = 1) give 1.83 and 2.37 against a CFT two-point value of 2 (SIM-2026-074): one size, not converged, disagreeing with each other by 29 percent, and not attributable to a single operator channel. No corrected exponent is established. The exchange channel is an open question. Treat 2.6 +/- 0.2 as the provisional open-chain value, not as a result. Also withdrawn or voided alpha = 3.92 +/- 0.16 (24 sites) and alpha = 3.97 +/- 0.15 (16 sites, exact) from stress-tensor exchange. Was: headline result and its first corroboration. Now: withdrawn. Why: the same estimator artifact: both move in lockstep under it (3.92 to 2.56, 3.97 to 2.75 on dropping the contact point), because they share one observable, one fit window and one fitting routine. scalar exchange (alpha = 2) excluded. Was: stated as excluded at about 12 sigma. Now: withdrawn. Why: the 12 sigma used the covariance error 0.16; at the bootstrap error 0.63 computed before release the exclusion is about 2.2 sigma, and under any window starting at separation 3 the point estimate itself falls to about 2.56. alpha = 4 is universal; alpha = 4.00 at Ising, tricritical Ising and Potts. Was: confirmed at three classes. Now: withdrawn; the operator towers at all three classes stand. Why: the exponent was measured only at Ising and inherited by the other two; the towers are spectra, not forces. third independent evaluation alpha = 4.07 (chi = 3 MERA), and with it the statement that this was the first holographic force measurement from an optimized tensor network state. Was: supporting evidence and a priority claim. Now: both withdrawn. Why: the profile changes sign inside its own fit window and cannot be a fixed-sign power law; the priority claim rests on that evaluation alone and was never gated against prior work. the discriminating test: stress tensor (Z_j Z_j+1) versus spin primary (X_j). Was: registered killer test. Now: void. Why: at the critical point these are one operator, related by exact Kramers-Wannier self-duality. Measured on the periodic ring: identical expectation values to 1e-15 and identical force profiles to 1e-13 at 14 sites, 2.4e-9 at 24 sites (SIM-2026-074). Open boundaries break the duality, which is why the open-chain run of this test (SIM-2026-073) showed a spurious difference between the two arms. The test compared the energy density to itself. Neither label was correct: Z_j Z_j+1 is the energy density, not the stress tensor; X_j is its dual, not the spin primary. transport time T = (pi/2) l_AdS to 1.2 percent as a geometric prediction. Was: confirmed. Now: measurement stands (T = 2.239 at N = 16); geometric reading not established. Why: l_AdS cancels in the cited derivation, which also gives pi rather than the pi/2 the manuscript compares against; the chi = 3 estimate of l_AdS gives a 57 percent miss; the transport driver never applies a MERA. The true spin primary Z_j was never in the design, and the direct replacement test is blocked: Z_j is odd under the Z2 symmetry, so the energy-difference observable used throughout this work subtracts across symmetry sectors and is undefined for it. A replacement test using two Z2-even probes has been pre-registered (PREREGISTRATION-T.md, committed before its driver) and run; its result is deliberately not part of this correction and will appear in a later version. Not previously reported The published fit has a reduced chi-squared of 6.008 on 9 degrees of freedom, and a bootstrap standard deviation of 0.63 rather than the quoted 0.16. Both were computed before release and omitted. What is unaffected Of the claims in this record: the two-phase optimization method, the chi = 3 criticality threshold, the exact-diagonalization gates, the measured OPE coefficient C_sigma-sigma-epsilon = 0.50 +/- 0.03 against the exact 1/2, and the conformal towers at all three classes. Not part of this record, mentioned only because they are sometimes read together with it: the later C_TTT stress-tensor self-coupling measurements (SIM-2026-067/068/069, dated after this record) and the matched off-critical ring control (SIM-2026-074) are unaffected by this correction and make no claim about the force exponent. How the error was found and what this record contains The error was found by the author's own internal adversarial audit, not by a reviewer; the journal submission it was found after is closed, and no review of this work has taken place. Files in this record: the full re-analysis (SIM-2026-072.json, driver, figure), the pre-registered chain test (SIM-2026-073.json) and ring test (SIM-2026-074.json) with both pre-registrations as committed before the runs, the runnable drivers with their shared module and the negative test suite for their validation gates, and the error register (ERRATA.md). Concept DOI 10.5281/zenodo.19660302 always resolves to the current version. The abstract of the original manuscript follows unchanged, for the record. Every claim in it about the force exponent should be read against the correction above. We report results from classical simulation of critical spin chains that establish quantitative physical content in the MERA-AdS correspondence. First, the interaction energy between boundary-primary excitations follows a power law F(dr) ~ dr^(-alpha) with three consistent evaluations yielding alpha = 3.92 +/- 0.16 (24q), 3.97 +/- 0.15 (16q), and 4.07 +/- 0.18 (16q chi=3 MERA), all consistent with stress-tensor exchange (alpha = 2*Delta_T = 4) and inconsistent with scalar exchange (alpha = 2); the exponent is explained by the Ising CFT fusion rule eps x eps = [1]. Because Delta_T = 2 is fixed by conformal symmetry in every unitary 2D CFT, alpha = 4 is universal: we confirm this at two further fixed points - the tricritical Ising model (c = 7/10), where a scale-invariant MERA recovers the full M(4,5) primary spectrum (Delta_sigma = 0.092, Delta_eps = 0.204, Delta_T = 1.999), and the three-state Potts model (c = 4/5), where a Z3-symmetric MERA at chi = 12 recovers Delta_sigma = 0.134, Delta_eps = 0.805, Delta_T = 2.001 - giving alpha = 4.00 at all three universality classes. Second, the holographic transport time matches the AdS_3 null geodesic prediction T = (pi/2) l_AdS to 1.2% at N = 16 sites on a time-grid-converged measurement, with the residual shrinking from 2.8% at N = 12. Third, we introduce a two-phase optimization method (ALM + Z2 projection) for Z2-symmetric MERA ground states at 24 qubits. Fourth, extending the MERA bond dimension from chi=2 to chi=3 overcomes the expressibility barrier, achieving 0.15% energy error at 16 qubits and enabling the first holographic force measurement from an optimized tensor network state. The OPE coefficient is also measured directly from the fixed-point tensors: C_sigma-sigma-eps = 0.50 +/- 0.03 against the exact Ising value 1/2. A hardware path is designed for Quantinuum Helios (57 CNOTs, 0.57% logical error). Version 4 changes (relative to v3): Transport: N=16 residual restated as the time-grid-converged value of -1.21% (dt = 1e-3), with -2.78% at N=12 showing the finite-size trend; the 0.72% figure in v3 was an artifact of the dt = 0.05 integration grid and is now labeled as such. The N=24 transport point carries a new reliability caveat (double-lobe trace structure). The l_AdS comparison table is recomputed against the converged transport time (best fit 1.425, deviation 1.21%). Effective-mass derivation rewritten in a consistent AdS3 convention m^2 l^2 = Delta(Delta-2); m_eff = 0.693 = 1/l_AdS follows from Delta = 1 exactly. NEW: universality section extended to a third fixed point - a Z3-symmetric MERA at chi = 12 recovers the three-state Potts (c = 4/5) tower, giving alpha = 4.00 at all three universality classes (c = 1/2, 7/10, 4/5). NEW: the OPE coefficient C_sigma-sigma-eps = 0.50 +/- 0.03 measured directly from the fixed-point tensors, with C_sigma-sigma-sigma = 0 at machine precision as the Z2 structural check. Supplemental table row SIM-007 annotated (record lost; script preserved); data availability expanded; Zenodo DOI added to the front matter.
CORRECTION NOTICE (v5, 2026-09-06). The central result of v1-v4 is WITHDRAWN. This record has not been peer reviewed. Issued 2026-09-06 by the author (v5 of this record). This notice was added to the archived record; the manuscript itself is unaltered. This record has not been peer reviewed. What is wrong The force exponent reported here as alpha = 3.92 +/- 0.16 is an artifact of the fitting procedure, not a property of the data. The fit was unweighted least squares in linear space applied to a steeply falling profile, which places 95.8 percent of its objective on the single point at the shortest retained separation. Re-fitting the same data with nothing discarded, changing only the error model, gives 2.82 (relative-error weighting) or 2.89 (log-space regression). Across fifteen combinations of standard estimator and fit window the exponent spans 2.53 to 3.92, and the value published here is the largest of them. What the data show instead, and how firmly The retraction is certain. The replacement is not. On the open 24-site chain the same data give alpha = 2.6 +/- 0.2, where the interval is the spread of a plateau in the local logarithmic slope over six consecutive separations, not a statistical error (the bootstrap error on the published fit to the same data is 0.63); the plateau value was reproduced at 2.5921 by a separately written implementation run on the same recorded state (SIM-2026-073). This is a single geometry at a single size. On a 24-site periodic ring, analysed with chord distance as pre-registered, two probes that are both energy-density-like (Delta = 1) give 1.83 and 2.37 against a CFT two-point value of 2 (SIM-2026-074): one size, not converged, disagreeing with each other by 29 percent, and not attributable to a single operator channel. No corrected exponent is established. The exchange channel is an open question. Treat 2.6 +/- 0.2 as the provisional open-chain value, not as a result. Also withdrawn or voided alpha = 3.92 +/- 0.16 (24 sites) and alpha = 3.97 +/- 0.15 (16 sites, exact) from stress-tensor exchange. Was: headline result and its first corroboration. Now: withdrawn. Why: the same estimator artifact: both move in lockstep under it (3.92 to 2.56, 3.97 to 2.75 on dropping the contact point), because they share one observable, one fit window and one fitting routine. scalar exchange (alpha = 2) excluded. Was: stated as excluded at about 12 sigma. Now: withdrawn. Why: the 12 sigma used the covariance error 0.16; at the bootstrap error 0.63 computed before release the exclusion is about 2.2 sigma, and under any window starting at separation 3 the point estimate itself falls to about 2.56. alpha = 4 is universal; alpha = 4.00 at Ising, tricritical Ising and Potts. Was: confirmed at three classes. Now: withdrawn; the operator towers at all three classes stand. Why: the exponent was measured only at Ising and inherited by the other two; the towers are spectra, not forces. third independent evaluation alpha = 4.07 (chi = 3 MERA), and with it the statement that this was the first holographic force measurement from an optimized tensor network state. Was: supporting evidence and a priority claim. Now: both withdrawn. Why: the profile changes sign inside its own fit window and cannot be a fixed-sign power law; the priority claim rests on that evaluation alone and was never gated against prior work. the discriminating test: stress tensor (Z_j Z_j+1) versus spin primary (X_j). Was: registered killer test. Now: void. Why: at the critical point these are one operator, related by exact Kramers-Wannier self-duality. Measured on the periodic ring: identical expectation values to 1e-15 and identical force profiles to 1e-13 at 14 sites, 2.4e-9 at 24 sites (SIM-2026-074). Open boundaries break the duality, which is why the open-chain run of this test (SIM-2026-073) showed a spurious difference between the two arms. The test compared the energy density to itself. Neither label was correct: Z_j Z_j+1 is the energy density, not the stress tensor; X_j is its dual, not the spin primary. transport time T = (pi/2) l_AdS to 1.2 percent as a geometric prediction. Was: confirmed. Now: measurement stands (T = 2.239 at N = 16); geometric reading not established. Why: l_AdS cancels in the cited derivation, which also gives pi rather than the pi/2 the manuscript compares against; the chi = 3 estimate of l_AdS gives a 57 percent miss; the transport driver never applies a MERA. The true spin primary Z_j was never in the design, and the direct replacement test is blocked: Z_j is odd under the Z2 symmetry, so the energy-difference observable used throughout this work subtracts across symmetry sectors and is undefined for it. A replacement test using two Z2-even probes has been pre-registered (PREREGISTRATION-T.md, committed before its driver) and run; its result is deliberately not part of this correction and will appear in a later version. Not previously reported The published fit has a reduced chi-squared of 6.008 on 9 degrees of freedom, and a bootstrap standard deviation of 0.63 rather than the quoted 0.16. Both were computed before release and omitted. What is unaffected Of the claims in this record: the two-phase optimization method, the chi = 3 criticality threshold, the exact-diagonalization gates, the measured OPE coefficient C_sigma-sigma-epsilon = 0.50 +/- 0.03 against the exact 1/2, and the conformal towers at all three classes. Not part of this record, mentioned only because they are sometimes read together with it: the later C_TTT stress-tensor self-coupling measurements (SIM-2026-067/068/069, dated after this record) and the matched off-critical ring control (SIM-2026-074) are unaffected by this correction and make no claim about the force exponent. How the error was found and what this record contains The error was found by the author's own internal adversarial audit, not by a reviewer; the journal submission it was found after is closed, and no review of this work has taken place. Files in this record: the full re-analysis (SIM-2026-072.json, driver, figure), the pre-registered chain test (SIM-2026-073.json) and ring test (SIM-2026-074.json) with both pre-registrations as committed before the runs, the runnable drivers with their shared module and the negative test suite for their validation gates, and the error register (ERRATA.md). Concept DOI 10.5281/zenodo.19660302 always resolves to the current version. The abstract of the original manuscript follows unchanged, for the record. Every claim in it about the force exponent should be read against the correction above. We report results from classical simulation of critical spin chains that establish quantitative physical content in the MERA-AdS correspondence. First, the interaction energy between boundary-primary excitations follows a power law F(dr) ~ dr^(-alpha) with three consistent evaluations yielding alpha = 3.92 +/- 0.16 (24q), 3.97 +/- 0.15 (16q), and 4.07 +/- 0.18 (16q chi=3 MERA), all consistent with stress-tensor exchange (alpha = 2*Delta_T = 4) and inconsistent with scalar exchange (alpha = 2); the exponent is explained by the Ising CFT fusion rule eps x eps = [1]. Because Delta_T = 2 is fixed by conformal symmetry in every unitary 2D CFT, alpha = 4 is universal: we confirm this at two further fixed points - the tricritical Ising model (c = 7/10), where a scale-invariant MERA recovers the full M(4,5) primary spectrum (Delta_sigma = 0.092, Delta_eps = 0.204, Delta_T = 1.999), and the three-state Potts model (c = 4/5), where a Z3-symmetric MERA at chi = 12 recovers Delta_sigma = 0.134, Delta_eps = 0.805, Delta_T = 2.001 - giving alpha = 4.00 at all three universality classes. Second, the holographic transport time matches the AdS_3 null geodesic prediction T = (pi/2) l_AdS to 1.2% at N = 16 sites on a time-grid-converged measurement, with the residual shrinking from 2.8% at N = 12. Third, we introduce a two-phase optimization method (ALM + Z2 projection) for Z2-symmetric MERA ground states at 24 qubits. Fourth, extending the MERA bond dimension from chi=2 to chi=3 overcomes the expressibility barrier, achieving 0.15% energy error at 16 qubits and enabling the first holographic force measurement from an optimized tensor network state. The OPE coefficient is also measured directly from the fixed-point tensors: C_sigma-sigma-eps = 0.50 +/- 0.03 against the exact Ising value 1/2. A hardware path is designed for Quantinuum Helios (57 CNOTs, 0.57% logical error). Version 4 changes (relative to v3): Transport: N=16 residual restated as the time-grid-converged value of -1.21% (dt = 1e-3), with -2.78% at N=12 showing the finite-size trend; the 0.72% figure in v3 was an artifact of the dt = 0.05 integration grid and is now labeled as such. The N=24 transport point carries a new reliability caveat (double-lobe trace structure). The l_AdS comparison table is recomputed against the converged transport time (best fit 1.425, deviation 1.21%). Effective-mass derivation rewritten in a consistent AdS3 convention m^2 l^2 = Delta(Delta-2); m_eff = 0.693 = 1/l_AdS follows from Delta = 1 exactly. NEW: universality section extended to a third fixed point - a Z3-symmetric MERA at chi = 12 recovers the three-state Potts (c = 4/5) tower, giving alpha = 4.00 at all three universality classes (c = 1/2, 7/10, 4/5). NEW: the OPE coefficient C_sigma-sigma-eps = 0.50 +/- 0.03 measured directly from the fixed-point tensors, with C_sigma-sigma-sigma = 0 at machine precision as the Z2 structural check. Supplemental table row SIM-007 annotated (record lost; script preserved); data availability expanded; Zenodo DOI added to the front matter.
Version 4 (2026-08-25). Two additions from the correction campaign, carried as dated in-body correction records. The (2,5) entry, printed as a prediction in v3, is now census-exact -- and it was the wall law's first divergence test. At the constructed maximal-wall stratum point the stiff transverse count is exactly 10, so alpha_stratum(2,5) = 5; a fresh 60k ensemble's calibrated read is consistent with 5, with alpha = 10 (the superseded single-wall count's prediction) excluded at p = 0.000 and demonstrated power ~ 1; and a stratum-conditional paired ladder tracks the exact rank-10 Hessian form to <= 0.002 while a rank-20 comparator separates by >= 2.7 on identical draws. The law m_C(2,d) = 2(d-1) is census-exact at d = 3, 4, 5, now including the first point where it diverges (by 2x) from the superseded count. The (3,4) entry, printed open in v3, is now a PAIR of statements, and neither alone is alpha(3,4). The posted product-wall counting landed census-exact (alpha_stratum(3,4) = 5, so the asymptotic exponent satisfies alpha(3,4) <= 5), while the accessible window at n = 3e4 is steeper (calibrated 90 percent set [5.4, 6.9], with the previously read 4.0-4.1 excluded at power ~ 1): the codim-10 stratum's prefactor has not engaged at reachable depth, and window and asymptote have visibly decoupled. This is the scope lesson of the (d >= 3) x (d' > d) regime -- census plus conditional ladder measure the law, global windows measure the pre-asymptotic shoulder -- and it retro-explains the earlier fresh-seed ladders' instability as shoulder reads. Version 3 (2026-08-20). One SUPERSESSION: the qutrit-qutrit exponent closes. Versions 1 and 2 left alpha(3,3) open, v1 by a small-sample fit reading 3.25 and v2 by the bracket [2.3, 3.0] read off a descending window ladder. Both readings were artifacts of the estimator problem for which the pair-type table was already corrected in v2. The descent is attenuation tracking sample count rather than tail depth: an ensemble drawn from an EXACT alpha = 3.0 law descends by 0.62 across the ladder against the real data's 0.34, so a descending ladder is evidence FOR a constant exponent, not against one. Replacing the window fit with a calibrated Monte-Carlo test and inverting it over candidate exponents gives alpha(3,3) = 3.0 at p = 0.517 with a 90 percent confidence set [2.75, 3.10]; v1's 3.25 is excluded at p = 0.017. Power against alternatives is 0.990 / 0.590 / 0.120 / 0.575 / 0.990 / 1.000 at true alpha = 2.50 / 2.75 / 3.00 / 3.25 / 3.50 / 4.00. An independent re-audit at n = 10^4 reads flat near three on two seeds. Disclosed defect, carried in the paper: the test's own calibration row missed at the low edge (rejection rate 0.207 at a nominal 0.10 when the truth is alpha = 2.50, 4.4 standard errors high), so the lower end of the confidence set is softer than printed. This ensemble separates 3.0 from 3.25 with about 58 percent power and has none to separate 3.0 from 2.95. The (3,3) CARRIER family remains unattributed: the exponent is settled, the stratum that carries the accessible tail there is not. Version 2 (2026-08). Changes from v1: the pair-type exponent table is corrected (v1's alpha(2,4) = 2.08 was a 50-sample order-statistics fluctuation, placed at the 0.15th percentile of its own estimator's sampling distribution; three independent codebases now agree on the wall law alpha(2,d) = d, census-exact at d = 3 and 4); the transverse constant 1/12 is derived in closed form (diagonal cost 1/6, halved by the congruent partner's equal-cost correction); the (2,3) tail's carrier stratum is fully attributed (an isotropic-intertwiner family sharing the exponent 3); the qutrit-qutrit exponent is honestly bracketed open at [2.3, 3.0]; and the dispersion rule (tail-exponent fits print bootstrap dispersion or do not print) is adopted. The v2 ledger appendix carries the correction anatomy. Why is the multipartite certification constant heavy-tailed, where does the tail live, and what kills it? Localization: the credential pencil is exactly block-diagonal over party-subset supports; the tail is the worst pair; geometry statistics reconstruct from pair statistics (14/14 factor-band comparisons). The law: a frame-congruence theorem: whenever the two parties' operation frames subtend equal Bloch angles, the rotation intertwining them is an exact common kernel direction; the zero set is codimension one at generic angles, transverse growth is universally quadratic (mu = (Delta theta)^2/12), and the qubit-pair tail exponent is exactly 1/2 (the previously measured 0.39 is the finite-window slope of this law). The dichotomy: pairs containing a d >= 3 party measure exponents 2.08 to 3.69 because higher-dimensional operation pairs carry many local invariants that must all match: freedom helps the certifier. Engineering: heterogeneous dimension profiles tame the tail; qubit-pair presence splits all measured geometries into two clean classes; screening is a five-minute two-party calculation. Pre-registered; two entry gates that caught wrong conventions and all deaths ledgered.
[NOTE, June 2026: This paper is part of the AME(4,6)/TOE series whose headline claims were partially retracted. In particular the "zero free parameters" framing and several numerical predictions are withdrawn; see the Status Note at DOI 10.5281/zenodo.20618848 and the maintained mathematics at DOI 10.5281/zenodo.20128951. The text below is unchanged and remains as the record of the programme's history.] We perform a seven-part holographic analysis of the SU(3)_3 ⊗ SU(2)_2 string-net model associated with the AME(4,6) quantum error-correcting code. The transfer matrix is reinterpreted as a discrete renormalization group (RG) operator, and its iterated action is studied as a proxy for the MERA tensor network that defines an emergent holographic bulk. Key results: (1) Perfect conformal self-similarity — gap ratios preserved to 15 significant digits through 5 RG steps; (2) WZW tower matching — entanglement spectrum matches (0,0)⊗σ primary at h=3/16 exactly (Δh=0.0000); (3) Entanglement temperature β_ent = 2.380; (4) N-layer stacking shows exponential RG convergence (gapped system); (5) Topological hierarchy: ξ_topo/ξ = 5171 at Lx=2, scaling as exp(4·Lx), giving ~10^17 at Lx=10 — matching the Planck-electroweak ratio M_Pl/v; (6) Brown-Henneaux G₃ = 0.156 lattice units from c=11/2, L_AdS=ξ=0.572; (7) Stress tensor candidates at h≈1.81 (9.5% below h=2, finite-size at Lx=2). The topological hierarchy mechanism is the most provocative result: an O(1) topological constant (α≈4) combined with modest system size (Lx≈10) generates the 16 orders of magnitude separating v from M_Pl, without fine-tuning.
Reproducibility note and two wording corrections (28 October 2026). The note’s appendix promises check_dissipation_law.py, which version 1 did not carry. It has been written and run: 109 checks, 109 pass, with 53 derived from the C60 adjacency alone, 45 from the stated premises, 6 internal-consistency, 4 Monte-Carlo and 1 using a reconstructed input. The MEASURED set is empty, and that is itself a check: the note’s own flow-position paragraph says it compares no kernel number with measured data, and that was confirmed rather than assumed. Definitions are tagged as such and are never counted as derivations. Every entry of Table 1 and every number in §3, §4, §5.3, §6.1 and §6.2 reproduces. 1. §3.1’s “fails by at least 19%” is a property of one draw, not a bound. On the setup described, the smallest control deviation is 40.6%, so the floor holds there comfortably. But across 500 random cases (25 draws × 5 β × 4 t) the minimum falls to 10.1%, with 0.6% of cases below 19%. The substantive content is far stronger than the stated floor and should be given instead: every one of the 500 control cases exceeds its own KMS error by a factor of 3.5×10¹³ or more. Suggested wording: “fails by factors of 10¹³ or more above the machine-precision residual.” Relatedly, §3.1’s “relative error 3×10⁻¹⁵” is the typical value, not an attainable bound: the median over 500 cases is 3.23×10⁻¹⁵, the 90th percentile 8.1×10⁻¹⁵, the maximum 2.2×10⁻¹³. 2. §6.2’s “Stratonovich simulation” label does not fit the reported figure. The number itself is right — the theory value 19.44 and the closed form are exact and confirmed — but a direct Stratonovich–Heun integral of the locked case carries a large O(dt) bias, because the phase-difference modes relax at rate ~K = 30: dt = 0.002 gives 14.94 and dt = 0.001 gives 17.16, so reaching the reported 0.15% would need dt ≈ 10⁻⁵, far beyond what “N = 6, D = 0.25, K = 30, 400 replicas” implies. The exact Itō form of the same quantity, D⁻¹(⟨ΣFi²⟩ + D⟨∇·F⟩), carries no stochastic-integral bias and gives 19.4651 at dt = 0.001, converging to theory as dt falls. So the estimator, not the result, is what the label misnames. Separately, the ω list is never given, so the printed simulated triple is not reproducible as such; the printed theory triple is internally consistent (24.42 − 19.44 = 4.98 exactly) and is reproduced exactly from a reconstructed ω with mean 0.9 and population variance 0.2075. The note’s “var” is unambiguously the population variance — the identity fails for the sample variance. 3. §1’s “the C60 spectral values 1, 4−φ and φ” is loose on the third. 1 is an eigenvalue of A with multiplicity 9; 4−φ is an eigenvalue of L = 3I − A with multiplicity 5, since 3 − 1/φ = 4 − φ; but φ is an eigenvalue of neither (nearest level 0.0565 away in A, 0.1796 in L). Only −φ is, with multiplicity 5. The note says so itself two paragraphs later, so this is internal looseness of wording rather than a numerical error, and the product identity (4−φ)·φ = 3φ−1 = 3.854101966249685 is exact. Two results are worth naming because they are stronger than stated. Aut(A) ≅ Ih is confirmed structurally, not merely by order: order 120, 31 involutions, centre of order 2 and no element of order 4, which pins A₅ × C₂ and rules out S₅ (25 involutions, trivial centre). And in §6.1 the garbled line is ΔSsys = −TC₁, the total correlation: the system’s entropy falls by exactly the correlation that forms, verified symbolically, with C/8 = H(p₁) exactly — which is why the printed closed form for (E/S)op holds. Ψop was rebuilt from ledger quantities alone, with no A, B or C in it, and agrees with the printed form to 2.5×10⁻¹⁷⁵. A scope and status note on the coherence dissipation law. Separates what the C60 adjacency forces from what it forbids, and states the open-system form that survives after the bare coefficient was retired in the record. The law in every surviving form is posited, not forced, and the paper says so wherever it matters. Includes the two-ledger theorem under stated premises, a no-go result limited to coherence functionals built from the adjacency, and a verification script.
Preprint. Not peer reviewed. The random quantum Ashkin-Teller chain with N Ising colours was solved by strong-disorder renormalization for every N except four, where internal states couple at second order and the standard decimation cannot discard them (Barghathi, Hrahsheh, Hoyos, Narayanan and Vojta, Phys. Scr. T165, 014040 (2015); arXiv:1404.2509, section IV.D). This record treats that case. An exact change of variables maps the 16-state site onto four-state Potts matter coupled to two binary charges. At zero transverse field and zero pair-bond coupling the charges are conserved and the matter is a q=4 Potts chain; at finite couplings their fate is the research problem. An equivalent transformation appears in the reference above and no priority is claimed for it. In the strong-field corner the retained site doublet supports an effective Ising chain for the four-colour product, with bond 3K^2/[4(g_i+g_j)] and field 4h. The leading composite coefficient is derived for general even N=2m, while for odd N the all-colour transition is forbidden at every order in K. The N=4 exception is therefore the first member of an even series rather than an isolated accident. Keeping the doublet mixing gives error scaling lambda^3 (measured 3.00087) against lambda^2 (2.00717) when it is dropped, so the mixing the published decimation could not discard is a leading-order term. DMRG on the full unprojected 16-state chain finds a composite-ordered regime: at K/g=0.20 the quartet endpoint correlation plateaus at 0.936034 from L=12 through L=24 while single-, pair- and triple-colour correlations stay short-ranged, within 5.34e-4 of the unfitted third-order prediction. Projection onto all four positive global parities changes it by 2.15e-7 while raising the central-cut entropy by log 2 to within 1.83e-7, confirming a symmetric cat state. At the self-dual point the entanglement profile matches an independently implemented q=4 Potts chain to 7.52e-6 nats. With finite charge-changing couplings h=J=1/epsilon the deviation from a matched q=4 Potts control is second order in 1/epsilon, separable from the DMRG residual, and its amplitude is length-independent across L=6,8,10 (5.03, 4.95, 4.91 x 10^-3), with the L=10 value predicted before it was computed. The mechanism is identified analytically: the second-order numerator is a constant plus twice the existing transverse term, so new operators can enter only through the matter-dependent energy denominator, and both mechanisms are local. The clean N=4 exception therefore resolves to q=4 Potts criticality with a fixed local perturbative correction. Review status. Sections 1-4 rest on results that passed this project's independent review process, three audit rounds included in the deposit. Section 5 has NOT been independently reviewed and is flagged as such in the manuscript and the README. A self-audit of the unreviewed stages is deposited; it is a starting point for a real review, not a substitute for one. A broad-disorder section was withdrawn before deposit. A 20-sample gap-scaling run gave a ln-gap width growth suggesting infinite-randomness behaviour; a 100-sample run under the same pre-registered rule returned INDETERMINATE, and the earlier value proved to be carried by two tail samples. Both runs, both pre-registrations and the analysis are deposited. The random critical point remains open. Not claimed: a thermodynamic phase boundary, scaling dimensions of the generated operators, anything about the random critical point, or priority for the variable transformation. Every stage's predictions were written before execution, every result file records the SHA-256 of its sources, and historical outputs are preserved unchanged. DMRG state checkpoints (about 93 MB) are excluded from the archive; each is reproducible from its recorded seed and settings, and its SHA-256 is stored in the result file it belongs to. AI assistance. Produced with substantial assistance from a generative AI system (Claude, Anthropic), and earlier stages with a second system (Codex, OpenAI), which also served as the independent reviewer between stages. The systems are not authors. The author defined the research direction, made the scientific decisions, and takes full responsibility for the content.