Publication history: 2026-07-20

Details

• experiments/e8-ladder-bed/ executed (preregistered hypotheses/e8_ladder_bed_v1.yaml). The blind ladder detector (assignment DP + scale fit + 5000-ladder Monte-Carlo null; the same detector class TFPT uses on search surfaces, e.g. hfqpo-ladder) on the only public known-answer mass-ladder dataset: BaCo_2V_2O_8 (Zou+ PRL 127, 077201; INS at the 4.7 T 1D QCP, Fig. 3a extraction QA-validated, 17 peaks blind) recovers 8/8 rungs, \chi^2/\mathrm{dof}=0.35, MC p=0.0056 (singles-only run p=0.0004; \sigma-variant robust); CoNb_2O_6 (Amelin+ PRB 102, 104431; verbatim THz values) recovers 6/8 in-window rungs, \chi^2/\mathrm{dof}=0.52, p=0.0038 (m_7/m_8 lie outside the 0.6-THz low-pass window; the broad 0.43-THz (m_1{+}m_2)-continuum onset is correctly left unassigned). Cartan–PF self-test: the sorted PF eigenvector of 2I-A(E_8) equals the Zamolodchikov ladder to 1.5\times10^{-15} (m_2/m_1=\varphi to 2.2\times10^{-16}; lowest Cartan eigenvalue 2-2\cos(\pi/30) to 4.5\times10^{-14}).
• Control battery — every class rejected. Scramble 0.5\%/1.5\% false-positive rate (200 log-gap permutations, near-duplicate accounting); offset \pm\{0.3,0.5\}m_1: 0/8 detections; jitter dose-response \le5\% at the destructive 30\% level; wrong ladders on the real data (harmonic 1..8, A_3-PF, D_8-PF, Airy confined-spinon) all beaten by E8; the synthetic Airy bed (the true zero-field physics of these compounds) yields 0 valid rungs. The one disclosed v1.1 criteria amendment (jitter as dose-response, scramble near-duplicates, \chi^2-gated wrong-ladder comparator) is fully documented in the hypotheses YAML with all v1 numbers preserved; the recoveries themselves were never touched.
• Integration (firewall intact). Scorecard row “E8 mass-ladder blind recovery bed” moves parked \to consistent (stage not_applicable, tier analog_positive_control, leakage detector_control — the executed-analog basket of qc-recovery-kernel and qgeo-eit-soff); counters 120 rows: 49 consistent / 3 parked; experiments/README.md catalog row + stats (generator); website predictions.ts EXPERIMENTS_AUDIT counters; experiments/next.txt. This validates the ladder-detector pipeline — it confirms Zamolodchikov E8, not the TFPT axioms: no [E], no \veri, no ledger row.

Details

• v493_celestial_wp2_clock_deformation.py (CELEST.WP2.01). WP2 of the celestial contract, sympy exact (47 checks), promoted from the experiments/tfpt-discovery/ probe celestial_seam_wp2_clock_deformation_probe.py. Geometry: P(iZ){=}P(Z) forces a_3{=}a_2{=}a_1{=}0 sharply and two-sided (\prod_k(Z-i^kw)=Z^4-w^4); XY{=}Z^4{+}a_0 is smooth iff a_0{\neq}0 (\operatorname{disc}=256\,a_0^3); the branch points Z^4{=}{-}a_0 are one free \mu_4 orbit in every fibre with cross-ratio 2; the binary-quartic invariants of w^2{=}Z^4{+}a_0 are I{=}12a_0, J{=}0 identically, so j{=}1728 and the \tau{=}i pillowcase shape (v168/v214) is frozen for all a_0 — a_0 is a pure scale, no shape modulus survives clock-invariance. Periods/monodromy: \Pi=t(i{-}1)(1,i,i^2), all three vanishing spheres carry the same volume \sqrt2\,t (lockstep); the clock acts on H_2 as a Coxeter element of W(A_3) (char x^3{+}x^2{+}x{+}1, eigenvalues \{i,-1,-i\} = the A_3 exponents, h(A_3){=}4{=}|\mu_4|{=}\Nfam{+}1), fixes no cycle (\det(A{-}1){=}{-}4), and is the Picard–Lefschetz monodromy of the family (a_0\to e^{2\pi i}a_0 gives the 4-cycle); the surviving direction is the weight-1 \chi_1-Fourier diagonal (1,i,i^2), not the naive invariant diagonal; the versal weights (a_3,a_2,a_1,a_0)=(1,2,3,0) are the regular \mu_4 representation. Algebra (BHS \Z_2\to\Z_4, arXiv:2305.09451): mode dictionary \{w[m,n]:m{\equiv}n\bmod4\}; the fibre bracket -4\,\mathrm{Nambu}(XY{-}Z^4{-}a_0) anchored at the a_0{=}0 orbifold (\{X,Y\}{=}16Z^3, Jacobi + Casimir exact, uniform clock-degree -1); S-algebra corrections exactly linear in a_0 at the \Z_4 wrap, conserving the \mu_4 grade — no sector leak, the v492 equivariant sector deforms consistently; a_0\leftrightarrow BHS's weight-0 c^2 slot; matrix factorisations deform along all orbit splittings, the clock fixing exactly the antipodal 2{+}2 sector (= the EH/\Z_2 middle node, 4{=}2{\times}2). Negative controls: a_1Z\Rightarrow j{=}0 (hexagonal); pure a_2Z^2 stays singular (A_1); a_2{\neq}0\Rightarrow j{=}1556068/81{\neq}1728; explicit grading leak — doubly sharp. Verdict B via three named [C]identifications (-4Nambu = the k{=}4 CCA bracket; period = root difference; seam-scale reading via clock^2{=}deck); the v216 residual is typed, not moved (given the order-4 clock the square is automatic — a relocation of the same input, no new derivation).
• Contract updated to WP2 done. tfpt_research_contracts CELEST.SEAM.01 section: WP2 bullet “finite, next” \to done (verdict B) with the two sharpenings (clock = Coxeter/Picard–Lefschetz monodromy; surviving direction = \chi_1-diagonal, a_0 pure scale); kill-test paragraph K1 “survived by WP1 and WP2”; status line CELEST.WP2.01 [E]/[C]executed, WP3–WP5 stay [O]. Ledger rows CELEST.WP2.01 (new) + CELEST.SEAM.01 (WP2 done) + GATE.WOLFRAM.02 (four exact v493 mirrors added to tfpt_readouts_extension.wl, counted with the next verified engine run — engine unactivated, same convention as v491); registry + run_all (487 modules, suite green); website mirrors (papers.ts contract section, generated script index). SEAM.EQUIV.01 stays [O]; no marker moves anywhere. Exact (sympy).

Details

• H3 stage 2 executed (experiments/hfqpo-ladder/results/archival/). The preregistered archival scan (hypotheses/hfqpo_v1.yaml, archival_design) ran end-to-end on public HEASARC data: 77 ObsIDs / 4.42 GB across all four 3{:}2-pair sources (GRO J1655-40, XTE J1550-564, GRS 1915+105, H1743-322). Sanity gate PASS (11/12 published pair lines reproduced, e.g. 450.3 Hz at 5.37\% rms 4.4\sigma, 280.1 Hz at 3.71\% 9.9\sigma); injection calibration PASS in all four sources (90\%-recovery sensitivities 5.11/2.68/0.89/1.65\% rms at the tooth frequencies).
• Blind-scan verdict: NULL with limits. Neither the geometric tooth \nu_3=1.5\,\nu_u (661.5/414/252/363 Hz) nor the integer control line 4\nu_0 (588/368/224/322.7 Hz) is detected in any source (\sim\!0\sigma single-trial; trials correction N{=}8 as preregistered). 3\sigma rms upper limits (tooth, primary bands): 3.06/1.61/0.53/1.26\% — in every source at or below the strength of the detected upper pair line. The ladder reading gains no support but is not killed (the harmonic_hit branch did not fire either; the anti-kernel record 92{=}184/2, 34/68 stands); GR parametric resonance stays the favorite. Caveats: GRS 1915+105 scanned in a proxy state (the 113/168 Hz epochs were never published at ObsID level); H1743's program is 80146 (YAML said 80138); GRO hard-band sensitivity 5.1\%.
• Integration. Scorecard row S1.e (hfqpo-ladder) data_limited\tonull (120 rows: 26 null / 33 data_limited), next decider eXTP-class sensitivity below the 0.5–3.1\% rms limits; HFQPO search-target paragraph updated in tfpt_horizon_readouts (+ the papers.ts mirror); website predictions.ts (hfqpo-tooth entry + EXPERIMENTS_AUDIT counters); predictions.txt; experiments/README.md; experiments/next.txt. No verification/ module, no ledger row, no marker move (the search target stays [O]).

Details

• v492_celestial_z4_orbifold.py (CELEST.WP1.01). WP1 of the new contract, sympy exact (36 checks): the v128 \mu_4-glue grading of E_8 (240=52{+}64{+}60{+}64, additive on all 6720 root pairs) is inner — h=(2,2,2,2,2;0^4) reads the glue class mod 4 on all 240 roots, so the glue is \operatorname{Ad}(\exp(2\pi ih/4)), an order-4 inner torus automorphism = a flat \Z_4 monodromy in the Kronheimer–Nakajima sense; the A_3-side detector h'=(0^5;1,1,1,-3) reads the same class = the diagonal (1,1) of the discriminant group \Z_4{\times}\Z_4 (the v92/v125 Lagrangian glue). \mathbb C^2/\Z_4 is verified as the A_3 singularity XY{=}Z^4 (Hilbert series (1{+}t^4)/((1{-}t^2)(1{-}t^4)), Molien exact); the glue-equivariant SDYM(E_8) sector closes with graded dimensions 60(d{+}1)/64(d{+}1) — possible only because \dim\mathfrak g_j=(60,64,60,64) — with zero modes = the carrier D_5{\oplus}A_3{+}Cartan =60 and density 1/4=1/|\Z_4|; the four glue-sector characters sum exactly to \chi_{(E_8)_1}=1{+}248q{+}4124q^2{+}34752q^3 (v377), with sector weights = the discriminant form (5x^2{+}3y^2)/8 and integer glue-diagonal h=(0,1,1,1) (= locality of the (E_8)_1 extension). Critical correction (verdict B): the A_3 deck acts on the celestial sphere as z\mapsto-z (order 2), not as the order-4 clock; the clock is the U(2) phase \operatorname{diag}(i,1) (normalising the deck, \det=i rotating the holomorphic symplectic form by the \mu_4 generator), with the exact spin bridge (\text{spin clock})^2= deck (\Z_8, 8=2|\mu_4|, the \cthree=1/(8\pi) winding integer). Clock-invariance selects the 1-parameter A_3 deformation XY{=}Z^4{+}a_0 whose four branch points are one \mu_4 orbit with cross-ratio 2 (v168/v214 pillowcase). Negative controls: the false action \operatorname{diag}(i,i) killed three ways, the false glue breaks additivity on 3112/6720 pairs, rigidity =\Aut(\Z_4).
• New research contract CELEST.SEAM.01 in tfpt_research_contracts (own section, the fourth contract alongside U_{\mathrm{wall}}/G_{\mathrm{metric}}/CONTRACT.F.01): hypothesis (seam = glue-equivariant \Z_4-orbifold sector of the CCA on the A_3 ALE; twistorial bulk = the self-dual sector only), typing/non-circularity (the continuum (E_8)_1 existence — the SEAM.EQUIV.01 target — is not an admissible input), work packages WP1 (done, verdict B) through WP5 (second continuum route, Costello–Li grade), pre-registered kill tests K1–K4 (K1 survived by WP1), and an honest success estimate (full success low, partial findings high). Ledger rows CELEST.WP1.01 + CELEST.SEAM.01; website mirror (papers.ts section, script index). SEAM.EQUIV.01 stays [O]; no marker moves. Exact (sympy).

Details

• \alpha_s running (prediction of record, consistent). The Starobinsky branch fixes the running of the spectral index: \alpha_s=-2/N_\star^2=-7.6\times10^{-4} at N_\star{=}51.4 (exact slow roll -7.09\times10^{-4}; band N_\star\in[50,60]: [-8.0,-5.6]\times10^{-4}) and \beta_s=-4/N_\star^3 (leading order; NOT -8/N^3) — the identity \alpha_s=-r/6 holds only at leading order (\sim7% off exact). Data: Planck 2018 -0.0045\pm0.0067 (+0.57\sigma), P-ACT +0.0060\pm0.0055 (-1.22\sigma), record leg P-ACT-LB +0.0062\pm0.0052 (-1.33\sigma, Calabrese et al. 2025 JCAP); \beta_s (Planck run+runrun) 0.010\pm0.013 (-0.77\sigma). Forecast: LiteBIRD+CMB-S4 \sigma(\alpha_s)\approx4.9\times10^{-3} (0.14\sigma); CMB-S4+DESI+Euclid statistical \sim3.3\times10^{-4} (2.2\sigma, systematics-limited). Same N_star_reheating independence group as the n_s/r/A_s rows (anti double-counting: never an independent hit); kill: robust \alpha_s<-5\times10^{-3} or >+3\times10^{-3} at \ge5\sigma; any robust POSITIVE running kills the plateau branch. Probe: experiments/tfpt-discovery/alpha_s_running_probe.py.
• \mu-distortion (prediction of record, data-limited). Chluba window integral (calibrated +20\% to the full computation): sharp branch N_\star{=}51.4 (A_s{=}1.76\times 10^{-9}) \mu\approx1.6\times10^{-8}, profiled record N_\star{=}56.1 (A_s{=}2.10\times10^{-9}) \mu\approx2.0\times10^{-8}, band 1.5–2.3\times10^{-8}; the 23\% branch split (\Delta\mu=3.0\times10^{-9}) gives a 3\sigma A_s/N_\star branch decision at \sigma(\mu)=10^{-9} (Voyage-2050 class; the PIXIE baseline |\mu|<9\times10^{-8} does NOT reach — factor 4–7 above the band; FIRAS |\mu|<9\times10^{-5}). Honest S15 typing: the frozen log-comb (\omega=2.5827, \varepsilon=0.0173) is STRUCTURALLY BLIND in the \mu window — window attenuation |F(\omega)|=0.033, \delta\mu=7.4\times10^{-12}=0.007\sigma even at Voyage 2050 — the theory itself predicts where it is invisible, so NO separate comb-search row is opened. Shares the Nstar_branch alternative group with the two A_s rows (one branch question, several readings). Kill: robust \mu<0.9\times10^{-8} or >4\times10^{-8}. Probe: experiments/tfpt-discovery/mu_distortion_probe.py.
• Three parked analog beds (parked_analog; honest typing: they validate E8 edge/spectrum physics or the comb DETECTOR, never the TFPT axioms). (i) Bosonic E8 phase / thermal Hall: \kappa_{xy}/T=8\times(\pi^2k_B^2/3h) with no charge Hall (seam edge c_-{=}8, v450/v451/v489); no engineered material yet (\alpha-RuCl_3 c_-{=}1/2 contested: ultraclean half-quantized plateau, npj QM 2025, vs phonon-dominated \kappa_{xy}, PRX 12, 021025). (ii) E8 mass-ladder validation bed (CoNb_2O_6/BaCo_2V_2O_8): all 8 one-particle masses published (Zou et al. 2021 PRL 127, 077201, NMR+INS; Amelin et al. 2020 PRB 102, 104431, THz m_1–m_6; Coldea et al. 2010 Science m_2/m_1{=}\varphi) — blind Cartan-PF ladder recovery on the published spectra (8/8 masses + rejection of scrambled controls) as detector validation; confirms Zamolodchikov E8, not TFPT. (iii) Efimov DSI tuning: s_0=\pi/(6\ln(3/2))=1.2914\Leftrightarrow\lambda=(3/2)^6=11.391 at M/m=8.67 (2 resonant pairs); best candidate ^{52}Cr_2–^{6}Li (M/m{=}8.635, s_0{=}1.2890, \lambda{=}11.44, +0.44\% vs (3/2)^6, gap deviation +0.18\%); alternatives ^{39}K_2/^{41}K_2–^{6}Li (\lambda=11.59/11.20, needs double Feshbach control), ^{176}Yb_2–^{23}Na (+5.9\%); solver validated on the Naidon–Endo anchors (homonuclear 22.69, Cs_2Li 4.877); first end-to-end HARDWARE injection of the comb detector at tunable \lambda\approx11.39; kill condition honestly “none on TFPT axioms — detector validation only”. Probe: experiments/tfpt-discovery/efimov_s0_massratio_probe.py.
• Scorecard regenerated (experiments/build_evidence_scorecard.py): 120 rows — 48 consistent, 9 tension, 25 null, 34 data-limited, 4 parked; website mirror (EXPERIMENTS_AUDIT in predictions.ts) synchronised. Experiments level only; the verification suite, ledger and papers are untouched.

Details

• v491_p2_partition_corollary.py (P2.PARTITION.01). Sympy-exact: a multiset of exactly 3 POSITIVE INTEGERS summing to 4 is UNIQUE — \{1,1,2\} — so e=(e_1,e_2,e_3)=(4,5,2) and hence \gcar=e_2=5, |\Z_2|=e_3=2, \Nfam=e_2{-}e_3=3 are corollaries, not inputs (consistency fixed point (2^4{-}1)/5=3=\operatorname{rank}H^1). [E]negative controls, each assumption load-bearing: drop positivity \to 4 solutions, e_2 ambiguous \{0,3,4,5\}; sum 3\to e_2{=}3; sum 5\to not unique; 2/4 parts \to e_2\in\{3,4\}/\{6\}; Mehta–Seshadri RATIONAL weights \to e_2=\tfrac{16}3 resp. \tfrac{44}9\neq5 (integrality = the Birkhoff–Grothendieck splitting-type typing, not MS weights). [E]the v53 sharpening: v53 pins (1,1,2) with ALL THREE targets (4,5,2); the partition needs only e_1{=}4. [E]sum rule: 4\times\tfrac{N-1}2=4 iff N{=}3; the v115 route |a|_1=|\mu_4|\operatorname{tr}(A_0)=4 agrees. Independence chain: \#marks =4 from v216 (P1-side, no \gcar input); \operatorname{rank}H^1=3 pure topology (v137/v228); |a|_1=4 \gcar-free (v115). [C]honest residual: P2 is NOT made axiom-free — the weight-TYPING postulate remains (integrality/positivity h^0{=}0/sum “given (U)”); AX.P2.01 stays a declared axiom, and the \Nfam direction reversal vs tfpt_constants is typed as an over-determination check (never double-counted). Integrated in introduction (anchor half-forced paragraph), tfpt_1 ((5,3) keybox), tfpt_2 (H2 winbox) and origin_theory ((5,3) keybox); ledger row P2.PARTITION.01; three exact Wolfram mirrors added to tfpt_readouts_extension.wl (counted with the next verified engine run, engine currently unactivated); website mirror (DAG node P2). Exact (sympy).

Details

• v490_seam_parity_census.py (SEAM.MU.01). The T^2 ground-state fermion parity of the v367 p{+}ip collar, resolved per spin structure (AA,AP,PA,PP) and determined TWICE — Read–Green TRIM product AND real-space Majorana Pfaffian (Schur), relative to the trivial M{=}3 phase, with the twisted real-space spectra matching the Bloch bands to 9\times10^{-15}. [E] per layer (+,+,+,-) (the \nu{=}1 Ising signature, TRIM \equiv Pfaffian in every sector); [E]the 16-layer carrier has \mathrm{parity}^{16}={+} in ALL FOUR sectors \Rightarrow gauged torus \mathrm{GSD}=4=\mu(SO(16)_1)=|\det\mathrm{Cartan}(D_8)| — the lattice ground-state witness of “\mu_{\mathrm{pre}}{=}4 before condensation” (step 1 of the v378 KLM chain); [E]the 16-fold-way bridge on MEASURED numbers: \theta_v=e^{2\pi i\nu/16}=1 exactly at \nu=2c_-=16 (v489), rivals \nu=1,2,8 not holomorphically condensable; [E]honest fence: the fermionic Kitaev–Preskill TEE is identically zero for BOTH M{=}1 and M{=}3 (\gamma_f{=}0.000001/0.000000) — it does NOT discriminate (E_8)_1 vs SO(16)_1. [C]the KLM step \mu:4\to4/2^2=1 stays the cited theorem (the condensed model is interacting); the numerics pin only the premise package \{c_-{=}8,\ \mu_{\mathrm{pre}}{=}4,\ \theta_v{=}1\}. [O]SEAM.EQUIV.01 stays [O](continuum existence, MMST v336). Integrated in tfpt_research_contracts (new S3-stack paragraph); ledger row SEAM.MU.01; website mirror (DAG node qft). Python (numpy + scipy Schur + sympy exact \theta_v).

Details

• v489_seam_modular_commutator.py (SEAM.CCC.01). The Kim–Shehab–Kim modular commutator J(A,B,C)=i\operatorname{Tr}(\rho_{ABC}[K_{AB},K_{BC}])=(\pi/3)\,c_- (PRL 128 (2022); arXiv:2110.06932/2110.10400) is evaluated on the EXACT BdG ground state of the v367 p{+}ip seam collar model, entirely from the Peschel Majorana covariance (W_X=-2\operatorname{artanh}\Gamma_X, J=\tfrac14\operatorname{Tr}([W_{AB},W_{BC}]\Gamma_{ABC})), on a disk about the torus centre cut into three 120^\circ wedges. [E]ground-state purity \operatorname{eig}(i\Gamma)=\pm1 to 6\times10^{-15}; [E]per-layer c_-=0.499998 at L{=}32 (convergence 0.499793 at L{=}16\to0.500000 at L{=}48, deviation -1.8\times10^{-7}); [E]controls: trivial M{=}3\to0.000000, orientation flip M{=}{-}1\to-0.499986; [E]layer additivity exact (1.4\times10^{-14}); [E]the 16-layer carrier lands on c_-{=}8{=}\gcar{+}\Nfam (direct 7.9967 at L{=}16, additivity route 8.0000); [E]clip invariance 5\times10^{-8}. The FIRST ground-state witness for premise (i) of SEAM.EQUIV.01 (c_-{=}8) that is INDEPENDENT of both the Chern-number route (v367) and the counting route (v378) — read from entanglement data alone. [O]honest fence: does NOT close SEAM.EQUIV.01; the continuum scaling limit (MMST, v336) and the cited KLM condensation step are untouched. Integrated in tfpt_research_contracts (new S3-stack paragraph) and tfpt_1 (the SEAM.EQUIV.01 package paragraph); ledger row SEAM.CCC.01; website mirrors (DAG node qft, papers/glossary/FAQ inventories). Numerical (numpy), Python-only by nature.