Status date: 2026-09-07
main is the shared research line. Claim strength follows evidence and chronology, not PR state. docs/ROADMAP.md ranks information gain; it is not a permission system.
GOVERNANCE.md §2 is the whole list, and it is short: don't fool yourself about a
number, don't destroy data, don't misdate a freeze, say which observable, and count
one random block once. Nothing else in this repository gates exploratory work.
The three that bear directly on this ledger: frozen predictions and result history are preserved rather than overwritten; a claim-bearing comparison uses identical observable semantics or an exact registered map; and correlated views of one raw random block are counted once, not as independent primary evidence.
Everything else — digests, provenance chains, second implementations, preregistration,
power — is publication-time work and lives in docs/PUBLICATION-CHECKLIST.md.
| Statement | Level | Current evidence |
|---|---|---|
| Square-site matching-odd orientation signal exists | C3 | Independent P43+P57 primary synthesis rejects global zero: chi2=31.1857355515/4, p=2.81e-6; fixed H4 predictions give 3.4622795373/4, p=.484 |
Central square-site odd sector is compatible with DeltaCos4*N^-13/8 |
C3 | P31/P32/P37/P43/P50/P57 |
| Frozen norm-5 H4 transfer beats H12/H8 aliases | C3 | H4 0.4163/2; H12 35.1931/2; H8 16.0120/2 |
| P57 child block alone rejects zero | negative refinement | No: zero 1.77635/2; its value is harmonic/transfer discrimination |
| N145->290 full curve is one scalar multiplier | C3 negative | No: three-level transfer 9.3520/2, p=.0093; the resolved shape mode fails while the common amplitude direction remains viable |
| Frozen finite-size center-slope correction predicts N290 | C3 | corrected slope residual z=-0.666; bare 2^(3/8) gives z=-22.690 |
Pure P4[S'] ~ N^-5/4 is sufficient |
C3 negative | Prospectively falsified; 52.71634/2 on P48 new geometry |
| One scalar width explains the higher thermal jet | C2 negative | No: full covariance norm-5 width score 24.5004/10; width-corrected q2 22.2386/10 |
| Rank-2/Jordan is uniquely established | C2 | No. Jordan/log is compatible (17.0513/10) and now has a precise Q4-module origin, but scale-log behavior alone is not module identification |
Intrinsic quantile-center transfer obeys N^-3/4 on N145->290 |
C3 | frozen ratio observed 0.59584549 vs 2^-3/4=0.59460356, z=-1.033 |
| Square/rectangular spin-4 ratio carries the area-normalized weight-4 shape | C3 negative | Prospectively falsified at N=290: ratio 1.880 +/- 0.177 excludes 11/4 at 4.9 sigma, area scaling 4 at 12.0, and no-dependence 1 at 5.0. Tests the fingerprint as constructed, not the module: the normalization assumption is a second conjunct (docs/astra/Q2) |
Weight-4 modular amplitude law (1, 2.75, 10.99) holds across aspect ratios |
C3 negative | N=580 ladder A4(4i)/A4(i) = 4.58 scored by Fieller contrast (the denominator is 3.6σ from zero, so the ratio z is not used). no_modulus_dependence (1.00) is excluded at 9.5 sigma; bare_aspect_ratio (4.00, z=+0.50), the weight-4 shape (10.99, z=−2.08) and plain area scaling (16, z=−2.56) all survive — underpowered, three survivors. Cross-rung covariance measured (ρ=−0.1648, #575 replay) and moves no verdict. notes/aspect-ladder-n580-result-20260905.md |
#582's Wasserstein remainder r_N is indexed by a pre-existing discrete label |
C2 negative | Re-frozen five transitions reproduce #582 affine statistics bit-for-bit; exact permutation null over ≤30 relabellings is beaten by no label — lineage p=.133, multiplier/interpolation .300, prime parity/min-component .700, prime cos4-sign .600. The remainder is structured but unlabelled and not smooth curvature (Taylor stat 1.82e6/1.19e6 on 7 df, curvatures 43–80° from r_N, never dominant). notes/type582-residual-20260906.md |
| P398's balanced realization factors through the reflection quotient | exact (bounded to the frozen I/O object) | #600 Phase C. A (microscopic, Catalan(w)) vs B (r_reflect(w) orbit quotient) agree bit-for-bit in every resolvable Hankel direction at w=4..8 (`max |
| #581's two typed Q-score pieces keep distinct scale/noise profiles to L=8 | C2 | square-bond p=1/2, L=3/4/8 at 10⁵ configs, unbiased paired estimator (L=3 reproduces the enumerated gate; telescoping exact to 1e-18): ambient homology X single-signed/monotone with Cov(wrap,X) ≈0.29–0.30 nearly size-independent; duality-even B_even alternating, opposite, 6–11× smaller; X degree-one decays ≈1/L while B_even's stays at the floor. notes/qtangent-empirical-20260907.md |
| #609's 55% curvature discrepancy is a real second scale | C2 negative | The discrepancy is an affine change of chart: a_curv = 2/(h0+h1)[a1 - a0/k + ell_C(r1) - ell_C(r0)/k] closes to 3e-13 on the eight committed productions with published g fixed, reproduces the published ratios exactly (1.53681/1.55744 spin0, 1.57891/1.44387 equal), and the chart term carries 89–117% of the excess (97.5%/94.9% on the primary weighting). notes/p612-n725-decision-20260907.md |
| #609's amplitude law forecast holds at N=725 within ±5% | C3 (weighting-conditional) | One production, 100 batches × 1M paired = 1e8 per orientation (#609's "100 batches × 100M" was 100× this; n290 metadata says samples_per_pair = 1e8). a_hat(290→725) = -4.8083e-04 ± 2.2941e-06; the 3se interval lies wholly inside the ±5% band, so the finite forecast is supported — but the point miss is 5.56 se (2.7%) and the spin0→equal weighting systematic is 12% (~25 se), under which the same rule reads stops. |
The Issue #43 even-sector channel correction remains
DeltaS_cross = -DeltaS_either
with corrected score 0.5700315436/2.
Finite Russo/chain rule is exact:
M'(p) = pivotal_mass_primal(p) + pivotal_mass_matching(1-p).
The N=26 frozen finite families remain falsified:
Beta(5,5): first k=5 difference = -96
Beta(7,7): first k=5 difference = +156
The durable empirical picture is a leading matching-odd H4-like sector with x=21/4 candidate scaling, plus non-scalar finite-size mixing in the derivative/full-curve state.
The exact LCFT bridge is now sharper: the percolation energy Jordan pair can be lifted by the repository Q4 descendant to a rank-2 x=21/4, spin-4 pair. In the repository normalization <Q4|Q4>=4930. The resulting logarithmic slope has the exact module relation
B_logN(tau) = -(lambda_top/2) A_q(tau),
A_q/A_epsilon = (493/96) g2(tau),
so the frozen module coefficient is -493/192. This supplies a representation-theory origin for Jordan/log scaling; it does not prove that the lattice P4[S'] overlaps that module.
The next identifying evidence must use shape/modulus information. Exact assets include the rectangular/CM 11/4 ratio and the hexagonal degree-2 E4 phase projector. A scalar-cancelled modulus fingerprint is more identifying than another radial exponent fit.
Pivotal normalization gives two stable archived relations:
N * P4[D']/Mbar' chi2 = 8.793/7
[P4[S']/Mbar']/P4[D] chi2 = 9.458/7
while N^(13/8)P4[S']/Mbar' is nonconstant (117.880/7). A genuinely local landing-marked pivotal H4 observable is measurably orientation-sensitive.
Microscopically the N=10 local odd tangent has two independent response rows,
[[15/8, 5/4],
[-3/64, 11/64]],
but at N130/N170 the second singular direction is unresolved (condition numbers about 1687 and 608). More samples of the same two rows are therefore low information. The multiradius N130/N170 prototype also rejects a simple constant shell-log story and shows R=8 is geometrically non-injective there. Future local tomography should change geometry/readout, not merely add replicas.
The exact neutral-area covector maps the full Krawtchouk expansion to E[K_plus-K_minus]/(N+1), but the expansion is severely ill-conditioned when truncated around the intrinsic center. The global rank gap is therefore not a redundant low-order thermal-jet coordinate. This closes the scalar-width/common-state shortcut.
Primitive homology characters form a separate mechanism from the square-site thermal Q4 candidate.
The continuum-subtracted non-scalar C3 character is directly observed with a passing reflection null. The simple scalar C proportional E4(tau) Pell phase bridge fails, so this sector should not be identified with the thermal Q4 one-point function.
Two prospectively frozen norm-2 generations instead select the negative rank-4 H4 phase:
first generation: H4 -1/2 chi2=5.4171/2
second generation: H4 -1/2 chi2=1.7077/2, p=.426
Frozen positive-phase alternatives are strongly excluded in both generations. Individual lineages do not converge monotonically to -1/2, so monotonic convergence is not claimed.
A zero-new-compute vacuum-KdV calculation predicts C30/C56=1.99068780; observed is 1.99360564, with the C-only score essentially exact. The scalar S residual is a separate direction. Current interpretation: a distinct x≈4, spin-4 identity/vacuum-family response with finite-size corrections.
The general integer-period backend is production-ready. Exact Gaussian-cover arithmetic shows norm-4 2i has deck group Z2 x Z2, and (1+i)^2=2i has an exact coarse/detail Hadamard character decomposition. There is no Gaussian scalar norm-4 cyclic Z4 comparator. Therefore quotient dependence should be tested with character-resolved readouts when cheap, not treated as an unspecified nuisance.
- Signal existence is no longer the bottleneck. Independent primary square-site blocks strongly reject global zero while remaining compatible with fixed H4 predictions.
- The central/derivative state is not scalar. N290 shape, norm-5 thermal jet, rank-gap and width analyses all point toward compact mixing/transfer rather than another free correction exponent.
- Jordan has a concrete module origin but is not identified by scale behavior alone. Modulus/shape is the next orthogonal discriminator.
- Local pivotal physics is real, but current N130/N170 readouts are nearly rank-one. Change the readout/geometry rather than buying more of the same samples.
- Primitive square-bond H4 is a separate
x≈4sector. Do not fold it into the thermalx=21/4story. - Norm-4 has exact deck-character structure. Use it to sharpen, not delay, the existing production design.
- The #582 dominant transferable direction is the robust finite object; its remainder is real but unlabelled. The remainder after removing the consensus
g_Nis structured yet matches no pre-existing discrete label above its permutation null, and is not a smooth one-parameter-law curvature artifact. Resolve it with one crossed transition or a changed readout, not with another fitted rank or exponent. - #581's two typed Q-score pieces are a usable typed fingerprint. On square bond the ambient-homology source is single-signed, low-scale and size-stable, while the duality-even Betti tangent alternates and stays small and opposite — a separation that survives to L=8. This is the square-bond baseline against which a square-site
X_sitecoupling can be read as bulk-like or topological. - The 55% "second scale" at the curvature is a chart, not a law failure. The exact chart identity closes to 3e-13 on every committed production and absorbs 95–98% of the old excess under the primary weighting. What remains after transport is a ~4% curvature misfit (7.3 se) and a structured full-law residual (1447/6 df at the new transition) — the amplitude forecast's ±5% pass does not establish the whole law, and the verdict is weighting-conditional (the
equalsensitivity reads stops). - The
Q_N(u) → p_cbridge is a scoped corollary, not a new theorem. It holds under three imported hypotheses — digital Alexander duality (the repository's own), Duminil-Copin–Tassion exponential decay (their §1.2 site adaptation), andp_c + p_c* = 1for amenable pairs (Grimmett–Li (1.3) +p_c = p_u, or van den Berg + sharpness; van den Berg's counterexample keeps it a genuine hypothesis). Duncan–Kahle–Schweinhart already have the sharp threshold for giant cycles, so no novelty claim is available. Thin tori (ell_N = O(log N)), unbounded weights andu → 0/1stay outside.
The project does not claim a closed form for square-site p_c, global uniqueness of H4 or 13/8, a unique q2/Jordan mechanism, a scalar-width explanation, proof of the lattice-to-Q4 overlap, a full matching/OPE automorphism, or a rigorous new percolation bound.