The Gap Registry
Every TBS and Open remark in the canon, machine-extracted, with its status, grouped by paper. Below each paper's recorded items sit its verifier-documented expected fails: claims the paper's verifier recomputes and records as failing, the registry in executable form. Each paper page carries the same panel inline.
confirmed-load-bearing: 23, refuted: 7, retired: 15, scope: 21, superseded: 1, unreviewed-or-open: 5 · verifier-documented: 326
00 Paper MonadRosettaMap 2 confirmed-load-bearing 10 verifier-documented
| id | status | closed by | excerpt / note |
|---|---|---|---|
| P000_1_c | confirmed-load-bearing | The geometric integral $4\pi^3+\pi^2+\pi = 137.036304\ldots$ and the CODATA value $\alpha^{-1} = 137.035999084\ldots$ differ by approximately $3\times10^{-4}$ … A279+A283: the alpha-comma (2.2234 ppm, ~1.45e4 sigma) typed as the time-average dressing of P03's oscillation: deficit = 1-sqrt(1-A^2); A = kappa predicts 2.2745 ppm (sign right, 2.3% high); inverted: first measurement … | |
| P000_3 | confirmed-load-bearing | The $R$-operator is described operationally but never formally specified as a map between defined function spaces with a stated domain, codomain, and continuity class … A295: R-operator never formally specified — formalization gap |
Verifier-documented expected fails (10) — claims verify_P000.py recomputes and records as failing Run
- geometric omega equals physical alpha inverse exactly (Expected fail: the geometric value is a close approximation, not exact equality to CODATA alpha inverse.)
- limit-normalization operator R is formally specified here (Expected formal-status fail.)
- C and P are defined enough to prove C o P = I consequences (Expected operator-definition fail.)
- representation dimensions 16, 3, 2 are derived in P0 (Expected derivation-status fail.)
- electron mass is completely determined by supplied data (Expected internal-status fail.)
- master operator is mathematically specified (Expected specification fail.)
- T^3=I is proved for a concrete layer-cycle operator (Expected formalization fail.)
- phenomenological consciousness/singularity claims are mathematical consequences (Expected non-formal-claim fail.)
- referenced Ged wheel implementation is present in TOE workspace (Expected reproducibility fail if the code is not included in this workspace.)
- identity plus C o P suffices to generate the entire TOE structure (Expected overstatement fail.)
01 Paper PerfectStableSphere 3 refuted 13 verifier-documented
| id | status | closed by | excerpt / note |
|---|---|---|---|
| P001_4 | refuted | The tri-bimaximal prediction $\theta_{13} = 0$ is refuted by current data. The reactor angle is measured at $\theta_{13} \approx 8.5^\circ$ … A344: tri-bimaximal theta_13 = 0 refuted; measured theta_13 ~ 8.5 deg (sin^2 theta_13 ~ 0.022, NuFIT-6.0), nonzero at >5sigma since Daya Bay 2012; a vanishing reactor angle is excluded — it is a leading-order angle, not … | |
| P001_5 | refuted | The agreement claimed here rests on a now-superseded central value. The $197^\circ \pm 25^\circ$ figure is no longer the global fit. NuFIT-6.0 (2024, normal ordering) … A344: delta_CP ~ 240 deg refuted on current data; NuFIT-6.0 (2024, NO) gives delta_CP ~ 177 deg (+19/-20), CP-conserving within 1sigma, with 240 deg ~3sigma above central; the claimed agreement used the superseded … | |
| P001_6 | refuted | This argument is refuted as a solution to strong CP: it constrains the wrong object. Setting the minimal-energy instanton winding number $n = 0$ fixes the topological … A344: topological strong-CP solution refuted (wrong object) — setting instanton winding n=0 fixes the gauge sector, not the Lagrangian theta-coupling (the physical strong-CP parameter); theta_QCD is an independent … |
Verifier-documented expected fails (13) — claims verify_P001.py recomputes and records as failing Run
- 4*pi^3 contribution (Expected fail: documents the paper's historical printed value 123.370055 for the 4*pi^3 term; the true value is 124.0251.)
- Dirichlet energy from displayed integral (Expected fail: the displayed integral evaluates to about 247444.81, not 18791.3.)
- scaled energy E/m0^2 (Expected fail: using the displayed rho gives about 13.1767.)
- exact symbolic scaled energy equals 1 (Expected fail: the exact symbolic value is not 1.)
- energy theorem stationary point follows from E[rho]=m0^2 (Expected fail: the premise used to motivate the later wave equation is numerically false.)
- mu3 (Expected fail: the moment formula gives about 77.062929.)
- mass scaling with beta=-19 (Expected fail: beta=-19 gives about 34.9; 82 would require beta about -23.6.)
- mass hierarchy discrepancy factor using beta=-19 prediction (Expected fail: using the actual beta=-19 prediction gives a factor about 5.9.)
- combined neutrino suppression from listed factors (Expected fail: the listed factors give about 8.36e5, not 2.5e6.)
- 1 GeV divided by claimed 2.5e6 suppression in eV (Expected fail: 1 GeV / 2.5e6 is 400 eV, not 0.4 eV.)
- Z3 mass-matrix small-b assumption (Expected fail: the stated estimate is incompatible with the small-b expansion.)
- 240 deg times O(kappa) uncertainty (Expected fail: O(kappa) around 240 degrees is about 0.53 degrees, not +/-10 degrees.)
- standard PMNS Jarlskog with cosine factors (Expected fail: the standard formula gives about -0.0288 for these angles and delta=240 deg.)
02 Paper GeometricSpectralTheory 1 confirmed-load-bearing 13 verifier-documented
| id | status | closed by | excerpt / note |
|---|---|---|---|
| P002_1 | confirmed-load-bearing | The identity $\Delta E/E_{\mathrm{self}} = 22\kappa$ conflates the purely geometric ratio $\kappa = \alpha^{5/4}$ with the experimentally measured fine-structure … A295: DE/E_self = 0.0464 vs 22k = 0.0469 (1.2%) — conflation real, numerically benign; derivation gap stands |
Verifier-documented expected fails (13) — claims verify_P002.py recomputes and records as failing Run
- Delta E / E_self agreement with 22*kappa is within 1.3 percent (Expected fail: the stated quantities differ by about 4.27%, as the proof later acknowledges.)
- optimal-density table: linear E_self (Expected fail: for rho=2*m0*x, E/m0^2 = 2, not 0.171.)
- optimal-density table: quadratic E_self (Expected fail: for rho=3*m0*x^2, E/m0^2 = 6, not 0.383.)
- optimal-density proof exhausts polynomial densities (Expected fail: checking uniform/linear/quadratic/cubic monomials is not an optimization proof over polynomial coefficients.)
- beta_geom/beta_QED using displayed geometric m0 formula (Expected fail: 70,205.483 uses experimental alpha, not beta_QED=2/(3*pi*m0^2).)
- exact C formula value (Expected fail: exact m0,m1 give about 1362.47528; the quoted value is a small arithmetic mismatch.)
- critical-point proof limit as s -> 0+ (Expected fail: the root value is correct, but this proof step is not.)
- rho_cubic satisfies Neumann boundary at x=0 (Expected fail: rho'(0)=2*pi.)
- rho_cubic satisfies Neumann boundary at x=1 (Expected fail: rho'(1) is large and nonzero.)
- rho_cubic is static equilibrium of stated wave equation at x=1/2 (Expected fail: at rho=rho_cubic, the RHS leaves rho_cubic'' instead of zero.)
- linearization reduces to eta_tt = (1-kappa) eta_xx (Expected fail: differentiating -kappa(rho-rho_cubic)rho'' gives a multiplicative rho_cubic'' term, not -kappa eta''.)
- displayed zeta'(0) log formula (Expected fail: the printed sum A_k log(1/k) is negative and not the derivative of the integral zeta function.)
- log10(M_Pl / exp(C)) with C=1362.477 (Expected fail: exp(1362) is enormous; the scale is around 10^-573 GeV, not 2.7e16 GeV.)
03 Paper MathematicalFoundations 1 confirmed-load-bearing 1 retired 13 verifier-documented
| id | status | closed by | excerpt / note |
|---|---|---|---|
| P003_3 | retired | A278 | The stated Neumann boundary condition $\rho'(0)=0$ is not satisfied by the density $\rho(x)=16\pi^3 x^3+3\pi^2 x^2+2\pi x$, whose derivative at $x=0$ evaluates to … |
| P003_2 | confirmed-load-bearing | The claim that $5/4$ is a global minimiser is not proved; Addendum P012 establishes it as a local rational minimum only. Whether the global minimum equals $5/4$ or … A295: 5/4 global minimality unproven (local result only) |
Verifier-documented expected fails (13) — claims verify_P003.py recomputes and records as failing Run
- Theorem 3.1 E_norm[rho] = 1 (Expected fail: the proof itself computes E_self ~= 13.177 and says it is not 1.)
- 5/4 minimizes alpha^n over all exponents (Expected fail: 5/4 is a good simple fraction, not the unconstrained minimizer.)
- rho_cubic satisfies Neumann boundary at x=0 (Expected fail: rho'(0)=2*pi.)
- rho_cubic satisfies Neumann boundary at x=1 (Expected fail: rho'(1) is nonzero.)
- rho_cubic is static equilibrium of stated wave equation at x=1/2 (Expected fail: the written equation leaves rho_cubic'' at zeroth order.)
- linearization drops the eta*rho_cubic'' term correctly (Expected fail: the displayed first-order equation does not imply the next line.)
- moment-ratio theorem lower bound at n=0 (Expected fail: the theorem says ratios are about 0.83-0.86 for n=0,1,2,... but n=0 is 0.7933.)
- moment-ratio theorem upper bound at n=3 (Expected fail: ratios soon exceed 0.86 and tend to 1.)
- beta_QED from displayed 2/(3*pi*mu0^2) (Expected fail: 1.130029e-5 is the experimental-alpha value, not the geometric-mu0 formula.)
- beta ratio from displayed geometric beta_QED (Expected fail: the quoted ratio again uses experimental alpha.)
- C/C_formula table value (Expected fail: the ratio is about 1.000001 with the stated formulas.)
- C relative error percent (Expected fail: the percent error is about 0.0001%, not 0.015%.)
- algebraic step (1+x) = 1/(1-x) (Expected fail: this is only an approximation; it changes the mass-log by about 0.00335%.)
04 Paper ThreeLayerOntology 20 verifier-documented
Verifier-documented expected fails (20) — claims verify_P004.py recomputes and records as failing Run
- quantum layer integral 4*pi^3 (rel err=+0.530965%, tol=0.0001%; Expected fail: 4*pi^3 is about 124.025107; 123.370055 is stale.)
- listed component sum 123.370055 + 9.869604 + 3.141593 (rel err=-0.478013%, tol=0.0001%; Expected fail: the listed components sum to about 136.381252.)
- f_Q theorem value 0.90006 (rel err=+0.554732%, tol=0.002%; Expected fail: with the stated formula the quantum fraction is about 0.90505.)
- integrated contributions are algebraically independent over Q (Expected proof-audit fail: the proof establishes Q-linear independence only, not algebraic independence.)
- two-layer QC alpha inverse (rel err=+0.491377%, tol=0.001%; Expected fail: the stated formula gives about 133.895.)
- two-layer QC relative error percent (rel err=-17.2373%, tol=0.5%; Expected fail: exact error is about 2.29%, not 2.77%.)
- two-layer QM alpha inverse (rel err=+0.5175%, tol=0.001%; Expected fail: the stated formula gives about 127.167.)
- two-layer QM relative error percent (rel err=-6.22158%, tol=0.5%; Expected fail: exact error is about 7.20%, not 7.68%.)
- QC dominance direction below x_QC (Expected fail: the inequality direction is reversed.)
- CM dominance direction below x_CM (Expected fail: the inequality direction is reversed.)
- derivative cascade literally maps quantum term to classical term (Expected proof-audit fail: only polynomial degrees line up; the displayed cascade is not an equality chain.)
- QC two-layer E_self (rel err=-1.68264%, tol=0.05%; Expected fail: exact two-layer calculation gives about 13.617.)
- QM two-layer E_self (rel err=-8.1265%, tol=0.05%; Expected fail: exact two-layer calculation gives about 13.891.)
- CM two-layer energy (rel err=+400.146%, tol=0.5%; Expected fail: exact 1/2 integral is about 790.23.)
- CM two-layer E_self (rel err=+401.923%, tol=0.5%; Expected fail: exact two-layer calculation gives about 4.668.)
- all two-layer self-lensing values fall outside later arena [4*pi, E_self + Delta E] (Expected fail: the QC two-layer value lies inside the later arena definition.)
- Hopf fibration uses S3 as the base of S1 fibers (Expected proof-audit fail: later statements sometimes use the correct S2 base, but this proof step is misstated.)
- no direct continuous operator B4 -> S1 exists (Expected proof-audit fail: the claimed obstruction is not a topological theorem.)
- black-hole fold-map determinant is computable from the definitions in this paper (Expected proof-audit fail: this is a geometric sketch/conjecture, not a derived theorem from the given data.)
- signed fractional alpha shift from monadic-state change (rel err=-199.675%, tol=0.3%; Expected fail if read as signed: delta alpha / alpha = -delta(alpha^-1)/alpha^-1; the magnitude is about 0.023.)
05 Paper GeometryOfReality 17 verifier-documented
Verifier-documented expected fails (17) — claims verify_P005.py recomputes and records as failing Run
- bulk contribution 4*pi^3 (Expected fail: 4*pi^3 is about 124.0251067; 123.370055 is stale.)
- displayed relative-error formula uses correct CODATA denominator (Expected fail: the displayed formula uses 137.036999, not CODATA 137.035999, and evaluates near 5.1e-6.)
- quantum + classical two-layer value (Expected fail: exact value is about 133.895; 133.24 follows from the stale 4*pi^3 number.)
- quantum + observational two-layer value (Expected fail: exact value is about 127.167; 126.51 follows from the stale 4*pi^3 number.)
- QC two-layer error percent (Expected fail: exact omission of the edge term is 2.2925%, not 2.8%.)
- QO two-layer error percent (Expected fail: exact omission of the boundary term is 7.202%, not 7.7%.)
- coefficient variant {15,3,2} (Expected fail: under the density-coefficient convention it gives about 129.285, not 133.3.)
- omega1 printed value 3.136 (Expected fail: exact kappa gives omega1 about 3.13824.)
- mass-ratio toy example (Expected fail: 0.830^-19 is about 34.48; the claimed 82 is stale.)
- toy mu/e discrepancy factor (Expected fail: with the stated formula the discrepancy is about 6x, not 2.5x.)
- wave equation has rho_cubic as exact equilibrium (Expected inherited P2/P3 wave-equation fail.)
- linearization yields eta_tt=(1-kappa)eta_xx (Expected inherited wave-equation fail.)
- 5/4 is globally selected by exponent scan (Expected proof-status fail.)
- L(4,1) is incompatible with S3 (Expected topology fail.)
- Z3 lens space topologically forbids any fourth family (Expected proof-status fail.)
- strong CP problem is resolved in P5 (Expected derivation fail.)
- random-coefficient probability estimate is reproducible (Expected statistical-model fail.)
06 Paper FermionSector 15 verifier-documented
Verifier-documented expected fails (15) — claims verify_P006.py recomputes and records as failing Run
- table nu_e mass vs abstract ~0.1 eV scale (Expected fail: 1e-7 GeV is 100 eV, not order 0.1 eV.)
- table nu_tau mass vs abstract ~0.1 eV scale (Expected fail: 1e-5 GeV is 10,000 eV, far above the stated neutrino scale.)
- neutrino table values are PDG experimental masses (Expected data-status fail: these are not the measured light-neutrino mass spectrum.)
- displayed U_tri off-diagonal Gram entry (Expected fail: the all-1/sqrt(3) matrix has identical columns, so it is not unitary.)
- displayed U_tri determinant (Expected fail: determinant is zero because the matrix has rank 1.)
- theta13 implied by displayed U_tri (Expected fail: standard TBM has Ue3=0; this matrix gives theta13 about 35.26 degrees.)
- CKM displayed positive rows are orthogonal (Expected fail: the displayed magnitudes cannot be treated as a real orthogonal matrix.)
- PMNS displayed positive rows are orthogonal (Expected fail: the displayed positive-entry table is a magnitude table, not a unitary matrix.)
- PMNS theta23 from displayed Umu3 (Expected fail: direct reading of the displayed matrix gives about 30.1 degrees, not 49.2 degrees.)
- mass predictions are reproducible from printed eigenvalues and A,B,C (Expected reproducibility fail.)
- mass formula uses zero fitted parameters (Expected status fail.)
- CKM and PMNS matrices are predictions rather than optimized fits (Expected status fail.)
- log-periodic node data are included (Expected reproducibility fail: no node table or solver output is present in this TeX.)
- exactly three families is consistent with the four triplets table (Expected internal-consistency fail.)
- Z3 irreps alone topologically forbid a fourth family (Expected proof-audit fail.)
07 Paper SelfReferentialObservation 1 confirmed-load-bearing 2 retired 8 verifier-documented
| id | status | closed by | excerpt / note |
|---|---|---|---|
| P007_2 | retired | A281 | The weight function $x^2(1-x)^2$ vanishes at $x=0$ and $x=1$ but its derivative does not vanish there, so it does not enforce the Neumann boundary conditions … |
| P007_1 | retired | A281 | The tridiagonal discretisation of the observation operator imposes zero boundary values at both endpoints, enforcing Dirichlet-like conditions, while the paper claims … |
| P007_3 | confirmed-load-bearing | The comparison of $\mu_1/\mu_0$ to $\ln(M_{\mathrm{Pl}}/m_e)$ is asserted without deriving why the geometric moment ratio should equal this particular logarithm … A295: the WHY of moments-to-hierarchy = the correspondence postulate (ties to OI-282-1) |
Verifier-documented expected fails (8) — claims verify_P007.py recomputes and records as failing Run
- printed matrix implements Neumann boundary at x=1 (Expected fail: the listed eigenvalues match the unmodified tridiagonal matrix, not a Neumann endpoint implementation.)
- x^2(1-x)^2 potential enforces the wavefunction boundary conditions (Expected proof-audit fail: vanishing potential does not impose boundary conditions on psi.)
- mu1/mu0 Planck-log comparison (rel err=-97.5538%, tol=1%; Expected fail: the printed log(e)/log(M_Pl/m_e)/log(e) is about 0.0194, not 0.7933.)
- beta has no scan/selection input (Expected status fail: this is a small discrete scan unless the factor 6 is independently derived.)
- zero free parameters (Expected status fail.)
- printed Yukawa mixing angles follow from the displayed matrix (Expected verification fail: no diagonalization convention is given that reproduces the printed angles from the displayed matrix.)
- three-family count follows from S3 topology as a theorem (Expected proof-audit fail.)
- Yukawa matrix entries are derivable from printed eigenfunctions (Expected verification gap.)
08 Paper TimeObservationBootstrap 2 confirmed-load-bearing 1 scope 8 verifier-documented
| id | status | closed by | excerpt / note |
|---|---|---|---|
| P008_3_c | scope | The Planck time $t_P$ is introduced as an external physical constant from standard quantum gravity, not derived from any formula in Papers 01--07. Corollary 4.2 … A295: technical/scope note — external anchor or theorem hypothesis caveat; corpus use unaffected | |
| P008_2_c | confirmed-load-bearing | The continuum limit argument above is circular: the discrete update $|\psi_{n+1}\rangle = \hat{O}|\psi_n\rangle$ is expanded to first order in $\Delta t$ by … A295: continuum-limit circularity stands | |
| P008_1 | confirmed-load-bearing | The dimension assigned to the self-intersection locus is not derived from a transversality argument; Addenda P031/P033 import intersection counts from external results … A295: dimension not derived from transversality |
Verifier-documented expected fails (8) — claims verify_P008.py recomputes and records as failing Run
- self-intersection dimension statements are internally consistent (Expected internal-consistency fail.)
- discrete update equation derives Schrodinger equation (Expected derivation fail.)
- Planck-scale discreteness is derived from prior formulas (Expected status fail.)
- measurement collapse is mathematically derived (Expected proof-status fail.)
- consciousness-observation duality is code-verifiable (Expected non-verifiable claim.)
- no-fourth-generation prediction is derived here (Expected proof-status fail.)
- prime-pattern mass correlation is testable from supplied data (Expected reproducibility fail.)
- zero unexplained constants is supported by P8 alone (Expected status fail.)
09 Paper WaterGeometricThermometer 1 confirmed-load-bearing 7 verifier-documented
| id | status | closed by | excerpt / note |
|---|---|---|---|
| P009_3_c | confirmed-load-bearing | The derivation of the triple-point temperature is circular: $T_{\mathrm{geom}}$ is obtained by dividing the experimental value $T_{\mathrm{triple}}=273.16\,\mathrm{K}$ … A295: triple-point circularity stands |
Verifier-documented expected fails (7) — claims verify_P009.py recomputes and records as failing Run
- E_scale equals kB*300K precisely (rel err=+3.12963%, tol=0.5%; Expected fail: E_scale is about 3.1% above kB*300 K, so 'precisely equals' is too strong.)
- T_geom / T_CMB equals pi (rel err=+1.56659%, tol=0.5%; Expected fail if treated as more than a loose approximation: the ratio is about 1.6% above pi.)
- triple-point temperature is predicted without using the triple point (Expected proof-status fail: the headline temperature relation is reverse-engineered unless E_scale is derived independently.)
- 3/r = 1/pi derivation is dimensionally complete (Expected dimensional-analysis fail.)
- S=1.5 is independently predicted rather than selected (Expected proof-status fail: the chosen realistic value is also effectively the fitted match value.)
- 2pi is closest among all natural constants (Expected scope fail.)
- future predictions follow from formulas without empirical tuning (Expected status fail.)
10 Paper ThreeFourthsCorrection 1 confirmed-load-bearing 7 verifier-documented
| id | status | closed by | excerpt / note |
|---|---|---|---|
| P010_3 | confirmed-load-bearing | The derivation of $c=3/4$ relies on a normalisation condition that itself depends on $c$, introducing a circularity. Addendum P012 provides five convergent numerical … A295: c=3/4 normalization circularity stands |
Verifier-documented expected fails (7) — claims verify_P010.py recomputes and records as failing Run
- c=4/3 worse factor (rel err=-21.4095%, tol=5%; Expected fail: exact ratio is about 4008 using the paper's target and rounded formula.)
- alpha^4 second-order term (rel err=+188428%, tol=100%; Expected fail: the next term is about 1.9e-5, not order 1e-8.)
- formula is zero-input rather than using target alpha on the RHS (Expected status fail: a self-contained prediction should specify whether alpha is solved implicitly or imported.)
- alpha-cube derives alpha without alpha as input (Expected circularity fail.)
- theoretical derivation of c=3/4 is closed (Expected status fail.)
- continuous optimization gives c=0.750000000 and distance <1e-9 (Expected internal-consistency fail.)
- Z3/family argument topologically forbids a fourth family (Expected proof-audit fail.)
11 Paper GeometricFirstPrinciples 9 verifier-documented
Verifier-documented expected fails (9) — claims verify_P011.py recomputes and records as failing Run
- equilibrium precision is lower than density precision (Expected wording fail: the equilibrium residual is smaller than the density residual.)
- density formulation has highest precision among the three listed formulas (Expected wording fail: the equilibrium formula is numerically closer to CODATA in this paper.)
- alpha^4 correction is beyond current alpha experimental precision (Expected wording fail: 1.9e-5 is far above modern alpha relative experimental precision.)
- three formulations are mathematically equivalent as written (Expected synthesis-status fail: they are compatible perspectives, not proved equivalent maps.)
- zero-free-parameter claim is consistent with open mysteries (Expected status fail: the core numeric formulas are fixed, but not all ingredients are derived from axioms here.)
- S3/Z3 topology proves exactly three fermion families (Expected proof-audit fail: this is a structural interpretation, not a proof from the displayed quotient.)
- LEP light-neutrino count confirms no fourth fermion family (Expected status fail: the experimental statement is overbroad.)
- charged-lepton mass prediction is code-verifiable from data in P11 (Expected verifier gap: the claimed 105.7 MeV and 1777 MeV cannot be reproduced from this TeX alone.)
- water nucleation 0.07 percent agreement is derived in P11 (Expected verifier gap: external inputs are needed.)
12 Paper FiveFoldConvergence 7 verifier-documented
Verifier-documented expected fails (7) — claims verify_P012.py recomputes and records as failing Run
- search table worse factor c=4/5 (rel err=-59.3729%, tol=3%; Expected fail for stale rows where the table factor does not follow from the displayed formula.)
- search table worse factor c=5/6 (rel err=+100.571%, tol=3%; Expected fail for stale rows where the table factor does not follow from the displayed formula.)
- search table worse factor c=7/9 (rel err=+29.7013%, tol=5%; Expected fail for stale rows where the table factor does not follow from the displayed formula.)
- first-order vs nonperturbative boundary difference percent (rel err=-90.5737%, tol=5%; Expected fail: the relative difference is about 0.0019%, not 0.02%.)
- wave-equation derivation is independent and established (Expected proof-status fail.)
- Z3 family topology forbids additional representation copies (Expected proof-status fail.)
- five derivations are logically independent derivations rather than post-hoc interpretations (Expected proof-status fail: the arithmetic convergence is real, but independence is not established by the proof sketch.)
13 Paper QuinticStructure 3 confirmed-load-bearing 9 verifier-documented
| id | status | closed by | excerpt / note |
|---|---|---|---|
| P013_3_c | confirmed-load-bearing | The claim that $\lambda_1(\alpha)$ depends rationally (or even algebraically) on $\alpha$ is asserted without proof. The first eigenvalue of the Sturm--Liouville … A293: rationality premise unproven and generically false for Sturm-Liouville eigenvalues; stands as the schema's deepest gap | |
| P013_2 | confirmed-load-bearing | The claim that denominator-clearing of the three consistency conditions yields exactly degree 5 rather than a higher degree is asserted but not proved; a complete … A293: degree bound unverifiable until the construction is supplied (see P013_1) | |
| P013_1 | confirmed-load-bearing | The coefficients $a_5,a_4,a_3,a_2,a_1,a_0$ of the claimed irreducible quintic are never explicitly computed from the three consistency conditions; only their existence … A293: quintic is a schema — C1,C2,C3 and F unspecified; coefficients uncomputable as stated |
Verifier-documented expected fails (9) — claims verify_P013.py recomputes and records as failing Run
- quintic polynomial coefficients are supplied (Expected reproducibility fail.)
- elimination generically yields degree five (Expected algebra-scope fail.)
- lambda1(alpha) depends rationally on alpha (Expected spectral-dependence fail.)
- electron mass constraint F is defined (Expected missing-definition fail.)
- irreducibility is proved (Expected proof-data fail.)
- Galois group S5 is established (Expected proof-data fail.)
- unique positive root equals physical alpha (Expected verification fail.)
- all numerical verification methods are shown (Expected reproducibility fail.)
- paper completes the structural link (Expected status overstatement.)
14 Paper CosmicBreathing 2 retired 8 verifier-documented
| id | status | closed by | excerpt / note |
|---|---|---|---|
| P014_1 | retired | A266 | Numerically, $432/430.51\approx 1.00346$ while $1+\kappa^{0.6}\approx 1 + \alpha^{3/4}\approx 1.00040$; the two sides differ by approximately a factor of 9. A corrected … |
| P014_2 | retired | A279 | The ratio $432/\pi^3\approx 13.955$ differs from the canonical $E_{\mathrm{self}}\approx 13.177$ by approximately $5.7\%$; the identification … |
Verifier-documented expected fails (8) — claims verify_P014.py recomputes and records as failing Run
- 432/430.51 ratio equals 1+kappa^0.6 (Expected fail: kappa^0.6 is about 0.02497, while the ratio excess is about 0.00346.)
- 432/pi^3 matches E_self (Expected fail: the gap is about 5.7%, much looser than the 14 comparison.)
- 14 is the nearest integer approximation to E_self (Expected fail: E_self≈13.177 rounds to 13, not 14.)
- 14 is close to E_self at the same level as 432/pi^3 (Expected fail: 14 is ~6.25% above E_self but only ~0.48% above 432/pi^3.)
- breathing period follows from C o P = I (Expected derivation fail.)
- 432=16*27 is evidence beyond a numeric encoding (Expected proof-status fail.)
- ancient contemplative access is mathematically verifiable here (Expected non-verifiable claim.)
- dimensional lifting by pi is uniquely derived (Expected proof-status fail.)
15 Paper ShadowUniverse 1 confirmed-load-bearing 2 retired 8 verifier-documented
| id | status | closed by | excerpt / note |
|---|---|---|---|
| P015_1 | retired | A293 | The claimed value $\langle|\cos\theta|\rangle = 1/4$ is incorrect; the standard computation on $S^2$ with the round measure gives $\langle|\cos\theta|\rangle = 1/2$. The … |
| P015_2 | confirmed-load-bearing | The quantities $4/(3\pi)\approx 0.4244$ and $1/\pi\approx 0.3183$ differ by a factor of $4/3$; the step equating or connecting them is not justified and the gap must be … A295: the 4/3 step unexplained | |
| P015_3_c | retired | A266/A267 | The $\pi/2$ bifurcation correction in the master equation $\alpha^{-1} = (432 - \pi/2)/\pi$ and the source value $432$ are both asserted without derivation. The … |
Verifier-documented expected fails (8) — claims verify_P015.py recomputes and records as failing Run
- S2 average absolute cosine (Expected fail: (1/4pi) integral_S2 |cos theta| dOmega = 1/2, not 1/4; Cauchy's S/4 has an additional geometric convention.)
- division by pi follows from displayed projection factor (Expected derivation mismatch.)
- pi/2 bifurcation correction is derived (Expected proof-status fail.)
- source value 432 is derived from B4/S3 geometry (Expected derivation fail.)
- two alpha derivations are mutually consistent as derivations (Expected consistency/bridge fail.)
- C o P = I cosmological operators are mathematically defined (Expected operator-definition fail.)
- Lambda is derived from the return operator (Expected cosmology-derivation fail.)
- verification script is present (Expected reproducibility fail.)
16 Paper ShellCompletion 1 refuted 10 verifier-documented
| id | status | closed by | excerpt / note |
|---|---|---|---|
| P016_3 | refuted | The stated count of $d_n<0.01$ values cannot be reproduced by applying the definition of $d_n$ given earlier in the paper; the computation is either using a different … A280: refuted under all four natural readings (best counts 2/10 vs claimed 14/19; means at/near uniform null); per-prime mean 0.193 matches claimed 0.187 within 3% — published table likely mixed readings; first formally … |
Verifier-documented expected fails (10) — claims verify_P016.py recomputes and records as failing Run
- proof line works with printed kappa 0.00213306 (abs err=197.102, tol=0.0001; Expected fail: the headline shell closure uses the exact kappa, not the rounded number shown in the proof line.)
- theorem's p52 ordinal agrees with discovered M52 (Expected fail: the paper acknowledges this later, but the theorem still labels the value p52.)
- observed d_n < 0.01 count (rel err=-92.8571%, tol=0%; Expected fail under the cumulative S_n definition and the 51 listed exponents.)
- observed d_n < 0.05 count (rel err=-52.6316%, tol=0%; Expected fail under the cumulative S_n definition and the 51 listed exponents.)
- mean shell distance (rel err=+18.3856%, tol=0.2%; Expected fail: the cumulative exact-kappa mean is about 0.221.)
- random expected count for d_n < 0.01 on [0,0.5] (rel err=-90%, tol=1e-10%; Expected fail: a uniform shell distance on [0,0.5] gives expectation 1.02, not 10.2.)
- random expected count for d_n < 0.05 on [0,0.5] (rel err=-50%, tol=1e-10%; Expected fail: this expectation is 5.1, not 10.2.)
- one-sided p-value for 14 distances below 0.01 (rel err=-100%, tol=10%; Expected fail: under the stated null, this tail is about 1e-12 and also does not match the observed count.)
- unique exhaustive search is reproducible from supplied data (Expected reproducibility fail.)
- Mersenne primality of 2^p-1 is established by exponent primality (Expected logical-scope fail.)
17 Paper GravityDroplet 2 refuted 7 verifier-documented
| id | status | closed by | excerpt / note |
|---|---|---|---|
| P017_3_c | refuted | The Dirac spectrum $\{m_1, m_2, m_3, \ldots\}$ above is not reproducible from the formulas given in this section alone. The explicit boundary conditions imposed on … A293+A295: printed system ill-posed (complex indicial exponents) AND printed spectrum not recovered by the natural repair (corrected spectra box-like, spacing ~pi); refuted as stated; corrected spectra filed | |
| P017_2 | refuted | A factor-of-7 gap between spectral levels is asserted but its derivation is not reproduced here; Addendum P018 re-derives the spectrum but is itself flagged for … A295: no factor-7 gap in the corrected Dirac spectrum (ratios 1.8-2.6 across all channels/BCs); refuted |
Verifier-documented expected fails (7) — claims verify_P017.py recomputes and records as failing Run
- pi/7 times mu1 shortcut (Expected fail: the displayed approximation is about 48.79, not 51.5.)
- bulk spectrum in body and appendix are mutually consistent (Expected internal-consistency fail.)
- Dirac spectrum is reproducible from the TeX alone (Expected solver-reproducibility fail.)
- Planck formula is derived from the solved Dirac eigenvalue problem (Expected proof-status fail.)
- 3pi/20 is derived from first principles rather than decomposed (Expected proof-status fail: the dimension identity is correct, but the derivation is explicitly still open.)
- three-family and strong-CP entries are verified within P17 (Expected proof-status fail.)
- zero-free-parameter gravity closure is established (Expected proof-status fail.)
18 Paper MasterOperator 2 retired 3 unreviewed-or-open 7 verifier-documented
| id | status | closed by | excerpt / note |
|---|---|---|---|
| P018_3 | unreviewed-or-open | The third sub-result --- that the four coefficients $(\alpha,\gamma,\zeta,\beta)$ are the only spectrum-matching assignment --- is the global injectivity of the … | |
| P018_4 | unreviewed-or-open | The first sub-result --- that each component $R_i$ is the only operator in its category --- is not an open search. An audit (Addendum 349b) classifies the eight … | |
| P018_5 | unreviewed-or-open | The second sub-result --- that additive composition is the only admissible composition --- is shown canonical but not exhaustively closed (Addendum 350b). Three legs … | |
| P018_2 | retired | A295 | The normalisation convention used here conflicts with the gravity theorem of P017; the same P036 ratio-formula workaround applies, but neither the normalisation conflict … |
| P018_1 | retired | A279 | Direct evaluation of the stated moment-operator normalisation integral yields $\approx 0.374$, not the claimed $51.53$; the discrepancy is a factor of $\sim 138$ … |
Verifier-documented expected fails (7) — claims verify_P018.py recomputes and records as failing Run
- first-excited Planck formula using P18 moment operator definition (Expected fail: M is defined with mu_n/mu0, so the first-mode expectation gives mu1/mu0 and the formula is about 0.374, not 51.53.)
- moment-operator normalization is consistent with gravity theorem (Expected internal-consistency fail.)
- free B4 Dirac/Laplacian spectrum is fixed as (2n+l+2)^2 (Expected spectral-formula fail.)
- ground-state alpha normalization follows from the master eigenproblem (Expected proof-status fail.)
- canonical spectrum quantitatively determines fermion masses (Expected status fail.)
- no-free-parameters conclusion is consistent with caveats (Expected status fail.)
- Schrodinger/Yang-Mills/Einstein/Dirac reductions are derived in P18 (Expected proof-status fail.)
19 Paper UnifiedFieldEquation 1 superseded 14 verifier-documented
| id | status | closed by | excerpt / note |
|---|---|---|---|
| P019_3 | superseded | P32 | The cosmological constant scale derived here does not match the observed value; Addendum P032 proposes an alternative route via corner residues of the spectral zeta … equivalence of routes unproved |
Verifier-documented expected fails (14) — claims verify_P019.py recomputes and records as failing Run
- 3/11 weak-mixing estimate is close to measured 0.23 (Expected precision/wording fail.)
- beta origin using standard unit B4 volume (rel err=+1.32118%, tol=0.5%; Expected fail: dim(S3)*pi/(dim(B4)*Vol(B4)) with Vol(B4)=pi^2/2 gives 3/(2pi), not 3pi/20.)
- naive cosmological constant scale mu2/mu0^4 (rel err=+2.5571e+117%, tol=100%; Expected fail: the displayed proportionality alone gives about 2.6e-7, not 1e-122.)
- Fermi coupling estimate alpha/(mu1 MW^2) (rel err=-99.9109%, tol=50%; Expected fail: direct GeV substitution is about 0.09% of observed G_F.)
- strong-coupling estimate supplies running factor (Expected reproducibility fail.)
- action variation is complete with field-dependent source (Expected variational-proof fail.)
- Schrodinger equation is derived rather than restored by hand (Expected proof-status fail.)
- Dirac equation follows from a justified square root of the UFE (Expected proof-status fail.)
- Yang-Mills equation follows from Delta_S3 A = D_mu F^mu nu (Expected operator-identity fail.)
- division-algebra gauge-group derivation is exact here (Expected status fail.)
- Einstein equations are derived with computed heat-kernel coefficients (Expected proof-status fail.)
- all coupling constants are encoded and derived from rho moments in P19 (Expected status fail.)
- prediction list is derived in this paper (Expected proof-status fail.)
- zero-free-parameter all-physics conclusion is supported (Expected status fail.)
20 Paper StandardPhysicsEmbedding 1 refuted 8 verifier-documented
| id | status | closed by | excerpt / note |
|---|---|---|---|
| P020_1 | refuted | The Higgs VEV formula derived here evaluates to $\sim 10^{17}\ \mathrm{GeV}$, approximately $15$ orders of magnitude above the physical value of $246\ \mathrm{GeV}$. No … A293: v = M_Pl/sqrt(mu0 mu1) = 1.0e17 GeV, off by 4.1e14 — refuted as stated; flags (unpromoted): ln(v/me) vs E_self (0.70%), exponent fraction vs 3/4 (0.53%) |
Verifier-documented expected fails (8) — claims verify_P020.py recomputes and records as failing Run
- Higgs VEV formula M_Pl/sqrt(mu0*mu1) (rel err=+4.06608e+16%, tol=1%; Expected fail: the formula gives about 1.0e17 GeV, matching the TeX unresolved note.)
- Higgs mass v*sqrt(E_self/mu0) (rel err=-38.9739%, tol=5%; Expected fail: direct substitution gives about 76.3 GeV.)
- neutrino scale m_e*(v/M_Pl) (rel err=-100%, tol=90%; Expected fail: the displayed suppression gives about 1e-11 eV before the unspecified Z3 factor.)
- gauge group is derived exactly without the P37 caveats (Expected status fail.)
- three families are topologically enforced without extra assumptions (Expected proof-status fail.)
- strong CP solution is derived in this TeX (Expected proof-status fail.)
- CKM/PMNS and full mass spectrum are supplied by explicit formulas here (Expected reproducibility fail.)
- zero free parameters is supported by this paper alone (Expected status fail.)
21 Paper PequalsNP 3 scope 7 verifier-documented
| id | status | closed by | excerpt / note |
|---|---|---|---|
| P021_1_c | scope | The invocation of $C \circ P = I$ to conclude ``P = NP for a single observer'' conflates two distinct formal systems. In standard complexity theory, P and NP are defined … A295: application-paper defect, recorded; P21-P26 are outside the load-bearing spine (package design); repair not scheduled | |
| P021_3_c | scope | The identification of the edge-layer fraction $\pi/\alpha^{-1} \approx 2.3\%$ with the fraction of hard NP-complete instances is asserted without proof. No … A295: application-paper defect, recorded; P21-P26 are outside the load-bearing spine (package design); repair not scheduled | |
| P021_2_c | scope | Theorem \ref{thm:resolution} does not resolve the formal Clay Millennium Problem and cannot do so within the framework as given. Parts (1)--(3) redescribe the … permanent honesty marker (Clay scope) |
Verifier-documented expected fails (7) — claims verify_P021.py recomputes and records as failing Run
- single-observer P=NP is a theorem of standard complexity theory (Expected formal-scope fail.)
- observer-dependent resolution settles the formal alternatives (Expected terminology/scope fail.)
- hard NP-complete instance fraction is derived (Expected empirical/proof gap.)
- 90.5/7.2/2.3 layer fractions classify all NP instances (Expected model-definition fail.)
- phase transition ratio follows from alpha^-1/32 (Expected numerology/status fail.)
- quantum speedup ceiling for NP-complete problems is proved (Expected proof gap.)
- self-reference implies bulk access as complexity theorem (Expected formalization fail.)
22 Paper XavierStokes 3 scope 7 verifier-documented
| id | status | closed by | excerpt / note |
|---|---|---|---|
| P022_2_c | scope | Proposition \ref{prop:coupling} derives $D/\nu = 1/\pi$ and $\delta\nu/\nu = \psi/\pi$ by asserting that inter-layer diffusivity ratios equal the geometric … A295: application-paper defect, recorded; P21-P26 are outside the load-bearing spine (package design); repair not scheduled | |
| P022_1_c | scope | The proof of Theorem \ref{thm:global} contains a critical gap in Step~4. The argument requires that when $\|\omega\|_{L^\infty} > M$ the enhanced dissipation term … A295: application-paper defect, recorded; P21-P26 are outside the load-bearing spine (package design); repair not scheduled | |
| P022_3_c | scope | The Kolmogorov-scale estimate $\eta_{XS} \approx 1.24\,\eta_{NS}$ requires $\langle\psi\rangle \approx 1$ in high-strain regions (``of order unity''), but this value is … A295: application-paper defect, recorded; P21-P26 are outside the load-bearing spine (package design); repair not scheduled |
Verifier-documented expected fails (7) — claims verify_P022.py recomputes and records as failing Run
- kinetic energy identity is valid for variable viscosity as written (Expected energy-identity fail.)
- high vorticity implies high strain (Expected regularity-proof fail.)
- quasi-steady psi approximation closes a rigorous estimate (Expected proof gap.)
- Poincare lower bound is available on R3 without hypotheses (Expected domain/hypothesis fail.)
- superlinear dissipation proves BKM integral is finite (Expected closure fail.)
- Xavier-Stokes has no calibrated free parameters (Expected parameter-status fail.)
- numerical verification is reproducible from included code/data (Expected reproducibility fail.)
23 Paper YangMillsMassGap 3 scope 7 verifier-documented
| id | status | closed by | excerpt / note |
|---|---|---|---|
| P023_2 | scope | The isomorphism $\mathrm{SU}(2)\cong S^3$ is invoked without specifying the metric normalisation constants needed to identify the round metric on $S^3$ with the Killing … A295: application-paper defect, recorded; P21-P26 are outside the load-bearing spine (package design); repair not scheduled | |
| P023_1_c | scope | The derivation is circular: $f_b = \pi^2/\alpha^{-1}$ is \emph{defined} by the three-layer decomposition of Paper 04 and is then used to derive the mass gap … A295: application-paper defect, recorded; P21-P26 are outside the load-bearing spine (package design); repair not scheduled | |
| P023_3_c | scope | Theorem \ref{thm:min-misalign} below is not established by a variational calculation: the assertion that the minimum of the alignment functional over topologically … A295: application-paper defect, recorded; P21-P26 are outside the load-bearing spine (package design); repair not scheduled |
Verifier-documented expected fails (7) — claims verify_P023.py recomputes and records as failing Run
- direct SU(2)=S3 route derives f_b rather than defines it (Expected circularity/status fail.)
- SU(2) is Riemannian-isometric to the unit S3 without metric normalization (Expected metric-normalization gap.)
- minimum misalignment equals f_b is proved (Expected proof gap.)
- mass-gap formula is internally consistent (Expected formula inconsistency.)
- alignment mass term is gauge-invariant Yang-Mills construction (Expected gauge-invariance fail.)
- reflection positivity follows from pointwise positivity (Expected OS-proof fail.)
- framework proves existence of 4D quantum Yang-Mills theory (Expected Millennium-scope fail.)
24 Paper RiemannHypothesis 2 scope 8 verifier-documented
| id | status | closed by | excerpt / note |
|---|---|---|---|
| P024_2_c | scope | The deficiency-index argument in Theorem \ref{thm:esa} is carried out for the multiplication operator $\gamma \mapsto \gamma$ on a subspace of $L^2(\mathbb{R})$, not for … A295: application-paper defect, recorded; P21-P26 are outside the load-bearing spine (package design); repair not scheduled | |
| P024_3_c | scope | Corollary \ref{cor:weil-trace} conflates two distinct equalities. The first equality $\operatorname{Tr}(h(\overline{H_\xi})) = \sum_n h(\gamma_n)$ is the spectral … A295: application-paper defect, recorded; P21-P26 are outside the load-bearing spine (package design); repair not scheduled |
Verifier-documented expected fails (8) — claims verify_P024.py recomputes and records as failing Run
- Mellin transform sign/normalization is consistent (Expected sign/normalization fail.)
- zero-supported odd part is a nonzero L2 subspace (Expected Hilbert-space fail.)
- constraint creates point spectrum at zeta zeros inside L2 (Expected spectral fail.)
- self-adjointness of H_xi proves RH (Expected circularity fail.)
- off-critical zeros are represented (Expected RH-circularity fail.)
- h(H_xi) is trace class on continuous-spectrum part (Expected trace-class fail.)
- Weil explicit formula is identified with this operator trace (Expected unresolved-gap fail.)
- resolvent has poles at real zeros (Expected resolvent fail.)
25 Paper HodgeConjecture 3 scope 7 verifier-documented
| id | status | closed by | excerpt / note |
|---|---|---|---|
| P025_1_c | scope | The proof of Theorem \ref{thm:non_middle} (Case~1, $p > n/2$) is circular. The induction step assumes ``Hodge holds for codimension $n-p$,'' meaning it assumes … A295: application-paper defect, recorded; P21-P26 are outside the load-bearing spine (package design); repair not scheduled | |
| P025_2_c | scope | Proposition \ref{prop:dual_span} is stated without proof. The claimed identity $(\operatorname{Eff}^\vee - \operatorname{Eff}^\vee) = \operatorname{Alg}^\perp$ (under … A295: application-paper defect, recorded; P21-P26 are outside the load-bearing spine (package design); repair not scheduled | |
| P025_3_c | scope | The appeal to Chow's theorem (``analytic = algebraic'') to justify that ``ungrounded'' Hodge classes cannot exist conflates two distinct settings. Chow's theorem states … A295: application-paper defect, recorded; P21-P26 are outside the load-bearing spine (package design); repair not scheduled |
Verifier-documented expected fails (7) — claims verify_P025.py recomputes and records as failing Run
- GSP annihilator argument proves W=V directly (Expected linear-algebra gap.)
- non-middle GSP is proved unconditionally (Expected circularity/reduction gap.)
- Hodge-Riemann positivity implies every nonzero rational Hodge class pairs with an effective algebraic cycle (Expected interpretation gap.)
- effective cone is closed as stated (Expected cone-geometry fail.)
- dual-cone span proposition is established (Expected cone-duality fail.)
- cone-theoretic characterization is equivalent to Hodge (Expected proof gap.)
- Chow/projectivity rules out non-algebraic Hodge classes (Expected overstatement.)
26 Paper BSD 3 scope 7 verifier-documented
| id | status | closed by | excerpt / note |
|---|---|---|---|
| P026_1_c | scope | The proof of Theorem \ref{thm:derivative-point} is circular. The argument begins by assuming the BSD formula $L^{(r)}(E,1)/r! = C_E \cdot R_E$ (where $r = … A295: application-paper defect, recorded; P21-P26 are outside the load-bearing spine (package design); repair not scheduled | |
| P026_2_c | scope | The converse direction of the Local-Global Consistency argument (a zero at $s=1$ implies a rational point) is established by Gross--Zagier + Kolyvagin only for analytic … A295: application-paper defect, recorded; P21-P26 are outside the load-bearing spine (package design); repair not scheduled | |
| P026_3_c | scope | Step~5 does not constitute a proof for $r_{\text{an}} \geq 2$. The Yuan--Zhang--Zhang formula cited is a theorem about certain Shimura curve situations and has not been … A295: application-paper defect, recorded; P21-P26 are outside the load-bearing spine (package design); repair not scheduled |
Verifier-documented expected fails (7) — claims verify_P026.py recomputes and records as failing Run
- Sato-Tate layer partition proves BSD rank equality (Expected scope fail.)
- higher-rank height formula is available as a proved BSD formula for all E/Q (Expected proof-status fail.)
- derivative-point correspondence proof is valid (Expected circularity fail.)
- local-global consistency theorem proves zeros iff points (Expected proof gap.)
- BSD formula implies Sha finiteness without assuming BSD (Expected conditional/circular status.)
- example y^2=x^3-x+1 has the stated conductor 37 data (Expected example-data fail.)
- Cremona-table BSD verification claim is sourced/reproducible (Expected reproducibility fail.)
27 Paper SecondObserver 1 confirmed-load-bearing 1 retired 12 verifier-documented
| id | status | closed by | excerpt / note |
|---|---|---|---|
| P027_3_c | confirmed-load-bearing | The formula $\log(M_{\mathrm{Pl}}/m_e) = \tfrac{3\pi}{20} \cdot \mu_1/(1 - \mu_1\alpha^2) \approx 51.528$ is stated without derivation. The symbol $\mu_1$ is not defined … A279+A282: provenance found — derived in P03 Thm beta_qed, uncited by P27; 3pi/20 = (1/10)(3pi/2), the 3pi/2 textbook one-loop QED; P27's dressing 1/(1-x) is a corruption of P03's derived (1+x), which hits measurement … | |
| P027_2 | retired | A276 | The Hopf map $\pi: S^3\to S^2$ is 2-to-1 and therefore not invertible, so the composition $C\circ P = I$ cannot be established via this map. Addendum P028 reformulates … |
Verifier-documented expected fails (12) — claims verify_P027.py recomputes and records as failing Run
- Hopf projection/collapse supply C o P = I (Expected proof-status fail.)
- S3 uniqueness theorem proves canonical projection-collapse structure (Expected proof-status fail.)
- B4 bulk is derived uniquely from S3 boundary (Expected proof-status fail.)
- coefficients 16, 3, 2 are derived in P27 (Expected derivation fail.)
- layer fractions prove information partition (Expected interpretation-to-formalism fail.)
- three social observers derive Z3 lens-space family topology (Expected proof-status fail.)
- Planck/electron formula measures consensus stacking (Expected interpretation-to-formula fail.)
- dark matter hidden-observer principle is mathematically testable here (Expected non-verifiable claim.)
- dark-energy proportionality predicts Lambda (Expected open/conjectural fail.)
- P vs NP claims are formal complexity results (Expected proof-status fail.)
- Big Bang as first disagreement is derived from equations (Expected physics-derivation fail.)
- complete Level -1 foundation is established (Expected status fail.)
28 Paper UniversalWaveGeometry 2 retired 6 verifier-documented
| id | status | closed by | excerpt / note |
|---|---|---|---|
| P028_3_c | retired | A263 | The identification of the mathematical Hopf lapse $m(q_{\mathrm{rel}}) = \sqrt{1-v^2}$ with the physical Lorentz time-dilation factor … |
| P028_2 | retired | A273 | The lifted propagation speed evaluates numerically to $2\pi\sqrt{1-\kappa}\approx 6.2735$, not exactly $2\pi\approx 6.2832$; the identification with $2\pi$ requires … |
Verifier-documented expected fails (6) — claims verify_P028.py recomputes and records as failing Run
- lifted speed equals exactly 2*pi (rel err=-0.106698%, tol=0.001%; Expected fail: 2*pi*sqrt(1-kappa) is slightly below 2*pi; the text later treats 2*pi as a normalization/approximation.)
- Lorentz lapse is derived as physical SR time dilation (Expected physical-identification fail.)
- simulation RMSE claims are reproducible from the TeX alone (Expected reproducibility fail.)
- Omega0 is forced by volume ratio without modelling assumptions (Expected derivation-status fail.)
- J3(O) upstream embedding is explicitly constructed (Expected proof-status fail.)
- Theta scaling by alpha worsens SR agreement is data-backed in TeX (Expected reproducibility fail.)
29 Paper TrainingExposure 1 retired 2 scope 8 verifier-documented
| id | status | closed by | excerpt / note |
|---|---|---|---|
| P029_2_c | scope | The proof of Theorem \ref{thm:isolation} does not establish that $\mathcal{L}(\theta^*+\delta)>0$ for an \emph{arbitrary} data distribution $\mu$. Local injectivity … A295: technical/scope note — external anchor or theorem hypothesis caveat; corpus use unaffected | |
| P029_3_c | scope | The isolation of $\theta^*$ (Definition \ref{def:isolated}) establishes only that no \emph{nearby} points achieve zero loss, not that $\theta^*$ is the \emph{unique} … A295: technical/scope note — external anchor or theorem hypothesis caveat; corpus use unaffected | |
| P029_1 | retired | A278 | The stated formula for the damped resonance peak frequency is incorrect; the correct peak of the amplitude response occurs at … |
Verifier-documented expected fails (8) — claims verify_P029.py recomputes and records as failing Run
- damped displacement response peaks exactly at omega0 (Expected fail: differentiating the displayed denominator gives omega_peak=sqrt(omega0^2-gamma^2/2) for gamma>0.)
- local injectivity alone implies positive population loss for arbitrary mu (Expected fail: the theorem needs full-support/positive-measure or continuity assumptions.)
- local isolation implies unique isolated global minimum (Expected fail: the stated hypotheses support a strict local minimum, not global uniqueness.)
- necessary and sufficient conditions are established (Expected theorem-scope fail.)
- all catalogued TOE identities are independently established in P29 (Expected dependency/proof-status fail.)
- zero free parameters in operational pipeline (Expected wording fail: zero trainable constants is narrower than zero operational degrees of freedom.)
- regularization or noise generically prevents convergence (Expected overbreadth fail.)
- single instance is sufficient for exposure in general (Expected scope fail.)
30 Paper GeometricObserverNetwork 2 confirmed-load-bearing 1 scope 9 verifier-documented
| id | status | closed by | excerpt / note |
|---|---|---|---|
| P030_1 | scope | The Riemannian logarithmic map on $S^3$ is singular at the antipodal point of any given base point and is not globally defined on all of $S^3$; all results depending on … A295: technical/scope note — external anchor or theorem hypothesis caveat; corpus use unaffected | |
| P030_2 | confirmed-load-bearing | The claimed norm drift bound $<10^{-15}$ is inconsistent with the $O(\varepsilon\cdot N)$ estimate derived from the internal error propagation analysis; one of these … A295: drift bound inconsistency — testable against the GON implementation; not yet run | |
| P030_3_c | confirmed-load-bearing | The $J_3(\OO)$ extension claims that the cubic Jordan invariant $\det_J(X)$ is ``an additional conserved quantity alongside $\mathrm{Tr}(X^2)$'' in the $\GON$ evolution … A295: J3(O) conservation claim structural, unverified |
Verifier-documented expected fails (9) — claims verify_P030.py recomputes and records as failing Run
- log map is defined at every S3 state (Expected fail: the implementation needs an explicit identity/antipode branch.)
- norm drift bound < 1e-15 is consistent with implementation estimate (Expected precision-threshold fail.)
- mini-batch noise makes exact parameters drift on clean identity data (Expected benchmark-claim fail.)
- finite-capacity MLP cannot reach zero error on the benchmark (Expected protocol-scope fail.)
- zero hyperparameters in full experiment (Expected wording fail: zero trainable core parameters is narrower.)
- two correct implementations produce bitwise-identical outputs (Expected reproducibility overstatement.)
- Z3 extension keeps Omega in real R3 without extra structure (Expected type/embedding gap.)
- J3(O) associative-subalgebra variant has dimension 27 (Expected algebra/dimension mismatch.)
- outside-domain behavior is silent rather than approximately wrong (Expected operational-spec gap.)
31 Paper NicomachusMonad 2 confirmed-load-bearing 1 retired 7 verifier-documented
| id | status | closed by | excerpt / note |
|---|---|---|---|
| P031_1_c | retired | A237 | The proof of Lemma \ref{lem:dim} (stratum modulus dimension $n = \max(d-1,1)$) contains two unjustified steps. (i)~It asserts exactly one holonomy constraint for … |
| P031_2_c | confirmed-load-bearing | The proof of Lemma \ref{lem:monodromy} ($\mathbb{Z}_k$ monodromy) for $d=3$, $k=4$ requires that the $\mathbb{Z}_4$ action $(z_1,z_2)\mapsto(iz_1,iz_2)$ corresponds to … A237/A295: d=3,k=4 monodromy case open | |
| P031_3_c | confirmed-load-bearing | The proof of Lemma \ref{lem:degree} (Hopf frame polynomial degree $k$) identifies the ``frame perpendicularity condition'' with the equation $T_k(t) = 0$ (the $k$-th … A237/A295: frame perpendicularity step open |
Verifier-documented expected fails (7) — claims verify_P031.py recomputes and records as failing Run
- Hopf modulus dimension is derived from explicit self-intersection equations (Expected proof-status fail.)
- Z_k monodromy is proved as stratum-linking monodromy (Expected topology proof fail.)
- degree-k Chebyshev frame equation follows from the Hopf bundle proof (Expected derivation fail.)
- Bézout count is an independently derived configuration count (Expected proof-status fail.)
- static 2^4 factorization would give weight 2^3 (rel err=-50%, tol=0%; Expected internal fail: using the paper's own integration factor 1/k with k=4 gives 16/4=4, not 8.)
- monad identity independently selects the dynamic mechanism without circularity (Expected proof-status/circularity fail.)
- first-principles unconditional closure is warranted (Expected status fail.)
32 Addendum CantorBridge 8 verifier-documented
Verifier-documented expected fails (8) — claims verify_P032.py recomputes and records as failing Run
- dimensional cascade d=6 (rel err=+9.62965%, tol=1e-10%; Expected fail: documents the recorded d=6 cascade claim 1 - pi^3/192; the recursion gives 0.91925, not 0.83851.)
- [-1,1]^4 has eight corners (Expected direct counting fail.)
- the hypercube {-1,+1}^4 has eight vertices (Expected direct counting fail.)
- octonion basis identification follows from the 4-cube vertex count (Expected structural fail.)
- Euler exterior face derives Lambda0 (Expected proof-status fail.)
- folded cube-net exterior maps to the cube interior (Expected topology/folding fail.)
- tesseract Euler characteristic is unambiguously zero (Expected ambiguity fail.)
- static Lambda0 resolves the cosmological constant problem (Expected status fail for any full-resolution reading.)
33 Paper SelfIntersectionMonad 2 confirmed-load-bearing 7 verifier-documented
| id | status | closed by | excerpt / note |
|---|---|---|---|
| P033_3_c | confirmed-load-bearing | The claim that the Hopf fibration \emph{absorbs} one power of $k$ from the self-intersection count is a structural assertion, not a construction. The self-intersection … A295: Hopf absorption claim structural, unverified | |
| P033_2 | confirmed-load-bearing | The formula $\mathrm{Vol}(S^{d-1})=\pi^d$ is false: for $d=1$, $\mathrm{Vol}(S^0)=2\neq\pi$; for $d=2$, $\mathrm{Vol}(S^1)=2\pi\neq\pi^2$; for $d=3$ … A295: Vol(S^{d-1}) = pi^d confirmed FALSE at every d (correct: 2 pi^{d/2}/Gamma(d/2)); downstream argument needs rework |
Verifier-documented expected fails (7) — claims verify_P033.py recomputes and records as failing Run
- original Hopf factorisation statement is literally true (Expected fail: the proof itself notices and corrects this.)
- pi^d is the exact volume of S^{d-1} for d=1,2,3 (Expected geometric-measure fail.)
- Hopf fibration absorption is derived by the arithmetic (Expected interpretation/proof gap.)
- fine-structure constant is exactly derived as physical alpha inverse (Expected precision/equality fail.)
- Nicomachus sum-of-cubes identity is used (Expected scope fail: this is a cube-sequence analogy, not a use of the identity.)
- self-intersection counts are independently derived in P33 (Expected dependency-status fail.)
- Paper 32/P33 circuit is fully established (Expected cross-paper overstatement.)
34 Paper KleisliMonadS3 1 confirmed-load-bearing 1 retired 8 verifier-documented
| id | status | closed by | excerpt / note |
|---|---|---|---|
| P034_2_c | confirmed-load-bearing | The proof of Theorem \ref{thm:assoc} (Associativity) claims that ``the geodesic centroid (extrinsic mean) is linear: for nested weighted averages the order of averaging … A295: associativity proof gap (extrinsic mean) stands | |
| P034_3_c | retired | A265/A273/A275 | The identification $\mathtt{BREATH\_PERIOD} = \pi \cdot \alpha^{-1} \approx 430.5\,\text{s}$ as the ``temporal scale of one full Wheel cycle'' and ``one full application … |
Verifier-documented expected fails (8) — claims verify_P034.py recomputes and records as failing Run
- referenced implementation files are present in this TOE workspace (Expected reproducibility fail in this paper folder: the cited code is not present here.)
- left identity holds for arbitrary f:S3->T(S3) (Expected monad-law fail for non-point outputs.)
- right identity preserves a non-degenerate distribution (Expected monad-law fail under centroid-collapse semantics.)
- centroid-collapse associativity holds for nested averages (Expected associativity fail: normalization after the first centroid changes the weights.)
- extrinsic mean laws are exact for all hemisphere-confined distributions (Expected scope fail.)
- plateau condition is a categorical fixpoint at Omega (Expected proof-status fail.)
- no learned weights follows from the displayed kernel alone (Expected scope fail.)
- no-free-parameters categorical invariant claim is supported (Expected status fail.)
41 Paper ObserverOriginOfSubstrate 2 confirmed-load-bearing 2 unreviewed-or-open
| id | status | closed by | excerpt / note |
|---|---|---|---|
| P041_1 | confirmed-load-bearing | The derivation models witnessing as coherent bilinear composition of distinctions (premise P1 of Definition \ref{def:prem}). This is the one structural assumption it … Paper 41 (a-lane): witnessing = coherent bilinear composition (premise P1); the witness-step = Cayley-Dickson doubling and the substrate dims {1,2,4,8} follow (BMK/Hurwitz). Rests on the P27 linear-coherence frame, not … | |
| P041_2 | confirmed-load-bearing | The inhomogeneous Maxwell equation holds exactly only in the flat limit $c\to0$; on the curved $S^3$ the field equation is $d{\star}F=c\,F$, carrying the curvature term … Paper 41: U(1)/Maxwell core closed (dF=0 and first-Chern c1=1 exact on S^3; d*F=cF curvature term derived; flat-limit source-free Maxwell; coupling alpha). Closes Paper 19's schematic U(1) reduction. verify_Paper41.py | |
| P041_3 | unreviewed-or-open | The full Standard-Model coupling and hypercharge normalisation beyond the $U(1)$ sector are not derived here; the higher rungs $SU(2)$ and $SU(3)$ are identified only at … | |
| P041_4 | unreviewed-or-open | The matter source $J$ (the ``boundary observing bulk'' term of Paper 19) is not constructed; the present derivation supplies the gauge sector and its source-free field … |
