Publication history: 2026-07-03

Details

• Uniqueness scan follow-up (no new results — presentation only). A structure scan for “what does TFPT predict that nobody else pins?” found three concrete, falsifiable readouts that were fully computed and ledgered but missing from the public prediction surfaces; they are now surfaced, with their existing typing unchanged. (i) Axion–photon coefficient: the determinant-line anomaly coefficient g_{a\gamma\gamma}=-4\cthree=-1/(2\pi), y^2=16\cthree^2=1/(4\pi^2)\approx0.0253 (v207, the [E]leg of GRAV.ASYMP.01; the [C]caveat — coefficient, not a parameter-free g_{a\gamma\gamma} in \mathrm{GeV}^{-1} — stated verbatim) joins the axion card in website/lib/predictions.ts and the frontier dark-matter mirror in papers.ts; the TeX source (tfpt_4_frontier) already carried it. (ii) Higgs free-seam band: the double-criticality prediction \lambda(\Mbar)=\beta_\lambda(\Mbar)=0\Rightarrow m_H=133.5 GeV (band 129–134, m_t/\alpha_s-sensitive; measured 125.25 sits a few GeV below — the known slight metastability, Buttazzo NNLO \lambda(M_{\mathrm{Pl}})=-0.0143\pm0.0057, 2.5\sigma) becomes a prediction card ([C]; v166, HIGGS.FREESEAM.01, kill: settled-(m_t,\alpha_s) RGE pull off the surface at >5\sigma). (iii) BH HFQPO ladder tooth: the one discriminating HFQPO test — a third tooth at \nu_3=(3/2)\nu_u (661.5/414/252/363 Hz), integer harmonics forbidden — that no published search ever targeted although the teeth lie in the searched RXTE band (experiments/hfqpo-ladder, preregistered): added as an [O]search-target bullet to the tfpt_horizon_readouts “Search targets (not claims)” gapbox (firewall language verbatim: non-canonical mapping, selection null 18.5\%, J1859+226 +9.2\sigma, GR resonance favored; even a tooth hit would be [C]) and as an [O]prediction card. Website mirrors updated in the same change (predictions.ts 23\to25 cards, papers.ts frontier + horizon sections incl. the new search-targets mirror section); scorecard, ledger and all markers untouched.

Details

• v472_quillen_detline_moduli.py (ALPHA.QUILLEN.DETLINE.01). ALPHA.QUILLEN.EXACT.01 names the \alpha^3 level as the curvature of the determinant line over the U(1) seam moduli (Quillen 1985 / Bismut–Freed CMP 106 (1986) curvature; Dai–Freed JMP 35 (1994) section); v470 computed the bulk Chern invariant only over the Bloch Brillouin zone (the translation-invariant shortcut). v472 computes the Quillen-shaped object itself: the same collar Hamiltonian (h(k)=\sin k_x\,\sigma_x+\sin k_y\,\sigma_y+(M-\cos k_x-\cos k_y)\,\sigma_z, v367/v470) in real space on an L\times L torus with twisted boundary conditions — the twist torus (\theta_x,\theta_y) is the moduli space of flat U(1) connections — and the Fukui–Hatsugai–Suzuki curvature of the determinant line of the occupied frame over that torus: \oint = 2\pi\cdot 1 exactly (integer to 10^{-9}) at M{=}1 for L{=}4 AND L{=}6 (size-independent); controls: trivial collar M{=}3\to 0, orientation flip M{=}{-}1\to-1; the twist-moduli integer equals the Bloch-BZ integer for all three M (Niu–Thouless–Wu PRB 31 (1985), exhibited on the S3 collar model); the Fermi gap (=2.0) stays open over the whole twist torus, so the Dai–Freed section has no zero. Reading [C]: det-line holonomy over the U(1) moduli = inflow level k_0=|C|=1 — the v470 bridge lemma “\delta\log\det_\zeta(\mathrm{seam})= the inflow response” holds verbatim at the finite/model level, where \log\det of the occupied frame replaces \log\det_\zeta. Not closed [O]: the continuum \zeta-determinant identification on the abstract seam (= the SEAM.EQUIV.01 face); ALPHA.QUILLEN.EXACT.01 stays [O]; \ainv stays [E]. Structurally the same manoeuvre as v471 for SEAM.THEOREM.01's replica side. 7/7 checks; suite green through v472 (466 modules); numerical (dense eigh + FHS twist grid), Python-only by nature. Papers updated: tfpt_1 (sixth honest step in the EM closure), tfpt_research_contracts (residual certification), tfpt_safeguards (\alpha-form lever), root README, zenodo_description.html. Exploration original: experiments/tfpt-discovery/quillen_detline_twist_moduli.py (same day).
• Bird's-eye whitespot rounds (sandbox, experiments/tfpt-discovery/, nothing else promoted). (i) electron_sector_cabibbo_probe.py: the \alpha metrology triangle (TFPT \ainv=137.0359992168 vs Rb-2020 +0.99\sigma / CODATA22 +1.90\sigma / a_e-route +3.39\sigma / Cs-2018 +6.33\sigma — TFPT takes the Rb side of the 5.5\sigma metrology split; new honest pressure point recorded); the v204 seam-vertex universality catch (a flavor-universal reading of a_\mu^{\mathrm{seam}}=2.879\times10^{-9} is excluded by the electron at {\sim}2\times10^4\sigma; linear scaling at {\sim}10^2\sigma; quadratic survives — the [C]bridge must scale at least quadratically in m_\ell); the Cabibbo-angle anomaly as a third dissolution watchdog (\lambda_C=0.2243762 exact sits +0.08\sigma on the PDG-2026 rescaled kaon average, between K_{\ell3} and K_{\mu2}; exact unitarity puts V_{ud}=0.97450 — superallowed is the outlier at +2.6\sigma, all neutron/pion routes agree). (ii) kernel_calderon_uv_universality.py: the raw-collar Calderón/DtN datum is UV-universal (mode-by-mode first-order convergence to the exact Bessel symbol m I_\nu'(mR)/I_\nu(mR), Richardson residual 3\times10^{-4}; N_\theta-independent; |k| principal symbol; \mu_4 block structure at machine precision; both spec-T masses; 3-fold mesh-defect negative control) — the operator equality demanded by QGEO.KERNEL.01 has a well-defined discretization-independent left-hand side (gate stays [O]). (iii) flat_budget_closure.py + scorecard row: see next bullet.
• Flat-budget closure enters the evidence scorecard (experiments-only, pattern candidate). The zero-dial closure \{\Omega_b=\phiz(1-\tfrac{1}{4\pi}) [frozen], \Omega_c=\tfrac27(1-\tfrac{1}{4\pi}) [the 2026-07-02 numerology-flagged Nebenbefund], \rho_\Lambda/\Mbar^4=(3/4\pi^2)e^{-2\ainv} [frozen], \Sigma m_\nu=0.0588 eV [v468 route]\} + spatial flatness determines the whole flat \LambdaCDM budget: H_0=67.15 km/s/Mpc (-0.39\sigma Planck18, -5.67\sigma SH0ES22 — the parameter-free Planck side of the Hubble tension), \Omega_m=0.3133 (-0.27\sigma), t_0=13.86 Gyr; honest stresses recorded: \omega_b -2.02\sigma (BBN-only -0.73\sigma), \omega_c -1.19\sigma, DESI-DR2 H_0 -2.16\sigma (one correlated low-h direction). Scorecard row cosmo / flat budget closure (consistent, composite: shares the phi0_seed group (and the \rho_\Lambda leg the \alpha engine), \Omega_c leg in alternative_group=axion_branch vs the axion-spine DM reading — never double-counted); nothing promoted to verification/.