Publication history: 2026-07-02

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• v471_seam_horizon_replica.py (SEAM.EHMODEL.04). The residual isolated by v150/v151/v152 — “the RP seam kernel is this BFK Calderón datum” — is exercised numerically on a discretized seam collar with the seam's own kernel and real replica sheets: the matched conical deficit has slope 2C(\gamma) on deficit cones (0.01–0.05\%) and replica sheets n{=}2 (0.8\%), n{=}3 (1.5\%); the EH coefficient is cutoff-independent (0.5\% drift) while the \zeta-scale \mu_{\mathrm{lat}} drifts — the v152 anchor exhibited on data, with no canonical \ln(m/\mu){=}3/4 emerging (recorded honestly); the BFK/Schur split is exact ({\sim}10^{-16}) with the Calderón factor conically clean measured on the kernel (pure cut-edge law, tip term 0, power-checked) and the halves carrying 2C_{\mathrm{cone}} via Kac doubling; the v302 transfer masses 6\ln(3/2), 6\ln 3 sit on the calibrated EH line (\le0.05\%); and the Perron/attractor mode (m{=}0) is IR-divergent — the recovery gap \Delta{=}6\ln(3/2) is what makes the induced-gravity coefficient finite (the same gap that makes the attractor unique makes 1/G finite). SEAM.THEOREM.01 stays [O]; its residual retypes to the continuum scaling limit (the MMST class — the same single residual as SEAM.EQUIV.01, v336) plus the one declared anchor. 16/16 checks; suite green through v471 (465 modules); numerical (sparse lattice determinants), Python-only by nature. Papers updated: origin_theory (new collar paragraph in the Seam–Horizon gapbox + residual retyping), tfpt_research_contracts (R3 premise), tfpt_4_frontier (3/4 audit note), root README, verification/README, zenodo_description.html. Exploration original: experiments/theory-contracts/seam_horizon_replica.py (17/17, same day).
• GW ringdown-echo channel hardened (experiments/gw-ringdown-echo, scorecard row data_limited{\to}consistent). (i) Strain coverage extended to the 10 loudest ringdown events incl. GW250114 (network SNR 78.6, O4b; new fetch_strain_4096.py crops the 4096 s GWOSC archive segments). (ii) Redshift correction: the GWTC catalogue reports source-frame masses, the observed ringdown is at f_0/(1{+}z) — all templates moved to detector-frame M(1{+}z) (before the fix GW190521, z{=}0.56, was filtered {\sim}1.6\times too high); all stages re-run. (iii) Stage 1b stacked search over 23 detector streams: stacked p{=}0.262, kernel-consistent streams 0/23 — STACKED NULL. (iv) Stage 1c signature battery (Bonferroni \times12): ratio semantics (amplitude (2/3)^6 vs energy reading (2/3)^3 vs step 2/3) \times \mu_4 per-bounce phases \{0,\pi/2,\pi,3\pi/2\} (the boundary-birefringence analogue — path birefringence from parity violation c_-{=}8 cancels in the inter-echo ratio; only a per-reflection phase does not) \times lags 0.5–350 ms (ECO through Planckian window), with joint (2,2,0){+}(2,2,1) subtraction and a template-agnosticism control: NO_VARIANT_ECHO on all 10 events — the null is robust against alternative signature readings. Search-target firewall unchanged: upper bound, no detection, no tension claim.

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• v295_flataway_a2_exact.py (FLATAWAY.A2.01). Alessandro's Git-baseline audit (commit 8cb8ad0) hit a platform-marginal failure in check 3: the exact divided-difference a_2 kernel is compared against an \varepsilon{=}10^{-3} second finite difference whose own truncation error is O(\varepsilon^2)\sim10^{-6}, yet the tolerance was 10^{-6} — on his machine k{=}3 landed at 1.1\times10^{-6} (ours: 2.9\times10^{-7}). Fix: tolerance widened to 5\times10^{-6} so it dominates the control's error floor, with the reasoning recorded in the check text; the load-bearing anchor remains the closed form at machine precision (v296), the numeric witness stays as the independent cross-check. A numerical-robustness patch, no claim or status change; ledger row updated; suite green (all checks passed through v470).

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• v469_seam_crossedproduct_route.py (SEAM.EQUIV.CROSSEDPRODUCT.01). The 128-spinor extension leg of SEAM.EQUIV.01 no longer rests on 2024/2025 preprints: [E]the SO(16)_1 spinor has h_s{=}N/16{=}16/16{=}1{\in}\Z, so its statistics phase is +1 — exactly the Longo–Rehren locality criterion — and the \Z_2 simple-current crossed product SO(16)_1{\rtimes}\{1,s\} is a local index-2 extension by the peer-reviewed subfactor package (Longo–Rehren, Rev. Math. Phys. 7 (1995); the level-1 so(N) net with its DHR sectors from even-CAR: Böckenhauer, Rev. Math. Phys. 8 (1996); simple-current extensions of nets: Böckenhauer–Evans, Comm. Math. Phys. 197 (1998)); KLM (Comm. Math. Phys. 219 (2001)) gives \mu(B){=}4/2^2{=}1 \Rightarrow holomorphic \Rightarrow (E_8)_1 by the v463 pin. The AGT/AMT lattice-VOA route (v459) is demoted to an independent second witness. [E]the index-4 \mu_4 glue runs on the same integer: h(J^k){=}\{1,1,1\} for k{=}1,2,3 (the v125 isotropy q(k(1,1)){=}k^2 at net level), \mu{=}16/4^2{=}1, same endpoint. [E]the realisation input is reduced from model fiat to invariants (R1'): quasi-free [C](v155/v160) + gap [E](v302) + class D + c_-{=}8 [E] (v456, from P1), with the invariants computed — per-copy FHS Chern |C|{=}1 vs 0 (control), \nu{=}16{\times}|C|{=}16, c_-{=}\nu/2{=}8 — and \nu\equiv 0\ (\mathrm{mod}\ 16) is exactly Kitaev's class-D phase whose edge admits a purely bosonic description = the (E_8)_1 level-1 state (Ann. Phys. 321 (2006), sixteen-fold way); the phase-invariance of c_- is cited (Kapustin–Spodyneiko, PRB 101 (2020); Kim et al., PRL 129 (2022)). [O]not closed: the cited theorems stay cited; SEAM.EQUIV.01 stays [O].
• Lean hardening. TfptCarrier/SeamResidualAxiom.lean gains the parallel peer-reviewed derivation seamResidualClosed$'$: the invariant-level axiom collar_invariants (R1') + one combined 1995–2001 package crossedproduct_route_theorem; the new joints are kernel facts with no axioms — lr_locality_integer (h_s{=}16/16{\in}\Z), glue_locality_integers (\mu_4 h(J^k){\in}\Z), klm_holomorphic (4/2^2{=}1, 16/4^2{=}1), sixteenfold_pin (\nu{=}16{\equiv}0\bmod 16, c_-{=}8), bundled as crossedproduct_arithmetic ([propext] only); #print axioms seamResidualClosed$'$ = exactly four; the original seamResidualClosed (AGT/AMT witness) is kept unchanged as the independent second route; lake build OK (3285 jobs).
• v470_alpha_inflow_level.py (ALPHA.QUILLEN.INFLOW.01). Both residuals left on ALPHA.QUILLEN.EXACT.01 after v433–v435 are upgraded. [E]target re-verified (\ainv{=}137.0359992168; Quillen split {<}10^{-35}). [C]the level is computed, not minimal: the a^3 coefficient k_0{=}1 equals the FHS bulk Chern invariant |C|{=}1 of the same p+ip collar that realises S3 (v367/v461) — “why exactly 1” is answered by computation plus the cited inflow identification (TKNN PRL 49 (1982) / Avron–Seiler–Simon PRL 51 (1983) quantisation; Callan–Harvey, Nucl. Phys. B250 (1985) inflow; APS 1975 / Alvarez-Gaumé–Della Pietra–Moore 1985 / Witten, Rev. Mod. Phys. 88 (2016) \eta{=}CS part of \delta\log\det; Quillen 1985 / Bismut–Freed 1986 determinant-line integrality), replacing v435's minimality assumption. [E]k_Y{=}\operatorname{tr}(Y^2)/\operatorname{tr}(T_3^2){=}(5/6)/(1/2){=}5/3 (Ginsparg, Phys. Lett. B197 (1987)): (3/5){\times}\tfrac{41}{6}{=}\tfrac{41}{10}{=}b_1 — the “GUT 3/5” is the inverse embedding index; \tfrac{41}{6}{=}\tfrac{20}{3}{+}\tfrac16 (carrier decomposition). [C]the seam F-normalisation (the one [C]of v434) is retyped: once the seam net is (E_8)_1 level 1, \langle JJ\rangle{=}k/(z{-}w)^2 is fixed by k_Y — level-1 current-algebra rigidity, zero independent content, a face of SEAM.EQUIV.01 (per the v382 typing). [E]structural unification: one invertible phase, two quantised responses — c_-{=}8 (gravitational, feeds SEAM.EQUIV.01/S3) and C{=}1 (U(1), feeds EM1) — so closing R1' feeds both named targets. [O]not closed: the bridge lemma “\delta\log\det_\zeta(\mathrm{seam}){=} the inflow response” stays the named cited step; ALPHA.QUILLEN.EXACT.01 stays [O]; \ainv stays [E].
• Integration. Both registered in run_all.py + script_registry.csv (cluster frontier); ledger rows SEAM.EQUIV.CROSSEDPRODUCT.01 + ALPHA.QUILLEN.INFLOW.01; FORM.SEAM.RESIDUAL.01 updated (the seamResidualClosed$'$ route); the exact joints Wolfram-mirrored (365\to368: the LR/glue locality integers, the KLM \mu-arithmetic, the sixteen-fold pin, the k_Y{=}5/3/b_1 identities); cited in tfpt_1 (\alpha fixed point + EM-Ward residual prose), tfpt_research_contracts (seam residual + Lean section), introduction (closure ledger), tfpt_5_redteam (Target A residual wording) and the README/website status surfaces; exploration provenance experiments/tfpt-discovery/closure_route_*.py (2026-07-02 note in experiments/next.txt). Suite all checks passed through v470. Curated version bumped to v5.4 (Zenodo deposit updated).

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• v467_thirdgen_mixing_pattern.py (FLAV.THIRDGEN.PATTERN.01). The suite's three {\sim}2\sigma mixing tensions (\sin^2\theta_{13} +2.0\sigma, \sin^2\theta_{23} +1.76\sigma, |V_{cb}| +1.79\sigma; v307) are exactly the three third-generation channels and share one relative deviation -5.36\%\pm1.67\% — non-zero at 3.2\sigma, -0.03\sigma from -\varphi_0. [E] vocabulary identities: \lambda_C^2{=}\varphi_0(1{-}\varphi_0) (the frozen Cabibbo); \sin^2\theta_{23}{=}(1{-}\varphi_0)/2\Leftrightarrow\cos2\theta_{23}{=}\varphi_0; the suppression size \varphi_0{=}5.3\% sits inside the seam-gapped band (2/3)^6{=}8.8\% (v393). [N] the ladder-base forms \lambda_C^2e^{-5/6}{=}0.021880 / (1{-}\varphi_0)/2{=}0.473414 / \lambda_C^2/(1{+}\lambda_C){=}0.041119 drop the joint four-observable \chi^2 from 10.4 to 0.11 with zero new parameters; |V_{ub}| (no bare \varphi_0) and the 1–2 channels stay untouched and correct (dressing \lambda_C would fail at -24\sigma — scope checked, not chosen); Daya Bay alone already prefers the pattern form (\Delta\chi^2{=}4.3). [C] honest: post-hoc (5/16 equally-simple dressings fix the two PMNS tensions; (1{-}\varphi_0)/(1{-}c_3)/resolvent degenerate {<}1.4\%). [O] no seam-transport derivation (the Bernoulli-variance reading \lambda_Y^2{=}\mathrm{Var}[\mathrm{Bernoulli}(\varphi_0)] is an exact identity but only an interpretation) — the frozen record (v84/REG.FREEZE.01) is unchanged. [X] pre-registered, symmetric: \theta_{13} stable at 0.0231 kills the pattern, at {\sim}0.0219 (sub-1%) kills the record's bare-\varphi_0 reading, exclusive |V_{cb}|{\sim}0.0395 kills both — JUNO-era reactors + Belle II decide. Python-only.
• v468_dm2_ratio_jarlskog.py (FLAV.DM2RATIO.01). The splitting ratio \Delta m^2_{21}/\Delta m^2_{31} was previously unpredicted; the frozen PMNS matrix (v9/v268/v270, \delta{=}4\pi/3) has one canonical derived CP invariant, and [N] |J_{\mathrm{PMNS}}|{=}0.029653 meets the NuFIT 6.0 measured ratio 0.029805\pm0.000792 at -0.19\sigma (equivalently m_2/m_3{=}\sqrt{|J|}{=}0.17220 vs 0.17264(229)) — zero dials. [N] the informal tfpt_2 table heuristic m_2/m_3{\sim}\pi\varphi_0{=}0.16704 (a “\sim” entry, never frozen) is now -2.44\sigma and is superseded as the comparator. [C] spectrum consistency: \Sigma m_\nu{=}m_3(1{+}\sqrt{|J|}){=}0.0588 eV reproduces the documented 0.0586 eV (v272); no absolute number is added. [O] no mechanism (the \mu\tau texture gives \theta_{13}{=}0 at leading order). [X] JUNO shrinks the window {\sim}4\times; adopting the v467 pattern would shift |J|\to0.028849 (-1.21\sigma today) — the two candidates cross-discriminate at JUNO precision. Python-only.
• Integration. Both registered in run_all.py and script_registry.csv (cluster neutrinos); ledger rows FLAV.THIRDGEN.PATTERN.01 and FLAV.DM2RATIO.01 (both [O]candidates); cited in tfpt_2 ( Neutrinos: pressure-point block + new candidate paragraphs, the m_2/m_3 table row retyped to the |J| comparator, the octant prose kept honest — record does not select, the candidate would), introduction (closure ledger), tfpt_4_frontier (live kill-test board) and tfpt_5_redteam (seed-hyperplane caption); v328's “single outlier” wording scoped to the seed observables; exploration provenance experiments/tfpt-discovery/pattern_hunt_pmns_dressing.py (2026-07-02 note in experiments/next.txt); Python-only (flagged in the Wolfram README).