#!/usr/bin/env python3
"""
Run all TOE verifier scripts and write a compact Markdown status report.

This runner treats both nonzero exits and textual FAIL markers as audit
findings. Some legacy scripts intentionally print control failures while
exiting successfully; those remain visible in the report instead of being
silently treated as clean passes.
"""

from __future__ import annotations

import os
import re
import subprocess
import sys
from pathlib import Path


ROOT = Path(__file__).resolve().parents[2]
VERIFY_DIR = ROOT / "TOE" / "verify"
REPORT = ROOT / "TOE" / "VERIFY_RESULTS.md"


IGNORE_FAIL_LINES = [
    "0 FAIL",
    "0/41 FAIL",
    "PASS, 0 FAIL",
    "PASS / 0 FAIL",
    "PASS   0/",
    "PASS / FAIL",
    "FAIL :  0",
    "FAIL : 0",
]


KNOWN_INTERPRETATION = {
    "verify_i.py": "New audit finding: Paper i's cover-paper arithmetic reproduces: the balanced ternary identity 1+T=0, Omega=4pi^3+pi^2+pi≈137.036304, the rounded alpha-inverse comparison, and the three harmonic contribution count all check, with the paper explicitly marked as outside the numbered corpus. The flagged issues are scope/status points: Omega is close to but not exactly CODATA alpha inverse; Paper i is conceptual framing rather than a proof that all numbered papers are mutually true; the balanced ternary does not derive three fermion families here; Nullity/Self/Unity are not formal code-verifiable constructs; and the cover paper summarizes Papers 00--34 rather than the later addenda through P200.",
    "verify_P000.py": "New audit finding: P0's reusable Rosetta-map arithmetic mostly reproduces: the cubic density integrates to 4pi^3+pi^2+pi≈137.036304, lambda is fixed to 1 under the GSP target, cubic degree is minimal under the assumed x^3 bulk term, 3/4 is the three-layer/four-bulk ratio, the division-algebra sphere dimensions check, and the Z3/lens-space pointer is topologically plausible. The flagged issues are status/overstatement problems: the monad value is close to but not exactly CODATA alpha inverse; R is explicitly a conceptual placeholder; C and P are not defined maps; the 16/3/2 representation dimensions are assigned rather than derived here; the electron mass and master operator are not computed; T^3=I is not proved for concrete maps; consciousness/singularity identifications are interpretive; the referenced Ged wheel implementation is absent from this TOE workspace; and the claim that the identity plus C o P generates the entire theory is stronger than the paper's own reference-document caveat.",
    "verify_P001.py": "New audit finding: P1's alpha integral and kappa-scale arithmetic mostly pass, but the central energy theorem is wrong by a factor of about 13; the moment/mass-scaling table has arithmetic errors; the listed neutrino-suppression factors do not give the claimed scale; and the Jarlskog expression omits the standard cosine factors.",
    "verify_P002.py": "New audit finding: P2's basic moment/energy arithmetic mostly passes, but the displayed QED beta ratio mixes geometric and experimental alpha values; the optimal-density table has wrong E_self values for linear/quadratic comparators; the stated wave equation does not have rho_cubic as a Neumann equilibrium; and several proof/formula lines are incorrect.",
    "verify_P003.py": "New audit finding: P3 repeats the cubic-density arithmetic correctly, but the theorem still claims E_norm=1 while its proof computes 13.177; the stated wave equation is not a Neumann equilibrium for rho_cubic; the moment-ratio theorem is overbroad; and the mass-log derivation contains an invalid (1+x)=1/(1-x) algebra step.",
    "verify_P004.py": "New audit finding: P4's core three-term alpha sum, transition-scale values, full E_self, kappa scale, and mu1/mu0 ratio mostly reproduce. The flagged issues are substantial internal/proof-status problems: the quantum layer integral is printed as 123.370055 even though 4π^3≈124.025107, which propagates into the 90.0% layer budget and two-layer QC/QM tables; the theorem calling the integrated terms algebraically independent proves only Q-linear independence; the QC and CM transition dominance directions are reversed; the derivative cascade is only a degree analogy, not an equality chain; the two-layer self-lensing values for QC/QM/CM are wrong, and QC lies inside the later oscillation arena; duplicate TeX labels make references ambiguous; the Hopf-fibration/no-direct-map claims are not valid topological proofs; and the black-hole fold-map determinant is not computable from the definitions given.",
    "verify_P005.py": "New audit finding: P5's reused alpha, layer-fraction, energy, kappa, beta-function, and Planck-log arithmetic mostly reproduces, including alpha inverse, 90.5/7.2/2.3 layer fractions, E_self≈13.1767, DeltaE≈0.6103, kappa≈0.002133, beta_geom≈0.793342, beta_QED≈1.13e-5, beta ratio≈70,205.8, and C≈1362.48. The flagged issues are stale arithmetic/proof-status points: 4π^3 is printed as 123.370055 instead of 124.025107, propagating into two-layer values and error percentages; one displayed relative-error formula uses 137.036999 instead of CODATA 137.035999; a coefficient-variant example is inconsistent with the density convention; omega1=3.136 is stale; the mass-ratio toy example gives about 34.5 rather than 82; the wave equation repeats the earlier non-equilibrium/linearization problem; 5/4 is not globally selected by the shown scan; L(4,1) does exist as an S3 quotient; Z3 does not by itself forbid any fourth family; the strong-CP solution is asserted; and the random-coefficient probability estimate is not reproduced by brute-force enumeration.",
    "verify_P006.py": "New audit finding: P6's basic rho integral, alpha value, Z3 representation count, Dirichlet boundary condition statement, mass-table log-error arithmetic, and several rounded CKM/PMNS angle reads reproduce. The flagged issues are larger internal/status problems: the table's neutrino masses are 100 eV, 958 eV, and 10,000 eV, not the abstract's ~0.1 eV scale and not PDG light-neutrino masses; the displayed 'tribimaximal' matrix with all entries 1/sqrt(3) is rank-1, non-unitary, and implies theta13≈35.26 degrees rather than TBM theta13=0; the displayed positive CKM/PMNS tables are magnitude tables and are not themselves orthogonal/unitary, and the PMNS table gives theta23≈30.1 degrees from U_mu3 rather than 49.2 degrees; the mass predictions are not reproducible because the eigenvalues, x_peak values, and fitted A/B/C parameters are omitted; the text explicitly optimizes A/B/C and Delta U despite claiming zero free parameters; log-periodic node/fractal-dimension data are not included; the triplet table lists a fourth neutrino triplet; and Z3 irreps alone do not topologically forbid additional representation copies.",
    "verify_P007.py": "New audit finding: P7's rough lepton-mass numerics mostly reproduce: mu0/mu1/mu2, beta=6*mu1/mu0≈4.760, the finite-difference eigenvalues near 16.52/51.28/102.07, the muon/tau mass predictions, and the 94.8 quality score all check at the paper's precision. The flagged issues are methodology/status problems: the listed tridiagonal matrix matches Dirichlet-like endpoint handling rather than the stated Neumann condition at x=1; the x^2(1-x)^2 potential factor does not enforce wavefunction boundary conditions; the printed Planck-log relation for mu1/mu0 evaluates to about 0.0194, not 0.7933; beta is selected from a small scan over n values; the zero-free-parameter claim conflicts with using the electron mass, imported E_self, and selected beta factor; the printed Yukawa mixing angles do not follow from the displayed matrix under a simple diagonalization convention; the three-family S3 explanation is not a theorem; and the Yukawa matrix cannot be recomputed from the printed data.",
    "verify_P008.py": "New audit finding: P8's explicit arithmetic mostly reproduces: density coefficients, later frame-count formula values, density integrals, mu0/mu1, beta=6mu1/mu0, kappa, prime-spacing identities, Planck length/time consistency, and the displayed Higgs VEV back-of-envelope estimate. The flagged issues are internal/proof-status problems: self-intersection dimensions conflict between main text and appendix, the discrete update equation does not derive the Schrodinger equation as written, Planck-time discreteness is asserted rather than derived, measurement collapse/consciousness duality are conceptual identifications rather than mathematical derivations, and no-fourth-family/prime-correlation/zero-unexplained-constants claims are not supported by supplied computations.",
    "verify_P009.py": "New audit finding: P9's water numerics mostly reproduce: rho moments, E[rho], E_self, kappa, T_geom=273.16/(10pi), required E_scale≈0.0267 eV, Kelvin critical radius at S=1.5, 3pi*d_H2O radius, radius ratio/agreement, enthalpy ratio comparisons, cluster size, and fog-resonance radius all check. The flagged issues are interpretive/proof-status problems: E_scale is about 3.1% above kB*300K despite the 'precisely equals' wording; T_geom/T_CMB is about 1.6% above pi; the triple-point relation is reverse-engineered from 273.16 K unless E_scale is independently derived; the 3/r=1/pi radius derivation is dimensionally incomplete; S=1.5 is essentially the fitted supersaturation required to hit 3pi*d_H2O; the 'closest natural constant' claim only compares a small finite list; and downstream predictions inherit those empirical choices.",
    "verify_P010.py": "New audit finding: P10's numerical 3/4 correction mostly reproduces when the target alpha value is used on the right-hand side: mu0/mu1/mu2, the base formula, correction scale, corrected alpha inverse 137.036114991, rational scan optimum at 3/4, c_required≈0.749854, and most alternative-comparison rows check. The flagged issues are internal/status problems: the formula uses alpha^2 on the RHS and the numerical evaluation imports alpha^{-1}=137.036, so the zero-input derivation is circular unless an implicit solve is specified; the alpha-cube side length is itself defined using alpha; the paper explicitly says a first-principles derivation of exactly c=3/4 remains open despite listing five derivations; the continuous-optimization remark saying c=0.750000000 and distance <1e-9 contradicts the printed analytic optimum c≈0.749854; the c=4/3 worse-factor is about 4008 rather than 5100; the alpha^4 second-order term is about 1.9e-5, not order 1e-8; and the Z3/family argument does not topologically forbid additional representation copies.",
    "verify_P011.py": "New audit finding: P11's density alpha value, moments, equilibrium formula, spectral Planck/electron log, beta-ratio factorization, kappa, boundary correction, and simple water-scale arithmetic mostly reproduce. The flagged issues are synthesis/status problems: the equilibrium formula is numerically closer to CODATA than the density formula, contradicting the 'density highest precision' and 'equilibrium lower precision' wording; the alpha^4 correction estimate is far above modern alpha experimental precision; the three formulations are compatible but not mathematically equivalent as written; the zero-free-parameter claim is stronger than the paper's own open caveats about rho, 5^4, 11pi, and 1/pi-1/10; the S3/Z3 family-count and no-fourth-family claims are not proved by the displayed quotient or confirmed solely by LEP Nnu; and the charged-lepton and water-nucleation comparisons are not code-verifiable from the P11 TeX alone.",
    "verify_P012.py": "New audit finding: P12's central c=3/4 search result reproduces: the base formula, mu0/mu1, mu1*alpha^2, corrected alpha inverse, rational scan optimum, continuous optimum c≈0.749857, and the simple dimension/complement/prime/family ratios all check. The flagged issues are comparison/status problems: several search-table worse factors are stale under the displayed formula (notably c=4/5, 5/6, and 7/9); the boundary spectral first-order/full difference is about 0.0019%, not 0.02%; the wave-equation route inherits the earlier invalid-equilibrium problem; Z3 family topology does not by itself forbid additional copied families or prove no fourth family; and the claimed five-way logical independence is not established because several methods are different readings of the same 3-vs-4 ratio while Method V is the fitted search.",
    "verify_P013.py": "New audit finding: P13's inherited density arithmetic reproduces: mu0, mu1, mu2, self-lensing energy≈13.1767, alpha=1/mu0, kappa=alpha^(5/4), beta=mu1/mu0, and the formal exponent-clearing step all check. The flagged issues are central reproducibility/proof gaps: the quintic coefficients and N(alpha),D(alpha) are not supplied; clearing denominators from a rational kappa_geom does not generically yield degree five; lambda1(alpha) is an eigenvalue of a differential operator and no rational dependence is shown; the electron-mass constraint F is undefined; irreducibility and Galois group S5 cannot be checked without a polynomial; root uniqueness/Newton/eigenvalue verification is not shown; and the structural-closure claim is therefore overstated.",
    "verify_P014.py": "New audit finding: P14's headline numerics mostly reproduce: alpha inverse, pi*alpha^-1≈430.51, the 0.344% gap to 432, higher hierarchy levels, 432=16*27, the mahakalpa factorization, omega1, the 4pi/E_self oscillation arena, 432/pi^3≈13.93, and the corrected 1018 manvantara arithmetic all check. The flagged issues are status/precision problems: 432/430.51 is not 1+kappa^0.6, 432/pi^3 is about 5.7% above E_self, E_self rounds to 13 rather than 14, the breathing period is selected rather than derived from C o P=I, the 432=16*27 encoding is not an independent derivation, ancient-transmission claims are not mathematically verifiable, and the pi-lift hierarchy is not proved unique.",
    "verify_P015.py": "New audit finding: P15's headline projection and density arithmetic reproduces: (432-pi/2)/pi≈137.009871 with about 0.019% error, the cubic density integral gives 137.036304 with about 0.000222% error, B4/S3 volume and area formulas check, c4=4/(3pi)≈0.424 checks, 432=2^4*3^3, 432/137≈pi at 0.37%, and 68/5≈alpha^-1/10 at rough precision. The flagged issues are derivation/reproducibility problems: the displayed S2 average |cos theta| integral is 1/2, not 1/4; the master division by pi does not follow from the displayed S3 projection factor 4/(3pi); the pi/2 bifurcation correction and source value 432 are asserted rather than derived; the projection and density routes produce different values with no bridge theorem; P and C are not defined as mathematical operators; Lambda is not calculated from C; and the referenced projection_verification.py script is not present.",
    "verify_P016.py": "New audit finding: P16's exact shell arithmetic mostly reproduces once the full M51 exponent list includes 42,643,801: S51≈1,237,518.625, the proposed triplet sum, Z3 condition, phi ratios, exact-kappa S54 shell distance≈4.8e-6, target-shell resonance, exponent primality, and digit threshold all check. The flagged issues are validation/proof-scope problems: the proof line using rounded kappa=0.00213306 does not reproduce the shell closure; the theorem still labels 160,964,569 as p52 despite the paper's own 136,279,841 M52 note; the statistical table's counts, mean distance, random expectations, and p-value do not follow from the cumulative S_n definition; the uniqueness search is not reproducible from the TeX alone; and exponent primality is not a proof that 2^p-1 is prime.",
    "verify_P017.py": "New audit finding: P17's headline gravity numerics reproduce: mu0 through mu3, moment ratios, self-lensing factor, 3pi/20 decomposition, Planck/electron log RHS≈51.52985, rounded-mass residual≈0.0053%, KK ratio, breath period, and kappa scale all check. The flagged issues are internal/status problems: the pi/7*mu1≈51.5 shortcut is arithmetically wrong; the body spectrum m2≈0.96,m3≈1.00 conflicts with the appendix m2=6.923,m3=7.763; the Dirac spectrum is not reproducible from the TeX alone; the Planck-log formula is not derived from the quoted Dirac eigenvalues; the exact 3pi/20 derivation is still listed as desirable; and the three-family/strong-CP/zero-free-parameter closure claims are asserted or inherited rather than proved here.",
    "verify_P018.py": "New audit finding: P18's coefficient arithmetic mostly reproduces: mu0/mu1, alpha, gamma=3/4, zeta=kappa, beta=3pi/20, alpha*mu0=1, the self-lensing boundary amplitude, and the explicit open assembly-uniqueness caveat all check. The flagged issues are internal/proof-status problems: the moment operator is defined with mu_n/mu0, so the first-mode gravity formula gives about 0.374 rather than 51.53; the claimed free B4 spectrum (2n+l+2)^2 is not the generic ball Dirac/Laplacian spectrum with boundary conditions; the ground-state alpha normalization is stated without solving the eigenproblem; the paper's own factor-66 mass failure contradicts claims that the canonical spectrum determines fermion masses; and the no-free-parameters/complete-reduction wording is stronger than the open uniqueness, mass-gap, and schematic-limit evidence.",
    "verify_P019.py": "New audit finding: P19's inherited UFE constants mostly reproduce: mu0/mu1/mu2, alpha, gamma=3/4, kappa, beta=3pi/20, E_self/mu0^2, the Planck-log formula, beta_geom, the alpha_weak/alpha_strong dimension-ratio formulas, and the 3/11 weak-mixing arithmetic. The flagged issues are formula/status problems: 3/11 is about +18% above measured sin^2(theta_W), the displayed beta-origin table is inconsistent with the standard B4 volume, mu2/mu0^4 does not give 1e-122 by itself, the G_F and alpha_s estimates need missing scale/running factors, and the Schrodinger/Dirac/Yang-Mills/Einstein reductions are schematic rather than derived from the UFE operator.",
    "verify_P020.py": "New audit finding: P20's dictionary arithmetic partly reproduces: mu0/mu1/mu2, mu1/mu0, kappa, beta=3pi/20, the Planck-log formula, strong low-energy inverse estimate, tree/SU3-corrected Weinberg angle estimates, and exp(mu1/mu0) all check. The flagged issues are status/scale problems: the Higgs VEV formula M_Pl/sqrt(mu0*mu1) gives about 1.0e17 GeV, not 246 GeV, and the TeX itself marks this unresolved; the Higgs mass estimate v*sqrt(E_self/mu0) gives about 76.3 GeV, not 125 GeV; the displayed neutrino suppression m_e*(v/M_Pl) gives about 1e-11 eV before the unspecified Z3 factor, not 0.01-0.1 eV; the exact gauge-group and three-family claims inherit the P37/P6 caveats; the strong-CP solution is asserted rather than derived; CKM/PMNS/full mass spectra are not supplied by explicit formulas in this dictionary; and the zero-free-parameter claim is not supported by this paper alone.",
    "verify_P021.py": "New audit finding: P21's layer arithmetic and scope disclaimer reproduce: bulk/boundary/edge fractions, self-lensing value, and alpha^-1/32 comparison are numerically consistent at the paper's rounded precision. The flagged issues are formal-status gaps: single-observer P=NP is not a theorem about Turing-machine P and NP; the observer-dependent resolution reuses complexity terms outside standard definitions; no instance distribution maps NP-complete problems to the 90.5/7.2/2.3 layer fractions; the hard-instance fraction and phase-transition link are unsupported; the quantum speedup ceiling is not proved in a quantum complexity model; and self-reference/bulk-access claims are not formal complexity results.",
    "verify_P022.py": "New audit finding: P22's basic Xavier-Stokes arithmetic checks: edge/boundary ratio 1/pi, layer fractions, strain-vs-divergence distinction, viscosity enhancement, Kolmogorov-scale estimate, and the non-Navier-Stokes disclaimer are present. The flagged issues are PDE-proof gaps: the variable-viscosity energy identity omits gradient(nu_eff) terms for the written operator; high vorticity does not imply high strain; the quasi-steady psi step is not an a priori estimate; the Poincare bound is not available on R3 as stated; the superlinear-dissipation argument does not close the BKM integral; beta and tau are calibrated flow-dependent parameters; and the numerical experiment is not reproducible from included code/data.",
    "verify_P023.py": "New audit finding: P23's numerical mass-gap arithmetic mostly reproduces: f_b, SU(2)/SU(3) Casimirs, sqrt(3)/24 and its residual, sqrt(f_b), group factors, and the QCD-scale estimate all check, with the Millennium-proof disclaimer present. The flagged issues are formal physics/proof gaps: the direct SU(2)=S3 route defines the f_b shell fraction rather than deriving it; Riemannian metric normalization is unspecified; minimum misalignment=f_b is qualitative; the proof derives m_gap=f0*f_b before switching to f0*sqrt(f_b)*c_G; the proposed |A|^2 mass term is not gauge invariant as written; reflection positivity is not proved by pointwise positivity; and no constructive 4D Yang-Mills measure/OS proof is supplied.",
    "verify_P024.py": "New audit finding: P24 acknowledges key Hilbert-Polya gaps, and standard background checks pass, but the central construction fails as an L2 spectral proof: the Mellin sign/normalization is inconsistent, countable zero-supported odd parts are zero in L2 and delta masses are distributions, the constraint cannot create point spectrum inside L2, off-critical zeros are omitted by definition, h(H) is not trace class on the continuous-spectrum component, the Weil formula is not identified with this operator trace, and the multiplication resolvent has continuous-spectrum singularities rather than isolated zero poles.",
    "verify_P025.py": "New audit finding: P25 correctly recalls standard Lefschetz/Hodge background and known low-dimensional cases, but its proposed GSP reduction has gaps: the annihilator argument does not directly imply W=V, the non-middle proof is circular as a general argument, Hodge-Riemann positivity does not guarantee pairing with an algebraic effective cycle, the effective cone need not be closed, the dual-cone span and cone-characterization propositions are not established, and Chow/projectivity does not rule out non-algebraic Hodge classes.",
    "verify_P026.py": "New audit finding: P26's Sato-Tate density normalization, layer fractions, root-number parity, rank-0/1 known-result boundary, and scope caveats check. The flagged issues are BSD-proof gaps: Sato-Tate marginal distribution does not imply rank equality of the global L-function, higher-rank height formulas are conjectural/incomplete in this generality, the derivative-point correspondence and local-global consistency arguments are circular/heuristic, Sha finiteness is assumed through the refined BSD formula, the rank-one example's conductor/equation data are not verified, and the large Cremona-table claim is not reproducible from the TeX.",
    "verify_P027.py": "New audit finding: P27's concrete reused arithmetic reproduces: the alpha integral, layer contributions, 90.5/7.2/2.3 percent fractions, the first moment, Planck/electron log formula, and trivial single-observer inverse construction all check. The flagged issues are proof-status and reference problems: a mutual-coherence definition is referenced without a label; Hopf projection S3->S2 is not an invertible C/P identity; the S3 and B4 uniqueness claims do not construct the required observer operators; the 16/3/2 coefficient and information-partition interpretations are not derived in P27; the Z3 family, consensus-stacking mass, dark matter, dark energy, P-vs-NP, and Big-Bang claims remain conceptual rather than formal derivations.",
    "verify_P028.py": "New audit finding: P28's concrete quaternion/Hopf and measure arithmetic mostly reproduces: monad/Theta integrals, mu1 downward Jacobian, Hopf v=cos(2beta), complementary amplitude, axis-resolved identity, V6/V3=pi^2/8, Omega0=pi^3/4, kappa, and the lifted-speed residual all check. The flagged issues are metadata/status/reproducibility problems: the file header says Paper 27, exact 2*pi arc-speed is only approximate under the displayed 2*pi*sqrt(1-kappa) lift, the SR-lapse theorem still requires identifying Hopf v with physical velocity, simulation RMSE/alpha-scaling claims are not reproducible from the TeX, Omega0's volume-ratio normalization is a modelling prescription, and the J3(O) embedding is only sketched.",
    "verify_P029.py": "New audit finding: P29's basic training/exposure arithmetic is coherent: exact implementation gives zero loss and zero gradient in a concrete model, the Hessian is positive under full support, exact gradient descent from theta* stays fixed, and the Hopf, Lorentz-lapse, Omega0, monad-closure, and displayed resonance-amplitude arithmetic checks reproduce. The flagged issues are theorem-scope problems: local injectivity alone does not imply positive population loss for an arbitrary data distribution; local isolation does not imply a unique global minimum; the necessary/sufficient-condition claim is stronger than what is proved; the TOE identity catalogue and empirical RMSE claims are imported from earlier papers; the pipeline has zero trainable constants but still external initial-condition and schedule inputs; regularization/noise and single-instance claims are overbroad; and the damped displacement response peaks at sqrt(omega0^2-gamma^2/2), not exactly omega0.",
    "verify_P030.py": "New audit finding: P30's concrete GON forward-pass arithmetic mostly reproduces: quaternion exponentials preserve unit norm in the sample, the relational quaternion remains unit, the Hopf projection/lapse/axis identity check, Omega0 and monad constants check, the input counts and MLP input dimension are right, and the stated FLOP total follows from the table. The flagged issues are implementation/protocol problems: the log-map diagnostic is singular at q=(+/-1,0,0,0); the norm-drift <1e-15 prediction conflicts with the paper's own O(eps*N) estimate; mini-batching clean zero-residual identity data does not by itself create gradient noise; finite sampled MLP benchmarks do not prove a nonzero residual floor; zero core trainable parameters is not zero experimental hyperparameters; bitwise-identical reproducibility is overstated; the Z3 extension maps real R3 schedules to complex values unless an embedding is supplied; the J3(O) associative-subalgebra dimension statement conflicts with the 27-dimensional octonionic case; and outside-domain silence is not specified by the formulas.",
    "verify_P031.py": "New audit finding: P31's explicit monad/count arithmetic reproduces: Omega=4pi^3+pi^2+pi, the density integral, c_d=(d+1)^max(d-1,1), c_d/k=k^(d-2)_+, Hopf exponent sums, k^3 factorization, and Chebyshev root counts all check. The flagged issues are proof-status/internal problems: the Hopf modulus dimension is not derived from explicit self-intersection equations, the Z_k actions are not constructed as actual stratum-linking monodromies, the Chebyshev frame equation is asserted rather than derived from the bundle data, the Bezout count follows only after those assumptions, the static 2^4/k weight is 4 rather than the text's 2^3=8, the monad identity is used circularly to select the dynamic mechanism, and the unconditional first-principles closure is overstated.",
    "verify_P032.py": "New audit finding: P32's main dark-energy arithmetic mostly reproduces: V4=pi^2/2, Lambda0=1-pi^2/32≈0.6916, the Planck sigma comparison, d=4 closest among d=1..8, cube-net 6+1 face count, epsilon, H0 scale estimates, and the dynamic addendum's C(k)/Lambda(k) table all check. The flagged issues are arithmetic/structural/proof-status problems: the d=6 dimensional-cascade value should be 1-pi^3/384≈0.9193, not 1-pi^3/192≈0.8385; [-1,1]^4 and {-1,+1}^4 have 16 corners/vertices rather than 8, so the octonion basis identification is missing a quotient/pairing map; Euler's exterior face is not connected by a measure-preserving derivation to 1-pi^2/32; the unbounded exterior of a planar net does not fold into the cube interior; the tesseract Euler-characteristic claim is ambiguous between boundary and solid; and the paper explicitly does not solve the old QFT cosmological-constant problem.",
    "verify_P033.py": "New audit finding: P33's screened self-intersection arithmetic reproduces: Paper-08 counts 2/3/16 give screened weights 1/1/4, the alpha sum equals 4pi^3+pi^2+pi≈137.036304, the corrected complement identities c_d*k^min(4-d,2)=k^3 hold, the three-factor exponent sums are 3, the Nicomachus cube values 8/27/64 check, and the P32 Lambda0 value is quoted correctly. The flagged issues are interpretation/status problems: the corollary's original literal product c_d=k^max(d-2,0)*k*k^min(4-d,2) is false before the proof corrects it; pi^d is not the exact volume of S^(d-1); Hopf absorption is not constructed by the arithmetic; the geometric alpha value is not exactly CODATA alpha inverse; the Nicomachus sum-of-cubes identity is not actually used; the self-intersection counts are imported from P8 rather than derived in P33; and the P32/P33 circuit is not fully proved.",
    "verify_P034.py": "New audit finding: P34's frozen-constant arithmetic mostly reproduces: Omega, layer fractions, FRAC_EDGE threshold ratio, BREATH_PERIOD, singleton centroid, and hopf_lapse range examples all check, and the paper correctly marks PLATEAU_THRESHOLD as calibration. The flagged issues are categorical/reproducibility problems: the cited Ged/Lumen implementation files are not present in this TOE workspace, bind-as-centroid-collapse does not satisfy left identity for non-point f(q), right identity collapses non-degenerate distributions to one centroid, associativity fails under intermediate normalization, the hemisphere condition does not fix support loss, plateau is an MDL convergence test rather than a proof of equality to Omega, and no-free-parameter wording conflicts with the calibration threshold and implementation choices.",
    "verify_P035.py": "New audit finding: P35's concrete group examples mostly reproduce: axis-aligned cube counts, the irrational/perfect-power obstruction samples, the Q8 coset criterion table, j having order four, j<i> having no involution, and the chiral pinwheel's scalene seed/quarter-turn arm mapping all check. The flagged issues are proof-scope problems: the axis-aligned tiling proposition does not by itself prove the unrestricted rep-2 obstruction; Q8 is not minimal because C4 already gives a smaller coset example with no involution; the criterion is described as conjugation even though it uses sigma*h*sigma rather than sigma*h*sigma^-1; the halfspace theorem is false for arbitrary compact X because reflection need not preserve X or map X∩H+ to X∩H-; halfspace intersections need not be disjoint/isometric bisections; the claimed universal Z2 bisection corollary fails for simple finite compact sets; and the pinwheel ambient-involution proof should state the needed arm separation/component hypotheses explicitly.",
    "verify_P036.py": "New audit finding: P36's sector-integral arithmetic is mostly solid: mu0/mu1, edge/boundary/bulk energies, layer fractions, S3 comparison ratios, and the muon near-hit m_mu/m_e≈208.016 all reproduce. The flagged issues are interpretive/status problems: the original Paper-18 absolute formula m_n=m_e exp(MU E_n) is re-anchored to a ratio formula because E_e=pi would otherwise not give m_e; the quoted tau value E_self(lambda_tau)=13.4187 is not derived by an explicit formula in P36, and a simple endpoint-linear interpretation gives about 13.42235 and m_tau/m_e≈3484.8; and the final all-inputs-proven wording overstates the paper's own earlier conjectural status for sector-energy identification.",
    "verify_P037.py": "New audit finding: P37's basic dimension and ratio arithmetic mostly reproduces: mu0, 16=2dim(O), dim/rank G2 and SU3, coset dimension 6, tree Weinberg 1/4, full dimension count 1/12, sector-energy ratios, J3(O) dimension 27, and the muon perturbation arithmetic all check. The flagged issues are group-fact and proof-status problems: Aut(C) as a real algebra is Z2, not U(1); Aut(H) is SO(3)=SU(2)/Z2, not SU(2) exactly; selecting physical SU(2)_L rather than SU(2)_R needs more than orientation convention; Hopf U(1) proves a fiber phase but its identification with hypercharge relies on a physical dictionary; Hurwitz forbids further normed division algebras but not arbitrary gauge factors unless the division-algebra ansatz is assumed complete; the off-diagonal 8 real octonion components are not the same as SU(3) color generators; and the complete J3(O) Standard Model decomposition remains conjectural.",
    "verify_P038.py": "New audit finding: P38's quark-sector arithmetic mostly checks, including charm, top/charm, Cabibbo, and bottom-energy claims. It flags one tau self-lensing inconsistency with the stated endpoints, a stale strange-quark energy table value, and a proof-audit issue that Z3 cyclic symmetry alone does not uniquely fix the full TBM matrix.",
    "verify_P039.py": "New audit finding: P39's basic constants and several Higgs-sector checks reproduce: mu0/mu1/MU, layer fractions, the C⊗O dimension split, tree sin^2(theta_W), MW/MZ tree ratio, lambda_H≈0.12964, and the v=e*MZ near-hit all check. The flagged issues are arithmetic/status and representation-consistency problems: using the paper's own M_H=125.11 and v=246.22 gives lambda_SM≈0.12909, not 0.12933, lambda_H is about +0.42% high, and M_H from lambda_H and v is about 125.37 GeV / +0.21% / 2.4 sigma, not 125.26 GeV / +0.12% / 1.4 sigma; the tree Weinberg deviation from the stated 0.2312 comparator is about +4.43%, not +4.24%; the proof assigns the lower Higgs component Y=-1/2 before the table assigns both Higgs components Y=+1/2; the J3(O) slice (e0 in x13, e7 in x23) is not invariant under a generic row-index SU(2) rotation as stated; and lambda_H remains a conjecture with its derivation left open.",
    "verify_P040.py": "New audit finding: P40's spectral-table mass arithmetic and PMNS Phase 3.5 formulas mostly reproduce: mu0/mu1/MU, Cabibbo angle, electron/muon/down/charm/top/bottom masses, theta13/theta23/theta12 conjectures, TBM residuals, and the u/s open-energy estimates all check. The flagged issues are bookkeeping and VEV arithmetic/status problems: the derivation-status sentence says 16 known, 4 candidate, and 7 open slots, but the listed slot ranges count as 17 known, 5 candidate slots, and 9 open slots; the e*MZ VEV residual has the wrong sign under the paper's usual calc-minus-PDG convention; the slot-12 to slot-20 one-block shift uses an unspecified slot-12 energy; and the tree-level Weinberg route uses sqrt((1+pi)/pi) as about 2.032 even though it is about 1.148, giving about 104.7 GeV rather than 185.3 GeV.",
    "verify_P041.py": "New audit finding: P41's new strange/up energy formulas are numerically close: Es=pi^2-1/7, Eu=pi^(7/5), the Fano displacement, and the rough s/u mass estimates reproduce within rounding. The flagged issues are table/status problems: the complete quark table's bottom mass should be about 4039.9 MeV, not 4141; charm should be about 1285.1 MeV, not 1267; the top formula gives about 176.1 GeV, not 188 GeV, because MU*(19.213-pi) is about 12.750 rather than 12.816; the associated bottom/charm/top residuals are stale; the alternative up candidate pi^2-ln(mu0) gives about 2.144 MeV, not exact 2.16 MeV / 0.0% error; the open-slot prose says five remaining slots while the table lists four slot entries; and the final derived/no-free-parameters wording is stronger than the paper's own conjecture-level status for I/J.",
    "verify_P042.py": "New audit finding: P42's sector-fraction Weinberg-angle algebra reproduces: edge/boundary fractions give 1/(1+pi)≈0.24145, the 4.4% MZ gap and fitted C_eff≈0.224 check, and CFP ratios gY^2/gW^2=1/pi and gs^2/gW^2=4pi reproduce. The flagged issues are proof/status problems: C_eff is fitted from the observed discrepancy rather than independently derived; the displayed one-loop coefficient formula evaluates to about 1.63, not order 0.2-0.3; literal one-loop running of the explicit CFP absolute couplings gives about 0.207 rather than 0.2313; the absolute CFP couplings need a normalization map before SM RG use; the Lambda_geom open item is duplicated; and CFP remains a postulate/conditional input.",
    "verify_P043.py": "New audit finding: P43's sector-charge arithmetic mostly reproduces: edge/boundary/bulk integrals, mu0, half-volume identities, bulk 8pi Vol(B4), 15/4 Vol(S6), G2 trace Casimir scalar, kinetic/calibration/monad density integrals, per-generator charge values, and tree Weinberg angle 1/(1+pi) all check. The flagged issues are proof-status problems: the standard Hopf fiber length is not literally 2pi*x on unit S3; H1 is still a monad-current definition rather than a standard Noether-current derivation; irreducibility of the adjoint representation does not imply transitivity on the unit sphere for G2; C2(7)=6 conflicts with I(7)=1 via C2(R)dimR=I(R)dimg; the bulk closure remains conditional on monad normalization; and the one-loop MZ running is imported rather than verified here.",
    "verify_P045.py": "New audit finding: P45's main quark energy/mass table, Cabibbo check, moment-log spectrum, Z3 dimension split, and finite pi^(n/3) lattice scan mostly reproduce. The flagged issues are internal consistency/proof-status problems: the explanation of the old P41 top error is incompatible with the shifted mass formula; the later top/charm ratio paragraph switches PDG input sets and its +1.1% ratio discrepancy does not correspond to the table's +1.9% top-mass residual; the D-moment section misidentifies exp(MU*pi) as m(E=pi)/m_e even though Eq. (1) gives m(E=pi)=m_e; the Fano-plane root-count sentence is not literal Fano combinatorics; and the proposed OP-B' triple product {alpha3,y,alpha3} is zero on off-diagonal Peirce components in the standard calculation.",
    "verify_P046.py": "New audit finding: P46's core trace arithmetic reproduces: mu0/mu1/MU, Tr(Xsec)=mu0, Tr(Xone)=mu1, Xone=Xsec∘K, the moment-log table, the G0-G1 link, the top/charm ratio comparison, the down-mass comparison, and the Xsec characteristic-polynomial coefficients all check. The flagged issues are localized formula/status problems: the Peirce-center rule is written as K_i=n_i/(n_i+1) for sector powers 1,2,3, but the displayed 2/3,3/4,4/5 values come from (n+1)/(n+2); the related center-of-mass integral is miscomputed; the displayed current top/charm inputs imply a +1.14% top-mass discrepancy rather than +2.0%; the G2 Killing-form route is ill-defined as written because the Killing form is on g2, not V1; the Bregman-divergence label is not justified by the displayed identity alone; and OP-B/OP-D remain structurally open by the paper's own checklist.",
    "verify_P047.py": "New verifier passes: P47's negative spectral-density result and positive harmonic-diagonal theorem are internally consistent. The Peirce spectrum, 27-dimensional spectral trace 9*mu0, spectral mean mu0/3, three-node Gauss nodes, non-matching normalized Peirce/center nodes, moment hierarchy mu_k=Tr(Xsec o D_k), rational F(z), pole residues, G0-G1 Stieltjes ratio, and open OP-B/OP-D status all reproduce.",
    "verify_P049.py": "New audit finding: P49's main electroweak numerics mostly reproduce: the E6 Killing-form sum gives 12, the Killing-form mass scale is only about 6 MeV, the observed W energy is about 18.224, lambda_H gives v≈245.98 GeV from observed mH, the TOE Weinberg ratio gives mZ/mW≈1.1482 and mW≈79.42 GeV from observed mZ, and the g_TOE chain gives mW≈75.79 GeV. The flagged issues are narrower: the closure table's mZ-from-mW row is stale because observed mW with TOE theta gives about 92.29 GeV rather than 91.09; the 'systematic scan' excluding simple E_W bridges is not reproducible from the TeX; the 5.7% g deficit is attributed to RG running only by an order-of-magnitude estimate, not a TOE RG calculation; and the \\sinW macro denotes sin^2(theta_W) but is used as a linear sin(theta_W) coefficient in the Z/photon generator formulas.",
    "verify_P051.py": "New audit finding: P51's corrective arithmetic mostly reproduces: mu0/mu1/MU, sector-density integrals, Tr(Xsec)=mu0, K=(2/3,3/4,4/5), Tr(Xsec∘K)=mu1, the harmonic diagonal moment hierarchy, the spectral-log G0/G1 link, and mass-map inverse formulas all check. The flagged issues are proof/status issues: the paper sometimes calls sector powers n_i=1,2,3 the cell dimensions even though the listed cells S1/S3/B4 have dimensions 1,3,4; the sector-idempotent bijection remains a natural-correspondence argument because the T2 uniqueness theorem is explicitly open; and the final mass-ratio step m_t/m_c=Tr(Xsec), with Conjecture D's closure downstream of it, remains OP-B-Mass rather than a derived consequence of the trace identity.",
    "verify_P052.py": "New audit finding: P52 is mostly internally consistent as a status-boundary paper: mu0/mu1/MU, Xsec trace, Ec=pi+pi^2, the EW sub-density integral, m_c≈1285 MeV, ln(mu0)/MU≈6.2019, E_t≈19.213, m_t/m_c=mu0, m_t≈176.1 GeV, the failed route-1 ratio, and the six-permutation gauge-consistency enumeration all check. The flagged issues are proof-scope/status points: OP-B-T2 uses the imported physical sector-gauge map rather than the abstract Z3 decomposition alone, the paper's own F4 remark acknowledges that TOE physical identification input, and the 2% top gap is attributed to QCD running without computing that correction here.",
    "verify_P053.py": "New audit finding: P53's headline type-I seesaw ratio arithmetic reproduces: the TOE Planck/bulk scale estimates, phenomenological M_R from e*MZ and 49.5 meV, Cabibbo-step y_i values, r_TOE≈0.03307, the anchored Delta m21 and light-neutrino masses, and the old-candidate comparison all check. The flagged issues are narrower internal/proof problems: the Planck-option seesaw mass is about 1.4e-4 GeV, not 10^-1 GeV; the PMNS-invariance proof states unitary U but uses U^T and orthogonality, so it only proves the real-orthogonal case as written; the TBM comparison row says theta13=theta23=0 even though TBM theta23 is maximal; and the stated non-universal M_R2/M_R3≈0.98 correction has the wrong sign in the simple M1=M3 model, which requires about 1.035.",
    "verify_P054.py": "New audit finding: P54's corrected body calculation is reproducible: cubic-norm polarization gives zero for different off-diagonal blocks with one diagonal slot, -Re(q hbar)/3 for same-block self-couplings opposite the diagonal, zero when the diagonal index lies inside the off-diagonal block, the VEV-overlap formula, and the Cabibbo sine values all check. The flagged issues are internal/status contradictions: the abstract and theorem statement still claim compatible different-block couplings equal 1/6, and the abstract Higgs-coupling summary lists nonzero 1/6 values that the proof later cancels to zero; the status-table democracy wording preserves the older equal-coupling claim; the trilinear form gives only the overlap mechanism, not the Cabibbo angle assignment; and generation-3 y3=1 does not follow from the standard Higgs-doublet cubic coupling, which P54 itself identifies as an open gen-3 gap.",
    "verify_P055.py": "New audit finding: P55's core five-option seesaw-scale arithmetic mostly reproduces: mu0/mu1/MU, the rounded M_R target, Option A branching-ratio table, most Option B energies, Option D pi^3 Casimir scale, and Option E's v_EW^2/sqrt(Delta m31) route all check. The flagged issues are internal/status problems: the printed E_Pl=pi+mu1/MU is about 140.178 rather than 137.3 and is inconsistent with the M_Pl table coordinate; two Option B physical-mass rows do not follow from their energies; the Option C RG equation has the wrong displayed sign for sub-Planck confinement and its b0=9/11 table values are stale under alpha_s(M_Pl)=0.039; Option E is not unique within 5% because the two Option B near-misses are also within 5% in E_R; the 1.64e15 GeV near-miss remains about 32% from the target, not within a 20% threshold; and the y_nu=1 statement is called exact in prose but listed as a structural argument not proved in the open-problem table.",
    "verify_P056.py": "New audit finding: P56's basic sine/Cabibbo arithmetic reproduces: h_G2=6, dim G2=2(h+1)=14, theta_C=pi/14, y1=sin(pi/14)≈0.22252, y2=sin(2pi/14)≈0.43388, y2/y1≈1.9499, and the quoted -0.8% V_us residual check. The flagged issues are proof/internal-consistency problems: the paper says a Coxeter element of order 6 lifts to order 14 in the same representation; the displayed 14th-root eigenvalue set has eight distinct values for a seven-dimensional representation and conflicts with the proof's 7th-root wording; the 'unique associative 3-plane through e7' claim is corrected inside the proof to a 6-dimensional family; strict imaginary associativity gives y1=y2=0, so nonzero Yukawas require the later SU(3) singlet-projection reinterpretation; the y=cos(theta) ordering inequality is reversed; k=7 gives pi/2, not an angle inside two Weyl chambers; and the minimal-step variational derivation, precise singlet projection, and PMNS compatibility remain open in the status table.",
    "verify_P057.py": "New audit finding: P57's sine/Cabibbo numerics reproduce: h_G2=6, dim G2=14, theta_C=pi/14, y1=sin(pi/14), y2=sin(2pi/14), y3=1, y2/y1=2cos(pi/14), the V_us residual, and the basic Jordan product E12 o E23 = (1/2)E13 all check. The flagged issues are proof/status problems: the advertised Jordan-doubling theorem is disproved inside its own proof because the e7-mediated route gives overlap 0 and the real-unit route gives y1 rather than y2; the Jordan square of a unit E12 block is E11+E22, not (1/2)(E11+E22); the Peirce double-grading says x12 is Peirce-0 with respect to E22 even though its eigenvalue is 1/2; Peirce ordering does not algebraically exclude k2=3,4,5,6; and the claimed Phase 5a-ii closure remains conditional on the CKM-y1 physical identification, generation labelling, PMNS compatibility, and the precise SU(3) singlet VEV projection.",
    "verify_P058.py": "New audit finding: P58's overall status claim that Phase 5b remains open is supported, and the Phase 5a r ratio checks. However, the listed 49.5 meV neutrino mass, M_R=1.24e15 GeV, and E_R=56.502 reflection chain are not mutually consistent at the printed precision; several formulas use sin^4 where neutrino masses require sin^2; the Sigma m_nu proof uses the wrong powers; the Cabibbo correction sign/magnitude is inconsistent; and the natural-expression and mirror-sector tables contain stale arithmetic/claim contradictions.",
    "verify_P059.py": "New audit finding: P59's conservative status conclusion is supported: Z3 charge alone does not determine mt/mc, Route C is equivalent to the minimal axiom, and OP-B-Mass is explicitly left open. The flagged issues are route-evaluation arithmetic/proof problems: the printed mass-formula exponent is 16.101 but exact Et-Ee≈16.0715; 4π^3/(π+π^2) is about 9.53, not 30.4; the top-mixing ansatz gives EB/Et≈6.46, not 0.646, so it is not a valid sin^2 value; Tr(Xsec^2) is about 15,489.506 rather than 162,710; 16π^6 is about 15,382.227 rather than 162,603; Tr(Xsec^(1/3)) is about 8.5966 rather than 8.438; the real solution of mu_k=1 is k≈528.07, not about 189; and the moment-ratio proof only analyzes the k=0 reduction, not arbitrary integer pairs.",
    "verify_P061.py": "New audit finding: P61 self-corrects a large E_R unit error in a later remark, but the theorem remains wrong; stricter recomputation also flags the quoted Planck/gap precision, reduced-Planck table, and two candidate-table arithmetic/label issues.",
    "verify_P062.py": "New audit finding: P62's Candidate I/II arithmetic and alternative-candidate table mostly reproduce. The remaining issues are wording/uncertainty details: a 0.009 residual over a 0.0088 uncertainty is about 1.02 sigma, just outside one sigma despite the text calling it within one sigma; the proof explicitly uses a 1.5-sigma-style inequality for a one-sigma claim; and 0.47% precision in Delta m31 corresponds to about 0.12 meV precision in sqrt(Delta m31), not 0.23 meV.",
    "verify_P063.py": "New audit finding: P63's main negative conclusion is supported: the PDG neutrino ratio, TBM mass matrix reconstruction, off-diagonal norm fractions, PMNS angle formulas, off-diagonal-only unphysical spectrum, energy-gap statement, displayed numerology table, and Hopf-lapse near-rejection all reproduce. The flagged issues are local formula/proof-status problems: the printed TBM formula (m2^2+m3^2/2)/(m2+m3) gives about 22.37 meV, not the quoted 27.7 meV; the quoted value comes from m2/3+m3/2; the diagonal-dominated perturbation paragraph applies nondegenerate second-order perturbation theory to the degenerate alpha2=alpha3 block and understates the 2-3 off-diagonal size as about 1% when the squared ratio is about 62.5%; and the claimed systematic numerology search is not reproducible from the TeX because the candidate generator/code is omitted.",
    "verify_P064.py": "New audit finding: P64's constants, embedding-index arithmetic, corrected body Casimir ratio, Option-B near-miss, implied Option-B neutrino mass, and V_R norm estimates mostly reproduce. The flagged issues are internal consistency problems: E_nu3=-17.231 is not produced by the stated 49.5 meV mass; the abstract's kappa=12/78 conflicts with the body's Casimir ratio 1; the Killing-form table uses E_bulk^n for n=1/2 and -1 even though the displayed formula E_bulk*(ratio)^n with ratio=1 gives E_bulk for every n; the text's conclusion E_R^(K)=E_bulk^n does not follow; the numerical spectral-reflection check using the stated v and 49.5 meV gives about 56.486 rather than 56.503; and the meV-to-GeV conversion shown in the E_nu calculation is off by 10^3.",
    "verify_P065.py": "New audit finding: P65's leading PMNS compatibility numerics mostly reproduce: y1/y2, theta_C, theta12=5π/28, theta23=π/4, the QLC sum, TBM comparison, rough theta13/J estimates, and the displayed leading PMNS matrix all check. The flagged issues are proof/status problems: the displacement-angle equivalence is miswritten; the moduli count alternates between three Yukawa constraints and two independent quotient moduli after anchoring; the text says Yukawa overlaps determine theta12/theta23 while later proving PMNS angles are independent observables; QLC and theta23 maximality are assumed from a pi/4/TBM/Z3 principle rather than derived from the displayed equations; the theta23 complement formula would give about 87.7 degrees, not 45 degrees; the sector-to-off-diagonal unitary map is not explicitly constructed; and the Phase 5a closure wording is stronger than the conditional status table.",
    "verify_P066.py": "New audit finding: P66's leading theta13 value and final CKM/PMNS phase formula are numerically reproducible, but the paper has unresolved internal inconsistencies: the Peirce norm trace argument is arithmetically wrong as written; the dihedral-angle fractions mix 17π/84 and 17π/42; the Bryant calibration numerics use stale cos/product values; the rotated-calibration proposition is not what its proof derives; the Jarlskog value recomputes to about 0.0317 rather than 0.0297; and the paper declares Phase 5b-ii closed while several inputs remain structural/open.",
    "verify_P067.py": "New audit finding: P67's finite Bryant/Fano algebra mostly checks: the seven lines, 21 pair incidences, phi_127=0, lines through 7, the unique line through {4,7}, the (1,2,7) associator, and e3e4=-e7 all reproduce. The flagged issues are overstrong uniqueness/equivariance and stale CP-angle arithmetic: {1,4,5} and {2,4,6} also connect Im(H) basis elements to e4, so only {3,4,7} is unique through both e4 and e7; cos(5pi/28), Phi=-s1*s2*cos(psi), and alpha are stale; the displayed alpha-to-delta conversion gives about 108.38° rather than 66.43°; the quark/lepton sign convention is internally inconsistent; nonzero e7 calibrations also occur on {1,6,7} and {2,5,7} absent extra gauge restrictions; and the KM-counting/color-requirement/OP-P66-5 closure claims remain structural rather than proved by this addendum alone.",
    "verify_P070.py": "New audit finding: P70's midpoint arithmetic is solid: the Candidate I/II values, midpoint E_R, half-splitting, and Wolfenstein order table mostly reproduce. The flagged issues are narrower: the theta23-to-Delta m31 extraction proof uses a singular derivative at maximal mixing; the abstract's 1-3% cubic proximity is stale relative to the exact 4-7% gaps; and the final midpoint neutrino-mass comparison accidentally switches from the predicted 48.7-48.9 meV mass to 49.5 meV, making the Delta m31 comparison/residual wrong.",
    "verify_P072.py": "New audit finding: P72's theta23 arithmetic using observed A passes, but the claimed A derivation has an identity error, inconsistent RG factors, and the final closure uses A_obs as an input.",
    "verify_P073.py": "New audit finding: P73's low-level Peirce and QLC corrections check out, but the Jarlskog/back-reaction closure is internally inconsistent and includes trigonometric/arithmetic errors.",
    "verify_P074.py": "New audit finding: P74's A68/NLO theta13 arithmetic and fitted delta_QLC route mostly reproduce, but the abstract's printed structural formula does not give 0.15003/8.627 degrees; the displayed QLC degree-correction formula gives about -0.468 degrees rather than -0.0817 degrees; the abstract has a 0.5 sigma typo and a missing label; and the paper contradicts itself on whether delta_QLC/Phase 5d is open or closed. The final PMNS table also has residual sign errors.",
    "verify_P075.py": "New audit finding: P75's final trilinear table arithmetic mostly passes, but the abstract/early theorem claims a different exact formula; the sigma offsets are overstated, and one structural G2 input is explicitly left without full proof.",
    "verify_P076.py": "New audit finding: P76's core CGF arithmetic checks: mu0/mu1/MU, MGF(0)=mu0, CGF'(0)=MU, the explicit MGF formula, the log-charge identity, exp(MU*gap)=mu0, bulk/charm fractions, and the SWS residual being open all reproduce. The flagged issues are internal/proof problems: the appendix's precise Ec, ln(mu0), gap, and Et values are stale and the printed Ec/Et pair gives m_t/m_c≈136.939 rather than mu0; direct entropy quadrature gives integral≈756.819, H≈-0.6025, and KL≈0.6025 rather than 756/-0.597/0.597; the lambda=1 condition is not selected at t=0 because Z(lambda,0)=mu0 for every lambda; uniqueness holds only for Delta, not for lambda; and the ln-bridge transcendence proof is not rigorous as written.",
    "verify_P077.py": "New audit finding: P77's Candidate I seesaw formula E_R=E_Pl-12+MU*pi/6 is numerically reproducible, giving epsilon≈0.415393 and E_R≈56.511. The flagged issues are precision/status/proof problems: exact substitution gives about 1.06-1.07 sigma rather than 1.02 sigma and is slightly outside one sigma; the neutrino-mass residual is about 1.9% / 2.7 sigma with exact values rather than 1.6% / 2.3 sigma; the claimed CODATA E_Pl anchor inherits the P61 rounded-anchor mismatch; and the structural proof overstates rank/root-system facts, derives a rotation/no-residual group computation before asserting one reflection, and remains conditional on the explicit spectral-angle conversion assumption.",
    "verify_P079.py": "New audit finding: P79's core spectral-weight arithmetic mostly reproduces: mu0, mu1, MU, sector weights, A(1)=mu0, EB/mu0≈0.9051, Ec/mu0≈0.0949, A^{-1}(EB)≈0.9746, the mu0 gap, bulk-only competitor, and PDG residual all check. The flagged issues are one arithmetic error and several proof/status gaps: Tr(Xsec^2) is about 15,489.506, not 150,505; the top-energy table's 19.212 is stale versus exact 19.213118; the SWS proof remains conditional on the top's mass-map image equalling A(1); e3 maximality does not by itself derive x_t=1; the Z3 argument assigns the ratio eigenvalue omega and then sets it equal to an invariant trace; trace uniqueness assumes unproved linearity/normalization restrictions; the GON formula leaves rho_n and a question-mark exponent unresolved; and the closure claim inherits P76's unresolved lambda=1 selection issue.",
    "verify_P080.py": "New audit finding: P80's rho-moment arithmetic checks: mu0, mu1, the sector decomposition of mu1, MU=mu1/mu0=CGF'(0), the comparison ratios that are not MU, epsilon=MU*pi/6, and E_R≈56.511 all reproduce. The flagged issues are proof/status problems: the paper's six-decimal MU=0.793338 is stale versus exact 0.793342208; the mass-coordinate derivative dE/dln(m/me)=1/MU means MU is the inverse of the log-mass-to-E conversion; the Hopf derivative calculation does not equal MU (direct averaging gives about 0.693 and derivative at x=MU gives about 0.810); therefore Assumption 4.1 is not proved by the moment computation alone and Phase 5b is not closed without that residual angular-conversion input. The final neutrino-mass/sigma arithmetic also gives about 48.53 meV and 2.8 sigma from the displayed inputs, not 48.7 meV and 2.3 sigma.",
    "verify_P081.py": "New audit finding: P81's headline numerical A_NLO formula reproduces: lambda, lambda^2, A0≈0.85636, 4lambda^2/5≈0.03961, A1≈0.82243, the residual to A_obs, and V_cb≈0.04072 all check. The flagged issues are derivational: with Hermitian off-diagonal conventions, a simple imaginary-unit test gives the two-step Jordan loop eigenvalue +1/4 rather than -1/4 because the second Peirce product needs the conjugate/sign; the paper's own correction formula -(1/4 * Sigma)/N with Sigma=4lambda^2 and N=5 gives -lambda^2/5, not -4lambda^2/5, so it would produce A≈0.84788 rather than 0.82238; the 8lambda^4/5 estimate is about 0.00392, not 0.00039; and the paper declares N=5 and Sigma=4lambda^2 proved while listing rigorous derivations of both as OP-81-2/3 open problems. Phase 5f is therefore only numerically matched, not unconditionally proved by the displayed loop derivation.",
    "verify_P082.py": "New audit finding: P82's lambda/A/delta/Jarlskog chain mostly checks, but the printed Bryant calibration Phi is not the value of the stated formula; that mismatch propagates into rho_bar, eta_bar, |Vub|, R_b/R_t, and the unitarity-triangle angle table. The paper also acknowledges an impossible direct normalization and relies on a structural dimensionless-triangle interpretation.",
    "verify_P083.py": "New audit finding: P83 abstract/Theorem D says the direct E_d-E_u gap is about 0.9774 with |epsilon| < 0.002, but the paper's direct formulas give about 0.9441; the body later acknowledges the discrepancy.",
    "verify_P084.py": "New audit finding: P84 top-mass recomputation/table says 172.4 GeV / -0.2%, but its formula gives about 176.10 GeV / +1.94%.",
    "verify_P085.py": "New audit finding: P85's final NLO Higgs arithmetic mostly passes, but an abandoned LO route remains in-theorem, the A39 mass cross-check uses inconsistent v_EW arithmetic, and the proposed NNLO c4 closure coefficient is wrong.",
    "verify_P089.py": "New audit finding: P89's core VEV arithmetic reproduces: lambda=sin(pi/14), 4lambda^2/5, lambda_H0=1/8, v0=2*mH0=246.22 GeV, the NLO Higgs/lambda_H values, and the NLO cancellation in m_H/sqrt(2lambda_H) all check. The flagged issues are internal/status problems: the boxed structural formula writes sqrt(2*hvee(E6)/N_gen)*mH0, which equals sqrt(8)*mH0≈348.21 GeV rather than 246.22; the correct factor from the derivation is sqrt(hvee/N_gen)=2; the all-order VEV protection statement is conditional on mH^2 and lambda_H receiving the same loop factor; the text alternates between closing W/Z absolute masses and leaving g_W open; and the conjectured g_W formula does not give 0.653 under the natural FRAC_bdy=pi^2/mu0 reading.",
    "verify_P090.py": "New audit finding: P90 has arithmetic mismatches in alpha_2^{-1}, charm/bottom spectral thresholds, and the E6 GUT mass-scale conversion.",
    "verify_P091.py": "New audit finding: P91's rounded J_LO/J_NLO proposition arithmetic mostly reproduces, but its exact trigonometric path is inconsistent: cos(5π/28), Phi, rho_bar, and eta_bar are wrong/stale, so exact-formula J values differ from the printed table. Several residual signs and the residual-decomposition argument are also inconsistent with the paper's own convention and listed PDG inputs.",
    "verify_P092.py": "New audit finding: P92's corrected required-eta inversion, phase-only obstruction, and single-loop obstruction mostly check: the central eta target is about 0.3749, phase-only closure requires sin(delta)>1, and natural single-loop orbit dimensions give the wrong-sign Phi correction. The flagged issues are internal consistency problems: the abstract keeps the stale 0.384/11.8% eta target even though the proof corrects it to 0.3749/+9.0%; the exact Phi formula gives about 0.743745, not 0.7429, propagating to rho/eta/J; and the final paired-correction table treats 8 lambda^2/5 as +0.792% instead of +7.92%, so the displayed Phi_NLO, eta_NLO, and J_NLO rows do not follow from the theorem.",
    "verify_P093.py": "New audit finding: P93's body calculation gives M_W≈77.42 GeV and M_Z≈88.34 GeV, but the abstract still reports stale 78.742/89.843 values; the explicit M_W^2 arithmetic contains a numerator typo; and the correction-sum table is internally inconsistent.",
    "verify_P096.py": "New audit finding: P96's basic lambda/A_NLO constants and the final uniform-rescaling arithmetic mostly reproduce, but the paper is internally inconsistent. The abstract still claims the A92 paired +8λ²/5 Phi correction, exact G2 protection, eta/rho/J values near the LO result, and OP-P92-1 proved; the body derives the opposite -4λ²/5 uniform Phi correction, J_NLO/J_LO=(1-4λ²/5)^3, and says OP-P92-1 is false as stated. Exact Phi-derived inputs also give Phi≈0.743745, eta_LO≈0.340844, J_LO≈3.035e-5, and exact uniform J_NLO≈2.688e-5 rather than the rounded/stale table route 2.714e-5.",
    "verify_P097.py": "New audit finding: P97's NLO Higgs mass, λ⁴ natural band, topology-(a) additive mass, and explicit open-status wording reproduce. The flagged issues are internal consistency/proof-status problems: the central PDG c4 target is about -2.19, not -2.945; the paper's -2.945 value comes from a stale target factor and closes the lower 1-sigma edge, not the central mass; the displayed required-c4 formula has an extra 5/4 factor and conflicts with the compact formula; the one-sigma c4 interval and c4 uncertainty are wrong; the double-insertion proof squares the NLO factor and would double the O(λ²) term if taken literally; the printed loop-eigenvalue formula gives λ²/10 rather than 4λ²/5; and the associator sign/origin, last-two antisymmetry claim, and nested-loop orbit dimension are not proved as stated.",
    "verify_P098.py": "New audit finding: P98's two-channel difference-of-squares arithmetic mostly reproduces if one assumes opposite +/-4λ²/5 loop factors, giving rounded-path J_NLO≈3.050e-5 and a roughly -0.99% residual. The flagged issues are internal consistency/proof-status problems: the exact Phi formula still gives Phi≈0.743745 and exact two-channel J_NLO≈3.020e-5 rather than the rounded table route; the displayed Fano correction formula with N=5 is a factor of four too small to cancel the G2 loop; the proof computes a -1/4 Moufang eigenvalue before using a positive correction; the Moufang/Peirce map definitions conflict with the claimed independent two-channel split; N_Fano=5 is conditional rather than first-principles derived; and the abstract's A_NLO factor uses 1-8λ⁴/25 while the body/table use 1-16λ⁴/25.",
    "verify_P100.py": "New audit finding: P100's synthesis table mostly reproduces when using the older corpus MU mass slope, but the displayed MU formula evaluates to about 113 rather than 0.79334; the M_W row's displayed expression gives about 79.92 GeV rather than 77.42; the theta23 closed-status threshold and claimed count of 20 closed observables are ambiguous/inconsistent; and the abstract's v=2m_H wording is only true if m_H means the LO mass.",
    "verify_P101.py": "New audit finding: P101's headline Higgs NNLO arithmetic reproduces: c4(c)=-(4/5)(1/6)(27)=-18/5, c4=16/25-18/5=-74/25, and m_H≈125.086 GeV rounds to 125.09. The flagged issues are target/proof problems: the exact value is just below the strict 1-sigma lower edge; c4_req=-2.945 is not the coefficient for the 125.20 GeV central mass; the +0.015 topology-b/residual argument closes only that lower-edge target and not the central value; the c6 sensitivity is about 0.00735 GeV per c6, requiring c6≈15.5 rather than 7; the claimed G2 average 1/294 is an independent sphere average, not a fixed Fano-triple orbit average; and the F4 orbit-factor proof treats J3(O) as an irreducible 27-dimensional F4 module even though the identity/trace line is fixed.",
    "verify_P102.py": "New audit finding: P102's final NNLO mass arithmetic is reproducible: c4=16/25+1/40-18/5=-587/200 and m_H≈125.089 GeV. The flagged issues are target/proof details: the quoted c4_req=-2.945 is not the coefficient required for the PDG central mass 125.20 GeV, which is about -2.19 in the signed convention; c4=-2.945 instead gives about 125.088 GeV near the lower 1-sigma edge. The c4 tolerance from the stated mass uncertainty is about 0.74, not 0.3. The nested-loop orbit calculation also has an unproved 11->10 normalization subtraction; without it c4b would be 1/44 rather than 1/40.",
    "verify_P103.py": "New audit finding: P103's headline bottom correction is numerically reproducible when using the older continuous-moment MU: m_b≈4039.9 MeV, delta=(4/9)alpha_s/pi≈0.03210, and corrected m_b≈4169.5 MeV within the PDG 1-sigma band. The flagged issues are that the displayed MU formula evaluates to about 113, not 0.79334; the printed pi^(7/3) and exponent are stale; the alpha_s^2/NLO correction is off by a factor of ten (the displayed formula gives delta2≈0.0118 and m_b≈4217 MeV, not 0.00118 and 4174.4 MeV); and the structural claim that only P23 is a pure G2 module needs proof beyond entrywise Aut(O), which acts on every octonionic Peirce block as 1+7.",
    "verify_P104.py": "New audit finding: P104's headline W-mass correction values mostly pass, but the leptonic-running proposition silently swaps from the displayed leading-log value to the standard constant-corrected value; the quoted PDG-top impact on M_W is about ten times too large under the paper's own formula; and two smaller scale estimates are off.",
    "verify_P105.py": "New audit finding: P105's golden-ratio Weinberg-angle numerics mostly reproduce, including the NLO/NNLO values, the c4 elimination, and the Peirce 3/13 calculation. The flagged issues are stale precision/wording: exact formulas give a near-miss gap of about 0.054% rather than separate 0.060% and 0.048% gaps; the Peirce+NLO value is about 4.15% below PDG, not 0.41%; the abstract's c6≈1.25 is inconsistent with the body, which requires about +56 after NNLO or -4.8 for the rounded NLO-only gap; and the Hopf projection text says 60 vertices of an icosahedron, though 60 is the icosahedral rotation-group order.",
    "verify_P106.py": "New audit finding: P106's BREATH_PERIOD scale, G2 root-ratio numerics, threshold positions, one-loop spectral-running deltas, and final alpha_s(M_Z)≈0.11862 all reproduce. The flagged issues are proof/status problems rather than arithmetic failures: uniqueness of the BREATH scale is asserted without enumeration/search; alpha_s(E_conf)=sqrt(3) is a boundary postulate based on the root-length ratio, not derived from matching equations; the one-loop run starts at alpha_s≈1.73 in a non-perturbative region; the displayed two-loop estimate gives about -0.011 over the full E_conf-to-E_Z interval rather than -0.003; the 3-through-5-loop add-back is not computed in the paper; and OP1 is only conditionally closed at one loop while OP1-NLO remains open.",
    "verify_P107.py": "New audit finding: P107's pQCD hadronic-running arithmetic mostly reproduces: mu0, m_conf, the QCD correction factor, charge factors, logarithm brackets, Delta alpha_uds/c/b, total Delta alpha_had^pQCD≈0.02526, the 8.6% residual, alpha_EM(M_Z)^-1≈129.27, and the linear W-mass updates to about 80.09/80.19 GeV all check. The flagged issues are one arithmetic typo and several status/method limits: the printed alpha/(3pi) prefactor 7.772e-4 should be about 7.7427e-4; the addendum says OP3 is completed even though its own summary leaves a -0.23% row, a final '? -> 0%' arrow, and OP3-Deltaalpha as an open spectral-function problem; m_conf is once called a UV cutoff although it is used as an IR cutoff; the single alpha_s(M_Z) factor is a leading pQCD estimate, not the non-perturbative dispersion integral; and M_W is updated via the P104 linear sensitivity rather than recomputed from the full electroweak relation.",
    "verify_P108.py": "New audit finding: P108's resonance arithmetic partly reproduces: the P107 uds pQCD baseline, residual by PDG subtraction, rho mass from 2sqrt(pi)m_conf, f_V^2=8pi, extracted f_rho^2, charge-factor magnitudes, resonance table sums, and appendix alpha(M_Z)^-1 chain all check. The flagged issues are internal/status problems: the residual 0.002383 is defined from the PDG dispersive value minus pQCD rather than independently derived; the printed GS resonance integral is 0.00365, about 1.53 times the residual, so it cannot by itself be the claimed residual without an extra subtraction/double-counting argument; the omega charge-factor prose has a sign/arithmetic error; and the paper's own open questions leave SU(3)-breaking and higher-resonance contributions unresolved, so the complete parameter-free closure claim is stronger than the displayed derivation.",
    "verify_P109.py": "New audit finding: P109's rounded NLO+c6 path mostly reproduces: lambda powers, the golden target, LO/NLO/NNLO table values, 600-cell cells/vertices and edges/vertices, c6=-24/5, the c6 shift, NLO+c6 value 0.23175, and the quoted -0.0065% gap all check. The flagged issues are series-consistency and proof-status problems: c6 is introduced as an NNNLO coefficient in the same expansion that contains c4, but the advertised near-hit is obtained only by skipping the NNLO c4 term; including c4 and c6 gives about 0.229995 and a -0.76% gap. Exact, unrounded formulas give required c6≈-4.29 and a c6 discrepancy around -11.9%, not the rounded -4.43/-8.4% path; the exact c8 estimate is about 10.3 rather than 9.6; and the 600-cell c6 weighting rule is asserted rather than derived by an explicit loop enumeration. P105-1 remains open.",
    "verify_P110.py": "New audit finding: P110's c8 face-density arithmetic mostly reproduces: lambda powers, F600/V600=10, c8=8, the c8 shift≈1.161e-5, the 600-cell-only c2+c6+c8 value≈0.231759, residual≈-3.4e-6, and improvement factor≈4.44 all check. The flagged issues are combinatorial/series-status problems: the displayed full expansion only matches the near-hit when the c4 term is skipped, 1/6/10/5 are not binomial coefficients binom(4,k), F/V=10 and C/V=5 are not binom(4,2) and binom(4,4), the single hvee*(sigma/V)/N_Fano formula does not generate c2=4/5 from C/V=5, the repeated rounded c6 target is stale under exact inputs, the proposed c10=-4/5 has the wrong sign to cancel the remaining negative residual, and the loop-weighting rule is asserted rather than enumerated.",
    "verify_P111.py": "New audit finding: P111's 600-cell subseries arithmetic partly reproduces: S*, LO, c2-only, c2+c6, c2+c6+c8, and the small c10 shift all check. The flagged issues are central proof/formula problems: the text gives lambda^2≈0.04894 though sin(pi/14)^2≈0.049516; the c2+c4 table value/gap are stale; the Freudenthal diagonal lemma T(X)=det(X)I is false under the paper's own cross-product definition, so the c4(theta_W)=0 proof does not follow; the finite 2I character/Molien sketch inserts a pi-dependent LO factor that finite-group character sums alone cannot produce, and the required Clebsch-Gordan weights are left open; the f-polynomial resummation remark does not land near S*; the master table's all-orders Weinberg value is about +0.235% above the stated PDG 0.23122, not 0%; and P105-1 remains conditional despite the proof title.",
    "verify_P112.py": "New audit finding: P112's corrected product-formula arithmetic mostly reproduces: the Sym^2(V2) and V2 character averages vanish, 3/4 * tau/2 equals 3/(8phi), the target value and PDG residual check, the 600-cell f-vector group-size ratios check, and the S(lambda) convergence table matches. The flagged issues are proof-status/interpretation points: 3/4 is not the ordinary non-singlet dimension fraction of the 7-dimensional G2 representation (that would be 6/7), the hypercharge projection into short-root space is stated rather than constructed, the physical selection of 5B over the other 5-fold classes remains open, and P105-1 is still conditional on that selection-rule derivation.",
    "verify_P113.py": "New audit finding: P113's printed rounded-MU muon correction mostly reproduces: lambda, A_LO, A_NLO, alpha*A_NLO, Z_mu, screening form, LO≈208.0103, corrected ratio≈206.7693, corrected muon mass≈105.659 MeV, and the EM self-energy scale all check on that rounded route. The flagged issues are precision/status problems: corpus MU is about 0.793342208 rather than 0.793338, and using exact corpus MU gives LO≈208.0161, corrected ratio≈206.7752, residual≈+0.00347%, and m_mu≈105.6619 MeV; the 1200x improvement is therefore stale under exact inputs, and Z_mu's first-principles derivation remains explicitly open despite the closure wording.",
    "verify_P114.py": "New audit finding: P114's light-quark arithmetic mostly reproduces: the initial u/d/s residuals, EM factors and small shifts, P103 bottom correction, the Peirce QCD correction 8/9*alpha_s(MZ)/pi≈3.356%, corrected u/d/s masses, residuals, u sigma comparisons, and one-sigma band checks all pass. The flagged issues are a direct confinement-scale formula error and proof-status limits: pi*mu0*m_e is about 220 MeV, not 1.27 MeV (the 1.27 number is close to pi*(mu1/mu0)*m_e); the MZ scale-selection principle is explicitly left open; the u-quark first-principles derivation remains open; and d/s derivational closure still depends on a proposed sign/scale scheme choice.",
    "verify_P115.py": "New audit finding: P115's Z_mu arithmetic reproduces: lambda, cos factors, A_LO≈0.8564, NLO factor≈0.96039, A_NLO≈0.8224, alpha, Z_mu≈1.006002, the rounded P113 mu/e route≈206.769, and the exact-MU route≈206.775 all check. The flagged issues are proof-status/group-geometry problems: pi/14 is not the literal G2 Weyl chamber angle (G2 gives pi/6), the two-vertex Peirce cosine walk and delta m/m=alpha*A_NLO normalization are assigned rather than derived from an operator/loop calculation, the Bryant/Wolfenstein-to-EM universality identification is asserted, the full charged-lepton first-principles closure is overstated despite open two-loop and P13/P23 questions, and electron/tau immunity is not proved by an exhaustive Peirce-loop exclusion.",
    "verify_P116.py": "New audit finding: P116's headline tau-ratio arithmetic reproduces: the P13 walk amplitude, complementary-angle identity, MU, lambda_tau, E_self(lambda=0/lambda_tau/1), tau exponent, tau/e ratio≈3474.61, tau/e residual≈-0.075%, P23 walk amplitude, and alpha*A_P23 all check. The flagged issues are local arithmetic/status problems: the text prints MU=0.79384 although corpus MU is about 0.793342; tau/e=3474.6 times the electron mass is about 1775.5 MeV, not the table's 1776.4 MeV; identifying the 8-real-dimensional P13 block literally with a Hopf S1 fiber is not derived; the fold-map detailed-balance equation is asserted rather than calculated from operator dynamics; the all-charged-leptons first-principles closure is overstated; and the -0.26 sigma residual is not reproducible from a supplied uncertainty.",
    "verify_P117.py": "New audit finding: P117's phi/K* arithmetic mostly reproduces: MU, MU^2, charge factors, bare J1 coupling, rho/omega SU3 values, omega gap conventions, f_phi^2≈179.69, phi residual, K* one-strange estimate, and the charge-factor times Peirce-factor decomposition all check. The flagged issues are local formula/proof-status problems: the rho residual sign is opposite TOE-minus-PDG convention, the summary proof's literal dP*pi/C_rho^2 formula gives 16pi rather than 8pi, the omega gap interpreted as |epsilon|^2 gives a huge amplitude≈0.535 rather than a small mixing parameter, and the MU-to-strange-current coupling rule is asserted rather than derived by an operator calculation.",
    "verify_P118.py": "New audit finding: P118's omega-mixing arithmetic mostly reproduces: SU3 baseline 72pi, original omega gap, charge-factor ratio C_rho/C_omega=3, epsilon=-alpha_s/3, suppression factor (1-alpha_s)^2, corrected f_omega^2≈291.16, residual≈+0.066%, gap-closed≈99.7%, mixing magnitude, P114 comparison scale, and phi table values all check. The flagged issues are sign/status/proof points: the rho row's -2.3% sign is opposite TOE-minus-PDG convention, the complete f_V^2-sector claim conflicts with P118's own open rho residual/OP1-NLO caveats, epsilon=-alpha_s/3 is asserted without a mixing-Hamiltonian derivation, and the MZ scale choice is imported rather than selected locally.",
    "verify_P119.py": "New audit finding: P119's rho correction arithmetic mostly reproduces: bare 8pi, the monadic integral pi, pi*alpha, corrected f_rho^2≈24.5566, charge-factor suppression, omega/phi table values, and the correction hierarchy all check. The flagged issues are sign/rounding/status problems: the exact TOE-minus-PDG rho residual is about -0.014%, not +0.01%; exact values close about 100.6% of the original gap rather than 99.6%; the abstract and body use opposite signs for the original residual convention; and the complete f_V^2-sector claim is stronger than the open omega/phi residual and propagator-selection caveats.",
    "verify_P120.py": "New audit finding: P120 is mostly internally consistent as a documented open result: MU, the P114 QCD correction, corrected u/d/s masses, u residuals/sigma, one-sigma band checks, m_conf=pi*MU*m_e≈1.273 MeV, m_u/m_conf≈1.892, and the finite candidate-ratio table all reproduce, with the best listed candidate still about 5.2% away. The flagged issues are limited: alpha*m_N is about 6.85 MeV if m_N is a nucleon mass, not 1.3 MeV; the 'all TOE-native ratios exhausted' wording is broader than the finite search shown; and consistency with a broad one-sigma band is weaker than pinning the central value.",
    "verify_P126.py": "New audit finding: P126's trace-scaling arithmetic checks conditionally: SU(3) has eight generators, a Peirce off-diagonal O sector is 8-dimensional, J3(O) is 27-dimensional, the standard C_A/C_F values check, Tr(X_a X_b)=2 delta_ab and T^a=X_a/2 give T_F=1/2 with zero residual, and the displayed b1=116/3 follows for n_f=5. The flagged issues are algebra/representation gaps: Im(O) is 7-dimensional, so it cannot have eight orthonormal imaginary unit generators; su(3) embeds in g2 as derivations, not as an 8-dimensional subspace of Im(O); Hurwitz norm multiplicativity does not force orthonormality; T^a=X_a/2 is an extra representation prescription rather than a consequence of the Jordan symmetrizer alone; the derivation mirrors the standard Gell-Mann normalization; octonionic matrix multiplication is not globally associative; first-principles b1 closure still depends on the standard C_F formula and the unproved Peirce-generator identification; adjoint trace conventions are mixed; and the all-SU(N) generalization is not constructed.",
    "verify_P128.py": "New audit finding: P128's C_F and b1 arithmetic reproduces: SU(3) adjoint dimension 8, fundamental dimension 3, T_F=1/2, C_F=T_F*8/3=4/3, the standard SU(3) C_F formula, zero C_F residual, and b1=116/3 for n_f=5 all check. The flagged issues are derivational: Im(O) is 7-dimensional, so the text's eight imaginary-octonion generator claim is false; a Peirce O cell is not the SU(3) adjoint Lie algebra; rank J3(O)=3 does not by itself derive the SU(3) fundamental representation; the proof uses a standard Casimir-index identity and standard SU(3) dimensions while claiming not to invoke group theory; T_F is inherited from the already-flagged P126 route; C_A=3 is still open inside P128; Hurwitz does not impose associativity of octonions; and full b1 first-principles closure is therefore overstated.",
    "verify_P130.py": "New audit finding: P130's headline C_A numerics reproduce: affine A2 marks sum to 3, standard SU(3) h-dual/C_A is 3, the Peirce sector ratio (3*8)/8 returns 3, and the G2/A2 root and dimension counts check. The flagged issues are proof-status gaps: the derivation still uses standard C_A=h-dual and affine Dynkin-mark theory; the claimed bijection from affine nodes to Peirce sectors is asserted rather than constructed; off-diagonal O cells do not carry eight imaginary directions; SU(3) has rank 2, so three diagonal idempotents are not three independent Cartan generators; the dimension ratio counts sectors rather than computing a quadratic Casimir through the adjoint trace form; Hurwitz norms do not force affine marks; and b1 closure remains conditional.",
    "verify_P142.py": "New audit finding: P142's negative GS log-symmetry result reproduces directly by Simpson integration: epsilon, xi, u_thr, f1, the u=0.3 running-width check, <e^u>, <e^-u>, their ratio/difference, u moments, Taylor reconstruction, geometric mean, cumulant approximation, and the open full-kernel K(s) status all check. The only flagged issue is wording: NWA=1 gives individual errors of about +16.8% for <e^u> and -3.3% for <e^-u>, not roughly +/-10% individually.",
    "verify_P143.py": "New audit finding: P143 correctly states the standard Gödel preconditions, second-theorem condition, Tarski real-closed-field escape route, local P7 number-theory overlay, alpha arithmetic, Con(TOE) candidate, and the physical-vs-formal completeness distinction. The flagged issues are formalization/scope problems: the current verifier report contradicts the 'no internal contradictions identified' premise; no recursive axiomatization is actually supplied; Tarski completeness is conditional because the named constants, analytic/spectral claims, and physical interpretation layers are not reduced to first-order RCF; the P7 eigenproblem is not fully grounded from the supplied hypotheses; the alpha uniqueness claim is not literally a Gödel diagonal sentence; the class of admissible TOE variants is not formalized; J3(O) classification does not yet prove the Wheel-operator map; and the claim that formal incompleteness cannot affect physical predictions is overstated relative to the paper's own G4 caveat.",
    "verify_P145.py": "New audit finding: P145's inherited P141 budget arithmetic reproduces: 4.11e-3/0.02750 gives 14.95% algebraic and 85.05% decoupled, the PDG/algebraic factor is about 6.69, the five vector poles give ten mass/residue parameters, the muon-g-2 scale ratio is about 1/53, and the 28%/72% HVP split plus lattice/dispersive limitation are present. The flagged issues are theorem-scope problems: PEW-projectability and Q_eff are not formal decidable criteria; the iff scale criterion lacks tail bounds; equation (alg) does not cover every listed algebraic observable; the R10-to-L2 dimension argument needs regularity/topology assumptions; finite extensions and QCD spectral-function spaces are overgeneralized; the alleged algebraic submanifold and relations are not constructed; algebraic/dynamical independence and the g-2 conclusion are conditional; and the theorem inherits upstream model assumptions.",
    "verify_P146.py": "New audit finding: P146's concrete operator/schema checks mostly reproduce: the five-component WheelState, five operator names, P7 boundary conditions, nonnegative self-lensing potential, plausible finite-interval Sturm-Liouville discreteness, absence of provenance in WheelState, Con(TOE)/fixed-point separation, and the open composite-trajectory problem all check. The flagged issues are implementation/physics-derivation gaps: Plateau fixed points for every Hopf face are not constructed; Fork/Weld heat conservation lacks update equations; the one-clock Type-2 blocking argument is verbal; eigenstate discreteness does not by itself solve the measurement problem or supply Born/collapse/decoherence dynamics; Hopf phase resolution is not connected to Plateau by a map; one-breath superposition collapse is not derived; the Butlerian kernel/witness boundary is asserted; and closed Oscillate cycles are still an open observer question.",
    "verify_P147.py": "New audit finding: P147's concrete CRT and example arithmetic reproduces: coprime periods 2 and 3 give lcm/product 6, the combined trajectory visits all six residue pairs once, the S3 distance examples give 0, pi/2, and pi/4 as printed, case (a) is below epsP, case (b) is above epsP, and the heat-depletion caveat is acknowledged. The flagged issues are bridge/scope problems: coprime integer periods are commensurate rather than literally incommensurate; geodesic proximity is not proved equivalent to MDL score margin; minimizers need not be unique; P27 cross-coherence is replaced by a threshold condition without constructing C/P operators; Plateau/Weld maps are not specified; commensurability matters outside the gcd=1 case because unreachable closest pairs can occur; the irrational-winding claim needs shared-torus/equidistribution hypotheses; and momentary Weld collapse is not derived.",
    "verify_P148.py": "New audit finding: P148's concrete tangent-encoding checks mostly reproduce: the tangent is R3-valued, basic S3 log distances and Oscillate step lengths check, Plateau is identified with v=0, Fork/Weld ambiguity and h_prev are acknowledged, the tangent is deterministic from endpoints, and CanonNode remains unchanged. The flagged issues are formula/schema/status problems: the written log map is also singular at p=q, exactly the Plateau case, so it needs an explicit zero branch; homotopy class of minimal geodesics does not distinguish operators; v alone is not unambiguous for all five operators; h_prev is a historical record whose one-clock status remains unaudited; v is three coordinates, so the amendment is not two scalar fields; unchanged Wheel tests are asserted but not shown; full Type-2 closure is overstated despite open Fork/Weld, Oscillate/Perturb, edge-typing, and P18-T2 issues; and zeta R is not proved disjoint from all 2pi/k.",
    "verify_P149.py": "New audit finding: P149's concrete stability checks mostly pass: the paper clearly separates Plateau convergence from Con(TOE), V_sl is nonnegative from the displayed rho' and quartic terms, the fixed-point equation is tautological for q=q*_k and h=0, and the local/global/provenance caveats are partly stated. The flagged issues are proof-scope problems: unique centroids on S3 need stronger hypotheses, the displayed Plateau rule does not send a welded state with h_c>0 to zero heat in one step, counting eigenstates does not prove face coverage, Hilbert-space spectral facts are not first-order RCF sentences, and the semi-algebraic midpoint/provenance claims need explicit face inequalities and branch assumptions.",
    "verify_P150.py": "New audit finding: P150's concrete G2 arithmetic mostly reproduces: root counts, length ratio, Cartan inner product, simple-root angle, listed positive-root lengths, A2 short-root fan, interleaved long-root fan, theta=pi/6, cot/sin values, matching exponent/scale, B4 radial x^3 measure arithmetic, bulk density integral, Hopf half-lapse, and CP-3 open status all check. The flagged issues are proof/measure-bookkeeping problems: W(G2) of order 12 does not contain a pi/6 rotation because Weyl rotations preserve root length and occur in pi/3 steps; the theta proof uses that false rotation step; Hopf alone does not create the B4 radial x^3 Jacobian; integrating rho against an additional volumetric x^3 weight would not give 4pi^3; and the claimed unique G2-compatible measure on this S3 is not constructed.",
    "verify_P171.py": "New audit finding: P171's G1/j(i) arithmetic reproduces: Omega, G1, j(i)/4=432, J_short^3=1728, the j-formula, Omega reconstruction, j(i)-4Omega≈5.951019, the deficit≈0.048981, the 4Omega polynomial/S2-area identities, tau(3)/432=7/12, and positivity/non-exactness all check. The flagged issues are metadata/proof-scope problems: the file is numbered 171 but the TeX calls it Addendum 167/P167, 432 is not literally the nearest integer to Omega (431 is), the modular-form impossibility proof only covers algebraic-coefficient CM values and not arbitrary transcendental scalar multiples, and the set {j(i)^(k/n)} is not equivalent to the full ring of CM modular-form values.",
    "verify_P174.py": "New audit finding: P174's G2/A2 branching arithmetic reproduces: Cartan determinant/eigenvalues, simple-root lengths and angle, root counts, pi/6 fan spacing, A2 long-root Cartan entry, dim G2=14, 7=1+3+3bar, pi/14=(pi/6)(3/7)=pi/dim G2, and sin(pi/14)=0.222520934 all check. The flagged issues are status and physics-bridge gaps: the actual theta_C=pi/14 derivation is imported from P94; pi/dim(G2) and the root-fan dimension-ratio identity are arithmetic/naturalness observations, not holonomy computations; no CKM mixing operator is constructed; equality to the measured Wolfenstein parameter is approximate rather than exact; and the cited script path does not exist in this TOE workspace, although a local verifier exists under TOE/verify.",
    "verify_P175.py": "New audit finding: P175's delta_QLC arithmetic reproduces: theta_C, lambda, lambda^4, 5pi/28, adjacent 3/3bar angle pi/3, gross mismatch pi/12, root mismatch 2pi/21, off-Cartan formula 7-2=5, primary coefficient 3/5, delta_QLC=(3/5)lambda^4≈0.0014711, and the alternative (7/12)lambda^4≈0.0014302 all check, with an explicit first-principles caveat present. The flagged issues are derivational: the nonzero weight space has six directions, so 7-rank(G2)=5 is not literally that dimension; the 3+2 quark/lepton split is a frame convention; the gross mismatch Delta does not appear in the final formula; lambda^4 order selection is motivated rather than derived from a QLC operator; exact 3/5 uniqueness is deferred to P176; and the fitted-parameter status is therefore reduced but not eliminated.",
    "verify_P201.py": "Extended corpus audit: P201 passes. The verifier recomputes the three-loop mu/e ratio route, inverts the CODATA residual to c4≈400305.875316, checks PSLQ absence bounds in two bases, confirms the rational near-hit 3202447/8, verifies the near-coincidence with -N*alpha^-1, and closes the four-loop self-consistency arithmetic.",
    "verify_P202.py": "Extended corpus audit: P202 passes 85 high-precision assertions for the regular 4-simplex on S3: unit vertices, all ten pairwise inner products -1/4, Gram matrix structure/eigenvalues, edge lengths, geodesic angle arccos(-1/4), centroid zero, Lie constants, f-vector, and E8 cross-checks.",
    "verify_P203.py": "Extended corpus audit: P203 passes. The verifier confirms the wheel-operator 4-simplex model: five unit vertices, ten equal edges, ten equilateral triangular faces, five regular tetrahedral cells, zero centroid, A2/G2/A4 dual-Coxeter data, the P200 f2 coefficient, and the equidistance/no-Harkonnen angle check.",
    "verify_P204.py": "Extended corpus audit: P204 passes. It verifies TOE constants, loop coefficients a1..a4, consecutive coefficient ratios, the r34≈-alpha^-1 self-similarity within tolerance, partial-sum/CODATA straddling, the S4_hyp=S2 identity, the 4-simplex f-vector, binomial coefficients, and h(E8)=30.",
    "verify_P205.py": "Extended corpus audit: P205 passes. It recomputes c_ex, delta, c4, the 4-simplex-augmented basis, PSLQ non-relations for c4/c_ex/delta/residuals at maxcoeff 2000, rational scans, and the near-coincidence (11/4)*Omega0*alpha^-2 in CODATA sigma units.",
    "verify_P206.py": "Extended corpus audit: P206 runs as a negative/open scan. The best simplex-only candidate is 207*(1-theta4/(4*pi^2))≈197.44 with a 4.512% mu/e gap, so the script's verdict is OPEN: 4-simplex geometry alone does not recover m_mu/m_e without the independent MU density moment.",
    "verify_P207.py": "Extended corpus audit: P207 passes 53 checks. It confirms the three-way convergence cluster near m_mu/m_e: Dirac^2, G2+loop, and CR/Hopf candidates, their k-values near the n=9 lattice, centroid/width, interval quantization, residuals from alpha^-1+9Omega0, and internal gap structure.",
    "verify_P208.py": "Extended corpus audit: P208 passes as a systematic candidate scan. The best candidate is 207*(1-g*alpha) with g=1/4, value≈206.62236 and 0.0706% gap, improving on the tree-level 207 gap of 0.1121%; the TeX still states first-principles derivation of that correction is an open problem.",
    "verify_P209.py": "Extended corpus audit: P209 passes. It verifies the monad/electron/omega identities, candidate-8 gap 0.070572%, rank-1 correction c2=3/(pi^3*mu), R_rank1 within about 1.12 ppm, null searches for the residual and prefactor 207, and the QED-scale identity c2=6/E_mu*alpha/(2pi).",
    "verify_P210.py": "Extended corpus audit: P210 passes 50 assertions. It identifies the correction integer as h_dual(A2)=3 on the lepton face, verifies R_star gap about 1.124 ppm, omega-h_dual defect arithmetic, 4-simplex Gram eigenvalues, A2 invariants, heat-budget decomposition, and uniqueness of n=3 among nearby integer candidates.",
    "verify_P211.py": "Extended corpus audit: P211 passes. It resolves the prefactor 207 as dim(G2)*(dim(G2)+1)-h_dual(A2)=14*15-3, verifies the same h_dual(A2)=3 in the correction term, and records the remaining 1.12 ppm residual as an open higher-order correction problem.",
    "verify_P212.py": "Extended corpus audit: P212 passes 45 assertions. It checks the sub-ppm third-term formula with c3=9/(e*mu^3)=9 alpha^3/pi, reducing the R_star residual to about 0.009 ppm, compares cross/geometric alternatives, and verifies numerator/denominator and ordering identities.",
    "verify_P213.py": "Extended corpus audit: P213 passes 65 assertions for the G2-A2 unified mass-ratio series: prefactor 207, T0/T1/T2/T3 forms, geometric ratio r=3*pi^2/mu^2, R_c8, R_star, R3, R_infinity, optimal-truncation behavior, and residual analysis.",
    "verify_P214.py": "Extended corpus audit: P214 passes 65 assertions. It proves the algebraic loop ratio T_{k+1}/T_k=-r with r=h_dual(A2)*E_mu*alpha^2=3*pi^2/mu^2, verifies the closed form R_infinity and deformed denominator, and leaves the geometric origin of the exponent shifts open.",
    "verify_P215.py": "Extended corpus audit: P215 passes 54 assertions. It verifies loop-order factorization T_k=(-1)^(k+1)*r^k*sigma, rapid convergence to R_infinity, the A2 adjacency trace checks for k=1,2, and explicitly marks the full G2 holonomy/resolvent route as conjectural because the direct resolvent mismatches by about 97.7x.",
    "verify_P216.py": "Extended corpus audit: P216 passes 65 assertions. It checks the delta_infinity identity, corrected factored numerator for R_infinity, gap delta_infinity about 2.30e-6 or 0.500 sigma CODATA-2018, candidate c/(r*S_infinity) near 0.01, and classifies R_infinity as conjectured pending higher-precision measurement.",
    "verify_P217.py": "Extended corpus audit: P217 passes 50 assertions. It verifies the exponent pattern from the conditional G2/A2 energy assignment, r/h per-step factor, A2 adjacency traces, OP-rSinf-100 near-miss c/(r*S_infinity) about 0.01 with epsilon about -2.20e-7, and records the energy-assignment derivation as conditional.",
    "verify_P218.py": "Extended corpus audit: P218 passes 65 assertions. It verifies the conditional P18-T2 closure: R_infinity, delta_infinity/sigma about 0.500, OP-rSinf-100 near-miss, adjacency-resolvent mismatch, and uniqueness checks for h=3 against h=2 and h=4; Theorem P218.1 remains conditional on Axiom ID.",
    "verify_P218b.py": "Extended corpus audit: P218b passes. It verifies the amended P18-T2 closure, rejects the reversed alpha assignment as nonsensical, keeps R_infinity within about 0.500 sigma, upgrades the exponent step conditional on alpha=Omega^-1, and explicitly leaves exact alpha=Omega^-1 as the residual foundational question.",
    "verify_P219.py": "Extended corpus audit: P219 passes 73 assertions. It verifies OP-AxID spectral-derivation numerics: monad closure f(pi)=mu, unique positive root e=pi, E_mu=pi^2, correct versus reversed root assignment, R_infinity within about 0.5 sigma, and the GON layer decomposition.",
    "verify_P220.py": "Extended corpus audit: P220 passes. It audits OP-rSinf-100, showing epsilon=r*S_infinity/(100c)-1≈2.2037e-5, the CODATA uncertainty in epsilon is about 2 and therefore much larger than the near-miss, PSLQ bases find no nontrivial epsilon relation, and the 100 factor is geometrically tied to (h_dual(E8)/h_dual(A2))^2.",
    "verify_P221.py": "Extended corpus audit: P221 passes. It closes the OP-G2A2-lattice resolvent attempt with an exact mismatch: G(mu/pi)/S_infinity≈97.7, solves the formal lambda roots where G(lambda)=S_infinity, checks alternative graph resolvents, and confirms no natural A2 resolvent reproduces S_infinity.",
    "verify_P222.py": "Extended corpus audit: P222 passes 60 assertions after runner ignore-rule correction. It verifies the monad closure polynomial, Nicomachus/Bezout counts, density integral, moments, breath period, spectral nonhits, Chebyshev root counts, R1-R8 coefficient checks, and explicitly confirms the geometric alpha inverse is close to but not exactly the experimental value.",
    "verify_P223.py": "Extended corpus audit: P223 passes. It audits alpha exactness: Omega exceeds CODATA and other alpha-inverse determinations by a stable about 2.223 ppm, CODATA-2018 discrepancy is about 1451 sigma, PSLQ returns only tautological identities, known QED/systematic scales do not explain the gap, and OP-alpha remains open rather than an exact theorem.",
    "verify_P087.py": "Known issue: P87 second-moment formula uses wrong exponent arithmetic; P162 is the correction path.",
    "verify_P154.py": "Negative/open result, not an arithmetic failure: no candidate naturally closes G1.",
    "verify_P178.py": "Expected control failures: Formula A/B are intentionally rejected.",
    "verify_P186.py": "Negative result: additive composition passes; Kleisli composition fails.",
}


def fail_lines(output: str) -> list[str]:
    lines = []
    for line in output.splitlines():
        if "[FAIL]" in line or re.search(r"(?<!_)FAIL(?!ED)", line):
            if any(marker in line for marker in IGNORE_FAIL_LINES):
                continue
            lines.append(line.strip())
    return lines


def main() -> int:
    py = sys.executable
    env = os.environ.copy()
    extra = "/private/tmp/codex_pydeps"
    env["PYTHONPATH"] = extra + os.pathsep + env.get("PYTHONPATH", "")

    rows = []
    for script in sorted(VERIFY_DIR.glob("verify_*.py")):
        if script.name == Path(__file__).name or script.name == "verify_common.py":
            continue
        proc = subprocess.run(
            [py, str(script)],
            cwd=str(ROOT),
            stdout=subprocess.PIPE,
            stderr=subprocess.STDOUT,
            text=True,
            env=env,
            timeout=180,
        )
        flagged = fail_lines(proc.stdout)
        status = "PASS"
        if proc.returncode != 0 or flagged:
            status = "FLAGGED"
        note = KNOWN_INTERPRETATION.get(script.name, "")
        if not note and proc.returncode != 0:
            note = f"Exited with code {proc.returncode}."
        if flagged:
            snippet = "; ".join(flagged[:3])
            note = f"{note} {snippet}".strip()
        rows.append((script.name, status, proc.returncode, note))

    total = len(rows)
    clean = sum(1 for _, status, _, _ in rows if status == "PASS")
    flagged = total - clean

    lines = [
        "# TOE Verifier Results",
        "",
        "Generated by `TOE/verify/run_all_verifiers.py`.",
        "",
        f"- Total verifier scripts: {total}",
        f"- Clean pass: {clean}",
        f"- Flagged: {flagged}",
        "",
        "| Script | Status | Exit | Note |",
        "|---|---|---:|---|",
    ]
    for name, status, code, note in rows:
        lines.append(f"| `{name}` | {status} | {code} | {note.replace('|', '/')} |")
    REPORT.write_text("\n".join(lines) + "\n")
    print(REPORT)
    print(f"total={total} clean={clean} flagged={flagged}")
    return 1 if flagged else 0


if __name__ == "__main__":
    raise SystemExit(main())
