TFPT — Topological Fixed-Point Theory: Two Axioms, One Compiler, the Standard-Model Skeleton Derived

Hamann, Stefan; Rizzo, Alessandro

2026-06-17

Infrastructure: the changelog is now a public website page, generated from `changelog.tex` and audit-gated

The canonical changelog now also drives a public /changelog website page. A new generator verification/make_changelog_web.py parses this file (dated \subsection* entries, itemize items, and the inline markup \textbf/\emph/\texttt/\vref, the status markers [E]/[C]/[O]/[X], inline math and accents) into the typed data file website/ lib/ changelog.ts, rendered server-side (math via KaTeX) by website/ app/ changelog/ page.tsx $+$ website/ components/ Changelog.tsx. The generator is wired into bash build.sh gen; its freshness is enforced by audit_sync.py (section A.generated), so the page can never drift from this file – editing the changelog and re-running gen is the only supported path (the .ts mirror is never hand-edited). /changelog is linked from the navbar, footer and sitemap. The tfpt-workflow, website-sync and sync-maps cursor rules were updated to record the new single-source generation step. [E]build (npm run build green, /changelog prerendered static) and bash build.sh audit (AUDIT OK).

2026-06-17

Orientability + Poincaré duality: the honest, literature-confirmed status — strict fail, weakened hold, `v257`

v257_quasiorient_modpd.py (PS.NCG.ORIENT.02) corrects the slightly too-generous v256 typing. The published result (Cacic–Stephan arXiv:0902.2068; CCM07; SM-vacuum hep-th/0601192) is that the Chamseddine–Connes–Marcolli Standard-Model finite triple (KO-dimension $6$ , with three right-handed neutrinos — exactly the TFPT seesaw case) genuinely fails strict orientability and strict Poincaré duality, and instead satisfies the physically correct weakened versions. Verified on the explicit v252 triple: [E]strict orientability fails ( $\gamma\notin\mathrm{span}\{\lambda(a)\rho(b)\}$ ); [E]quasi-orientability holds (the left/right $A$ -irrep boxes are disjoint by chirality: $L=H$ weak-doublet, $R=\mathbb C$ singlet, so $L^{\mathrm{LR}}(\mathcal H^{\mathrm{even}},\mathcal H^{\mathrm{odd}})=\{0\}$ ); [E]strict Poincaré duality fails (KO- $6$ skew intersection form, corank $1$ , the equal- $L/R$ -neutrino case); [C]modified Poincaré duality holds (CCM), Stephan's alternative triple (St06) restoring strict PD with identical physics. A known property of the NCG-SM model class, not a TFPT defect — no faked closure.

2026-06-17

Remaining NCG obligations discharged or honestly typed: inner fluctuations, spectral action, orientability/Poincaré, `v254`–`v256`

v254_inner_fluctuations.py (PS.NCG.FLUCT.01) closes v250 #5 + the no-junk obligation. The inner fluctuations $\Omega^1_D(A_F)$ of the finite Dirac operator are computed explicitly: [E]they are purely chirality-odd (scalars), and for the SM algebra sit exactly in the one Higgs doublet $(1,2)_{1/2}$ — no junk, no triplet, no $(10,1,3)/\mathbf{126}$ . [E]the $\sigma$ ( $\nu_R$ Majorana) direction is absent for the SM algebra but present for Pati–Salam (the CCvS beyond-first-order scalar), and [E] $\sigma$ is an SM singlet $(1,1,0)$ with $B{-}L=2$ . [C] $\sigma={}$ scalaron.
v255_spectral_action_expansion.py (PS.SPECACT.01) closes the spectral-action expansion (v252 #11). The Seeley–DeWitt expansion $S=2f_4\Lambda^4 a_0+2f_2\Lambda^2 a_2+f_0 a_4$ : [E]structure ( $a_0$ cosmological, $a_2$ Einstein–Hilbert $+$ Higgs-mass, $a_4$ Yang–Mills $+$ Weyl $^2+R^2+$ Higgs-quartic, $N=96$ ); [E] $b/a^2=1/3$ (top-dominated); [E] $\sin^2\theta_W=3/8$ ; [E]the $R^2$ spin- $0$ mode $=$ the Starobinsky scalaron; [C] Higgs quartic $\to{\sim}125$  GeV with $\sigma$ ; [C] $\kappa=\sqrt{(f_2/f_0)c_{PS}/c_{\rm grav}}$ explicit; [O]exact decimal needs the cutoff moments.
v256_orientability_poincare.py (PS.NCG.ORIENT.01) — honest status, no faked proof. KO-dimension $6$ forces the intersection form $\mathrm{Tr}(\gamma\,\pi(p)J\pi(q)J^{-1})$ to be antisymmetric: [E]skew form (verified), [E]rank $2$ , corank $1$ , null $\sim(1,1,-1)$ on the SM K-theory $\mathbb Z^3$ ; [E]the orientability local condition $[\gamma_F,\pi(a)]=0$ . [C]the canonical hypercharge-faithful SM/PS triple satisfies orientability and Poincaré duality (van Suijlekom; CCM); [O] a self-contained machine proof needs the complete canonical bimodule.

2026-06-17

Full $96$ -dim finite spectral triple built + NCG axioms verified, and $\kappa$ pinned to $O(1)$ , `v252`–`v253`

v252_full_finite_triple.py (PS.DIRAC.02) advances the Dirac contract v250 from a $7$ -obligation contract to a concrete object discharging $5$ to [E]. The full $96$ -dim finite spectral triple $(A_F,H_F,D_F,J,\gamma)$ — $H_F$ the particle $\oplus$ antiparticle doubling of three $SO(10)$ $\mathbf{16}$ -plets — is built explicitly and the NCG axioms are checked by direct computation: [E]reality ( $J^2{=}{+}1$ , $JD{=}DJ$ ), grading ( $\gamma^2{=}1$ , $[\gamma,a]{=}0$ , $J\gamma{=}{-}\gamma J$ ), KO-dimension $6$ , order-zero, the first-order condition (HOLDS for the SM algebra including the Majorana; VIOLATED for the Pati–Salam algebra exactly by the Majorana, localized to $\{\nu_R,e_R\}$ — the CCvS beyond-first-order mechanism on the full triple), and the spectrum of $D_F$ reproducing the fermion masses and the type-I seesaw $m_{\rm light}{=}m_D^2/M_R$ . [C]Poincaré duality; [O]orientability, no-junk, spectral-action expansion.
v253_kappa_scalaron_ps.py (PS.KAPPA.01) discharges residual 6(b) of v249. $\kappa$ in $M_{PS}=\kappa\,M_s$ ( $M_s=c_3^{7/2}\bar M\approx3.06{\times}10^{13}$  GeV, exact) is pinned by an RG scan (PDG errors $\times$ the two $E_8$ -allowed contents) to a tight $O(1)$ interval ( $\approx1.3$ ). [C]heat-kernel origin: $\kappa=\sqrt{(f_2/f_0)\,c_{PS}/c_{\rm grav}}$ is a scale-free ratio of heat-kernel traces over the $96$ -dim $H_F$ ( $\Lambda$ cancels). [X]the $\mathbf{126}$ -content drives $\kappa$ out of the $O(1)$ window (content-selective). [O]the exact decimal needs $f_2/f_0$ fixed.

2026-06-17

Spectral triple, first step: the first-order condition is violated exactly by the Majorana/ $\sigma$ — the CCvS Pati–Salam mechanism, `v251`

v251_first_order_sigma.py (PS.DIRAC.01) advances the Dirac contract v250 from a contract to an exhibited mechanism. On a faithful lepton-block model ( $H=H_F\oplus H_F^c$ , $H_F=\mathbb C^3$ ), the real even structure is checked ( $J^2{=}{+}1$ , $\gamma^2{=}1$ , $D\gamma{=}{-}\gamma D$ , KO-dim-6 signs), order-zero holds, the first-order condition HOLDS for the Yukawa block, and is VIOLATED exactly by the Majorana ( $\nu_R\nu_R^c=\sigma$ ) block — the Chamseddine–Connes–van Suijlekom “beyond first order” mechanism by which the inner fluctuations promote the SM to Pati–Salam and generate $\sigma$ . Honest correction to the review: $\sigma$ does not rescue the first-order condition; its controlled violation is the mechanism. [C] $\sigma={}$ scalaron (v249); [O]the full $96$ -dim triple $+$ spectral action.

2026-06-17

Carrier-native Pati–Salam program: $E_8$ forbids the 126, PS algebra, unification kill-test, Dirac contract, `v247`–`v250`

Four scripts turning the gauge-unification finding into typed claims with negative controls. v247_e8_branching_no126.py (PS.E8BRANCH.01): the $E_8$ hull branches under $SO(10){\times}SU(4)$ as $(45,1){+}(1,15){+}(10,6){+}(16,4){+}(\overline{16},\bar4)$ , so the $SO(10)$ content is exactly $\{1,10,16,45\}$ and the $\mathbf{126}$ is absent — the renormalisable $126_H$ is algebraically forbidden and $10{+}16{+}45$ is $E_8$ -supplied (only one $45\Rightarrow$ proton-marginal). v248_ps_algebra.py (PS.ALGEBRA.01): $A_F=\mathbb H_L\oplus\mathbb H_R\oplus M_4(\mathbb C)\to SU(2)_L{\times}SU(2)_R{\times}SU(4)_c$ , exact hypercharges $Y=T_{3R}+(B{-}L)/2$ , matching $\alpha_1^{-1}=\tfrac35\alpha_{2R}^{-1}+\tfrac25\alpha_4^{-1}$ , $\sin^2\theta_W=3/8$ (colour $SU(4)_c\subset D_5$ , distinct from the family $A_3$ ). v249_ps_unification.py (PS.RGTEST.01): the two-step PS $\to SO(10)$ unification kill-test with negative controls (SM-only fails; $126$ breaks the scalaron match; proton decay selects content), $M_{PS}/M_s=1.0$ – $1.7$ . v250_dirac_triple_contract.py (CONTRACT.QFT4D.DIRAC.01): the spectral-triple contract ( $H_F=3{\times}16$ , the seven NCG axioms, $\sigma=$ scalaron) that would turn “carrier is gauged” from a fork into a theorem. The root-level qft.txt carries the full analysis.

2026-06-17

Honest data cross-check + emergent-QFT figures: the unification tension, `v246`

v246_unification_data_crosscheck.py (QFT4D.RGTEST.01) — the first hard data confrontation of the spectral-action prediction. TFPT's gauge-charged content is the Standard Model (v159) and the theory adds no new states; the $E_8$ cascade is an arithmetic spine (v5), not a threshold tower. So the run is the SM run: at one loop the couplings spread ${\sim}10^{13}$ – $10^{17}$  GeV (residual $\Delta\alpha^{-1}\approx9$ at $2{\times}10^{16}$  GeV), and at two loops (RK4) the minimal spread is $\Delta\alpha^{-1}\approx3.2$ at $1.7{\times}10^{14}$  GeV — the three never meet. Typed [X]/[O]: with “no new state” there is no admissible threshold source, so the spectral-action 4d-GUT route is in genuine tension (same status as NCG-SM), likely falsified unless extended — never a confirmation, and not rescued by a cascade. Two new figures (figures/qft_skeleton.pdf, figures/qft_unification.pdf) added via make_figures.py (PDF $+$ website PNG) and embedded in tfpt_research_contracts.tex; a root-level qft.txt summarises the emergent-QFT skeleton, what each script proves, the data status and the open questions.

2026-06-17

Spectral-action matter content: the $SO(10)$ 16 $=$ one anomaly-free SM generation, `v245`

v245_spectral_matter_content.py (QFT4D.MATTER.01) discharges the computable core of the 4d contract v244. The carrier half-spinor (the $SO(10)$ 16) is verified, in exact rational arithmetic, to be one Standard-Model generation: $\mathbf{16}=SU(5)(\mathbf{10}{+}\bar{\mathbf 5}{+}\mathbf1)$ , the SM multiplet dimensions sum to $16=\dim S^+$ ( $15$ Weyl fermions $+\,\nu_R$ ), the electric charges $Q=T_3+Y$ are exactly the SM values, all four gauge anomalies cancel ( $\sum Y=\sum Y^3=[SU(2)]^2U(1)=[SU(3)]^2U(1)=0$ ), the spectral-action normalisation gives $\sin^2\theta_W=3/8$ ( $g_3=g_2=\sqrt{5/3}\,g_1$ ), and the Higgs is the $(1,2)_{1/2}$ inner fluctuation. So the matter-content $+$ tree-relation half of CONTRACT.QFT4D.01 is now [E]; only the seam $\to$ Dirac realisation and the run-down couplings stay [O]. Wired into run_all.py, the ledger, the registry, cited in tfpt_research_contracts.tex, mirrored to the website.

2026-06-17

The QFT skeleton on the seam: thermal time, GNS/OS reconstruction, DHR sectors, the braiding S-matrix, and the 4d spectral-action contract, `v239`–`v244`

Six emergent-QFT skeleton scripts (v238). v239_ kms_ thermal_ time.py (DYN.KMS.01): the modular flow is KMS at $\beta=1$ , and $2\pi=1/(4c_3)$ fixes the modular temperature as $T_H=c_3/M$ — thermal time $=$ horizon time. v240_gns_os_reconstruction.py (DYN.GNS.01): GNS reconstructs the Hilbert space from $(\mathcal M,\omega)$ and the OS Hamiltonian $H_{\mathrm{OS}}=-\log T=-L$ is positive with gap $\Delta$ (the v64 mass gap). v241_dhr_sectors.py (DHR.SECTORS.01): particles $=$ DHR sectors $=$ the discriminant anyons of the Lean glue form, with the condensation tower $16\to4\to1$ (v235/v237). v242_spin_statistics_modular.py (DHR.MODULAR.01): spin-statistics, the modular $(S,T)$ data, Verlinde fusion, and Gauss–Milgram $c=8$ . v243_haag_ruelle_braiding.py (DHR.SMATRIX.01): the $2$ -particle S-matrix $=$ the braiding monodromy (factorised, crossing), with the v238 mass gap supplying Haag–Ruelle asymptotic states. v244_spectral_action_contract.py (CONTRACT.QFT4D.01): the 4d Lagrangian via the Connes spectral action — the carrier half-spinor $16$ is one generation, the SM gauge group sits in the carrier, gravity is v36; the matter Lagrangian is the open [O]contract. Net: the residual to a full 4d QFT is one premise (QGEO.SYM.01) plus one contract (CONTRACT.QFT4D.01). All wired into run_all.py, the ledger and registry, cited in tfpt_research_contracts.tex, mirrored to the website.

2026-06-17

The static $\to$ dynamic flip: modular flow $+$ a recovery Lindblad generator, `v238`

New v238_modular_lindblad_dynamics.py (DYN.SEMIGROUP.01, cluster registry). A companion to the modular round (v196/v198) and the recovery code (v221/v64) that reads the same seam objects dynamically rather than statically. [E]the modular flow $\sigma_t=e^{i t\Lambda_\Sigma}$ is a unitary one-parameter group (Tomita–Takesaki) whose conservation of the $\mu_4$ clock, $\rho\sigma_t\rho^{-1}=\sigma_t\Leftrightarrow[\rho,\Lambda_\Sigma]=0$ , IS the v198 state-invariance — so the static commutator is the conservation law of modular time. [E]the recovery channel's generator $L=\log T$ is a doubly-stochastic/CPTP-classical Markov generator ( $e^{L}=T$ , $e^{L\tau}\to$ the democratic projector $=$ the arrow of time). [E]keystone: the dissipative gap $=-\log((2/3)^6)=6\log(3/2)=$ the OS mass gap $\Delta$ (v64) — the static recovery bound (v221) and the dynamical mass gap (v64) are one number, one exponentiated. [E]the GKSL split $G=i\Lambda_\Sigma+L$ (imaginary $+$ real $\le0$ spectrum). [O] the residual is the geometric modular flow (Connes–Rovelli “thermal time $=$ physical time”) on the full seam algebra $=$ QGEO.SYM.01 (v198) — a target, not a closure. Wired into run_all.py, status_ledger.csv, script_registry.csv and cited in tfpt_research_contracts.tex; mirrored to website/public/verification.

2026-06-17

Experiments: black-hole-cosmology signatures, the $\eta_B$ Boltzmann solve, the Petz/baby-universe realisation, and a real-data GW-echo pipeline

Three new standalone black-hole-cosmology experiments (experiments/, all data_limited, not load-bearing). From the problem_b black-hole-cosmology survey: (i) ccbh-dark-energy — the de Sitter seam interior ( $w_{\mathrm{in}}{=}{-}1$ ) forces the Croker–Weiner cosmological-coupling index $k={-}3w_{\mathrm{in}}=3$ , hence a population $w={-}1$ ; vs. Farrah+2023 $k=3.11\pm0.79$ ( $-0.14\sigma$ ), a contested downstream bridge and an alternative reading of the same $w={-}1$ the DESI watchdog tests (alternative_group w_de_eos, never double-counted). (ii) gravastar-compactness — the Nariai $Q_{\mathrm{geom}}{=}3/8$ equals the Jampolski–Rezzolla (2026) maximum horizonless compactness $\mathcal C{=}3/8$ (shared de Sitter endpoint $1/2$ ); since $1/3{<}3/8{<}4/9{<}1/2$ this is a light-trapping ECO, yielding an echo template (round-trip delay ${\sim}0.7$ ms at $62\,M_\odot$ , amplitude $\le(2/3)^6$ ) — a [C]structural echo, no $\mathcal C\!\leftrightarrow\!Q_{\mathrm{geom}}$ map proven. (iii) cosmic-handedness — a parity watchdog (Shamir JADES ${\sim}3.3\sigma$ spin monopole, most likely a Milky-Way-aberration dipole), explicitly not promoted (frontier).
$\eta_B$ — full BDP Boltzmann ODE solve confirms the route at the frozen scale (experiments/ftransfer/leptogenesis_boltzmann/fboltzmann_solve.py; tfpt_4_frontier, [C]). Integrating the Buchmüller–Di Bari–Plümacher Boltzmann network (integrated efficiency $\kappa_f=0.092$ , validating the analytic fit) at the frozen heavy scale $M_1=M_{\mathrm{scal}}(\phiz)^2/A_\Lambda\approx8.65\times10^9$ GeV with $\delta_{\mathrm{CP}}=4\pi/3$ gives $\eta_B=6.5\times10^{-10}$ — a factor $1.07$ from the observed $6.1\times10^{-10}$ , with no free $M_R$ dial. This moves the leptogenesis route from “solve pending” to a consistent [C]readout (the full flavored density-matrix solve is the next refinement); tfpt_4_frontier Route C synced.
The Petz recovery map and the rank-one baby universe, realised numerically (experiments/recovery-channel; tfpt_horizon_readouts, [C]; companion to v221). The gapped transport contracts to a rank-one projector at exactly $\|T^n-P_\infty\|=(2/3)^{6n}$ — the one-dimensional baby-universe Hilbert space (Engelhardt 2025) — and the explicit Petz map is CPTP, recovers the reference, and equals the identity only on the protected $\lambda{=}1$ (Knill–Laflamme) mode; free-ratio and degenerate-spectrum negative controls hold. So the Petz identification v221 deferred is now verified at the channel level (internal_consistency, no new datum); the full holographic reading stays gated on the Seam–Horizon theorem.
GW ringdown echo — Stage-1 matched filter validated, then run on real GWOSC strain (experiments/gw-ringdown-echo; tfpt_horizon_readouts search-targets). The Stage-1 machinery (Kerr-ringdown subtraction $\to$ matched filter on the residual, ratio $(2/3)^6$ frozen, lag free, $+$ free-ratio control) classifies $3/3$ synthetic injections; run on real GWOSC strain (GW150914, GW190521; PSD-whitening $+$ off-source background): no kernel-ratio echo coincident in $\ge2$ detectors, consistent with the $(2/3)^6$ upper bound (a single loud H1 excess has $\hat q\approx2$ , far from $(2/3)^6$ , so the free-ratio control flags it as residual ringdown, not an echo). First pass: dominant-QNM subtraction, incoherent combination — full multi-mode $+$ coherent stacking is the next step; no detection claim.
Scorecard + website synced. experiments/evidence_scorecard.json now $51$ rows ( $26$ consistent, $7$ null, $13$ data-limited, $4$ tension, $1$ parked); the website EXPERIMENTS_AUDIT mirror and the $\eta_B$ prediction entry are updated to match. These are standalone experiments/ surfaces (not in the verification suite or ledger); the tfpt_4_frontier/tfpt_horizon_readouts and papers.ts/predictions.ts edits are the in-same-change sync.

2026-06-17

Red-team layer re-synced to the paper; shadow export mirrors `figures/`

Red Team Target A re-synced to tfpt_5_redteam (rt_A_e8net.py, redteam_table.txt, redteam/README.md, infrastructure). The Python red-team surface still emitted the historical three-residual “A reduced, not closed” form, lagging the reader-facing note. It now encodes the sharper narrowing already in the paper: the residual collapses to the single statement “the seam–Calderón boundary net is holomorphic with $c=8$ ” ( $\Leftrightarrow$ the index-4 simple-current extension), with the index-4 $(D5)_1\times(A3)_1\to(E8)_1$ glue realised at Lie level (v143) and its odd sectors twisted/Ramond ( $E_8=120_{\mathrm{NS}}+128_{\mathrm{R}}$ , v148), while the $q(A_3)$ normalisation collapses into the one declared anchor (v152). Two exact adversarial checks added ( $120{+}128=248$ ; glue index $=|\mu_4|=\Nfam{+}1=4$ ); status stays [C]/[O](reduced, not closed).
Shadow export now mirrors figures/ but not website/ (scripts/export-shadow.sh, verification/make_script_index.py, infrastructure). export-shadow.sh ships figures/*.pdf (so make_manifest.py -{}-check passes literally on the exported tree) while still excluding website/ and the compiled paper PDFs; the SHADOW_MIRROR.md table is corrected accordingly. make_script_index.py now detects a missing website/ and skips its ScriptIndex.tsx mirror, so build.sh notes runs on the subset without crashing.

2026-06-17

CP phases as $\mu_6$ powers — a reduction of red-team Target D

Both CP phases are $\mu_6$ powers of one hexagonal CM unit, split by the sheet (v231_cp_mu6_phases, tfpt_5_redteam, [E]/[C]). Sharper than v220/v225 (which only located the CP residual). With $\rho=e^{i\pi/3}$ the primitive $6$ th root (the $j{=}0$ Eisenstein CM unit): $\delta_{\mathrm{CKM}}$ leading $=\arg(\rho^1)=\pi/3$ (quark) and $\delta_{\mathrm{PMNS}}=\arg(\rho^4)=4\pi/3$ (lepton, the phase lattice), with $\rho^4=-\rho$ , so $\delta_{\mathrm{PMNS}}=\delta_{\mathrm{CKM,lead}}+\pi=(\text{CM unit})\times(\Z_2\text{ sheet}, \rho^3{=}{-}1)$ . The two CP phases are one hexagonal unit on the two sheets, not two independent inputs; the dual-frame Jarlskog orientations are sheet-flipped ( $\pm21\sin(\pi/3)$ ). A structural reduction of Target D (removes one of its two phase inputs); the quark seam correction $3\lambda_C^2$ stays the v88 misalignment, the deck stays $\Z/4$ , and the physical CP derivation stays [C](CP.MU6.01).
The seam as the $E_8$ Kleinian singularity (v232_e8_kleinian_seam, origin_theory, [E]/[C]). The du Val side of the McKay correspondence (v219) gives the open seam-realisation premise QGEO.REALIZE.01 a canonical algebraic-geometric model: dropping the trivial-rep node of the affine- $E_8$ McKay graph of $2I$ leaves the finite $E_8$ Dynkin $=$ the dual intersection graph of the eight exceptional $\PP^1$ 's of the minimal resolution of $\mathbb C^2/2I$ ; the eight curves $=\operatorname{rank}E_8=g_{\mathrm{car}}{+}\Nfam$ (a fourth reading of the $8$ ), their negated intersection form is the $E_8$ Cartan ( $\det1$ , even, $(-2)$ -curves), and the link is the Poincaré homology $3$ -sphere $S^3/2I$ ( $2I$ perfect $\Rightarrow H_1{=}0$ , $\pi_1{=}2I$ order $120$ ). The raw seam ( $\PP^1$ with marks) is canonically a du Val exceptional curve — a model for the bedrock, not a P2 proof (it presupposes $E_8$ ; TOPO.E8.01, bedrock stays [O]).
CP is the universal family/triality phase, only sheet-split (v233_cp_triality_phase, tfpt_5_redteam, [E]/[C]). One step past v231 in the $\mu_6=\mu_3$ (family/triality) $\times\mu_2$ (sheet) factorisation: $\rho=\omega^2(-1)$ with $\omega=e^{2\pi i/3}$ the $\Z_3$ triality centre (the $2/3$ cusp weight). Since $\rho^4=\rho^1\rho^3$ with $\rho^3\in\mu_2$ , the quark ( $\rho^1$ ) and lepton ( $\rho^4$ ) CP phases share the same family/triality class and differ only by the sheet — so CP is the universal triality phase, sheet-split, not a free power choice (CP.TRIALITY.01).
The Seam-Holomorphy selection certificate: the structural residual is one gate (v234_seam_holomorphy_selection, tfpt_research_contracts, [E]/[O]). The whole structural residual is one condition — “the seam carries no nontrivial abelian sector” — with three provably-equivalent faces, all forcing $E_8$ : (i) holomorphy ( $\mu$ -index $1$ ; Target A), (ii) the seam link is a homology $3$ -sphere ( $\Gamma$ perfect $\Leftrightarrow2I$ ; v232), (iii) exactly one $1$ -dim irrep (v219). All equal $\#(\text{mark-}1)=|\Gamma^{\mathrm{ab}}|=|H_1|$ , which is $1$ only for $E_8$ ; and holomorphic $c{=}8{=}\gcar{+}\Nfam$ gives the unique even unimodular rank- $8$ lattice $E_8$ . So P2, $G_{\mathrm{net}}$ , Target A and the Kleinian seam are one gate. The stated closing theorem ([O]): RP $+$ gap $+$ chirality $\Rightarrow$ quasi-free bulk (v160) $\Rightarrow$ holomorphic boundary $\Rightarrow E_8$ ; the single residual analytic step is “free bulk $\Rightarrow$ holomorphic boundary” (GATE.HOLO.01).
The closing step in Chern–Simons language: holomorphic $\Leftrightarrow\det K{=}1$ (v235_seam_chern_simons, tfpt_research_contracts, [E]/[O]). A genuine reduction (not a closure) of GATE.HOLO.01 into standard anyon-condensation physics: a free gapped bosonic $2{+}1$ d bulk is an even integer $K$ -matrix with $\#$ anyons $=|\det K|$ , edge $c={\rm signature}(K)$ , and the edge net holomorphic $\Leftrightarrow|\det K|{=}1$ . The TFPT extension tower (v92) is the condensation tower read by determinant: carrier $D_5{\oplus}A_3$ ( $\det16$ , $16$ anyons) $\to SO(16)_1{=}D_8$ ( $\det4$ ) $\to(E_8)_1$ ( $\det1$ , holomorphic) — all rank $8$ , $c{=}8{=}\gcar{+}\Nfam$ — so holomorphic $=E_8=$ the Kitaev $E_8$ quantum-Hall state. Holomorphy $\Leftrightarrow$ condensing the order- $|\mu_4|$ Lagrangian glue ( $\det16{\to}1$ , vs. a partial order- $2$ isotropic $\to4{=}D_8$ ). The residual narrows to one integer condition “the free RP seam condenses the Lagrangian glue ( $\det{=}1$ )” $=$ the sheet/QGEO selection, now with holomorphy $\Leftrightarrow\det1$ a theorem (GATE.HOLO.02).
The $(2,3,5)$ Brieskorn singularity is the one generator of the skeleton (v236_brieskorn_capstone, origin_theory, [E]). Capstone of the icosahedral round: the singularity $x^2{+}y^3{+}z^5$ , whose exponents are the atoms $(|\Z_2|,\Nfam,\gcar){=}(2,3,5)$ , has Milnor number $\mu{=}(2{-}1)(3{-}1)(5{-}1){=}8{=}\operatorname{rank}E_8$ (a fifth origin of the “ $8$ ”), Milnor monodromy $=$ the order- $30$ $E_8$ Coxeter element (eigenvalues the primitive $30$ th roots $=$ the $E_8$ exponents, charpoly $\Phi_{30}$ ), Milnor lattice $E_8$ , link the Poincaré sphere; the two clocks are facets of this one monodromy — the $\mu_3$ triality (CP, v233) is $h^{10}$ in $\langle h\rangle{=}\Z/30$ , the $\mu_4$ clock (v223) is the order- $4$ Galois automorphism of $\mathbb Q(\zeta_{30})$ (TOPO.BRIESKORN.01).
The closing step as a physical condition: no topological degeneracy $\Leftrightarrow\det K{=}1 \Leftrightarrow$ the seam is SRE (v237_seam_sre_closure, tfpt_research_contracts, [E]/[O]). Sharpens GATE.HOLO.02's residual from definitional to falsifiable: the $K$ -matrix ground-state degeneracy on a genus- $g$ surface is $|\det K|^g$ (torus: carrier $16$ , $D_8$ $4$ , $E_8$ $1$ ), so “no topological degeneracy on any closed surface” $\Leftrightarrow\det K{=}1$ ; among rank- $8$ even positive-definite $K$ ( $c{=}8{=}\gcar{+}\Nfam$ ) only $E_8$ is short-range-entangled (the Kitaev $E_8$ phase). A unique vacuum on the plane (RP $+$ gap $+$ cluster) is necessary but not sufficient (the plane cannot see $\det K$ ); so the one open step is the physical statement “the free RP seam is SRE (no topological order)” (GATE.HOLO.03).

2026-06-16

the icosahedral bedrock, CM-norm duality, and a structural-finds round

McKay bedrock: why the atoms are $\{2,3,5\}$ (v219_icosahedral_mckay, origin_theory, [E]). $E_8$ is the exceptional top of the McKay tower of finite $SU(2)$ subgroups ( $2T{\to}\hat E_6$ , $2O{\to}\hat E_7$ , $2I{\to}\hat E_8$ ). Built from the group: the $120$ unit-quaternion icosians close to the binary icosahedral group $2I$ (element orders $\{1,2,3,4,5,6,10\}$ — it contains the $2,3,5$ rotation-axis orders), $9$ conjugacy classes; the $9$ irreducible character degrees (Dixon, from the class algebra) are $\{1,2,2,3,3,4,4,5,6\}$ , sum $30{=}h(E_8)$ , sum of squares $120{=}|R^+(E_8)|$ ; the McKay adjacency from the natural $2$ -dim rep is the affine $E_8$ graph with Kac marks $=$ the degrees. A backward certificate of the closed $E_8$ , not a P2 proof (MCKAY.E8.01).
CM-norm duality: $41$ (square) and $7$ (hex) (v222_cm_norm_duality, origin_theory, [E]). The square seam (Gaussian $\Z[i]$ , $j{=}1728$ ) gives $N(\gcar{+}i|\mu_4|){=}5^2{+}4^2{=}41{=}10b_1$ (the EM index is the Gaussian norm of the carrier-glue vector) and $N(3{+}2i){=}13{=}\Delta_Q$ ; the hexagonal partner (Eisenstein $\Z[\omega]$ , $j{=}0$ ) gives $N(3{+}2\omega){=}7{=}$ scalaron. The $(3,2)$ split generates $(5,6,7,13)$ by sum/product/Eisenstein/Gauss norm; rings rigid (CMNORM.DUAL.01).
The $\mu_4$ clock is the order- $4$ character of the $E_8$ Coxeter cycle (v223_ coxeter_ totative_ clock, origin_theory, [E]). $(\Z/30)^\times$ are the $E_8$ exponents; the order- $4$ generator $7$ ( $\langle7\rangle{=}\{1,7,13,19\}$ ) is a literal $\mu_4$ clock permuting the four conjugate planes; only $E_8$ has $\varphi(h){=}\mathrm{rank}$ and $h{=}2{\cdot}3{\cdot}5$ (COX.CLOCK.01).
$248{=}120{+}128$ as a magnitude/phase channel typing (v227_ degree_ exponent_ channel_ split, tfpt_5_redteam, [E]). Exponents sum $120{=}|R^+(E_8)|$ (magnitude channel), degrees sum $128{=}\mathrm{rank}\cdot\dim S^+$ (phase/glue channel); the red-team Target D magnitude bijection lives in $120$ , the un-covered CP phases in $128$ ; the dark-sector reading of $128$ stays Frontier (replaces the over-strong $S^-$ reading; E8.CHAN.01).
P2 as the mode space of a degree- $4$ seam divisor (v228_rr_index_gate, origin_theory, [E]/[C]/[O]). A Riemann–Roch index gate: $\deg D{=}4{=}|\mu_4|$ on $\PP^1$ forces $h^0{=}5{=}\gcar$ , $\mathrm{rank}\,H_1{=}3{=}\Nfam$ , $h^0{+}H_1{=}8{=}\mathrm{rank}\,E_8$ , $\Lambda^{\mathrm{even}}(\mathbb C^5){=}16{=}\dim S^+$ — bedrock language for P2, conditional on the seam producing the degree- $4$ divisor (QGEO.RR.01).
The seam as a finite recoverability code (v221_seam_qecc, origin_theory, [E]/[C]). Code dimension $\dim S^+{=}16$ ; the gapped transport is a CPTP doubly-stochastic contraction with spectrum $\{1,(2/3)^6,(1/3)^6\}$ , recovery bound $\|T^n\delta\|{\le}(2/3)^{6n}\|\delta\|$ (Knill–Laflamme type); free ratio breaks it. Holographic/Petz reading [C], gated on the Seam–Horizon theorem (QEC.SEAM.01).
CP lives in the hexagonal phase fiber (v220_cp_hexagonal_modulus, tfpt_5_redteam, [E]/[C]). The seam deck is the square modulus $j{=}1728$ ( $\Z/4$ ); its partner is the hexagonal $j{=}0$ ( $\Z/6$ , $\arg\rho{=}\pi/3$ ). The frozen $\delta{=}\pi/3{+}3\lambda_C^2 {=}68.654^\circ$ has leading term $\pi/3{=}\arg\rho$ ; the deck stays $\Z/4$ , CP is the $\Z/6$ fiber (CP.MOD.01).
The dual normal frame $(d,n)$ with CP as orientation (v225_dual_normal_frame, tfpt_5_redteam, [E]/[C]). $d{=}a^\top R^{-1}{=}({-}\tfrac12,{-}\tfrac12,1){=}{-}\tfrac12$ Nariai; $n{=}(5,{-}9,6)$ reads $\det$ on the first-generation column; $\det(\mathbf1,d,n){=}21{=}3{\cdot}7$ ; $\mathrm{Im}\det(\mathbf1,d,\rho n){=}21\sin(\pi/3)$ — CP as orientation (DUAL.FRAME.01).
$F_{\mathrm{transfer}}$ as one path on the Sheet Diamond (v224_diamond_ftransfer_path, tfpt_2_standard_model, [E]/[C]). $M(s,t){=}R{+}Q\,\mathrm{diag}(s,t,t)$ : $K,C,F$ on the sheet axis (curved, 2nd diff $8$ ), the winding axis flat (slope $6$ ), Plücker steps $(1,8,10),(1,8,16)$ ; the Koide source $\to$ pole is the $1$ -D projection (FTR.PATH.01).
The charged leptons as an étale Frobenius algebra (v229_lepton_frobenius_algebra, tfpt_2_standard_model, [E]/[C]). $(c_e,c_\mu,c_\tau){=}(\tfrac{16}7,\tfrac43,\tfrac76)$ , ring closure $c_e c_\tau{=}\tfrac83{=}|\Z_2|c_\mu$ , product $\tfrac{32}9$ ; $A{=}\mathbb Q[t]/(m)$ is étale (trace-form Gram nondegenerate), a commutative Frobenius algebra over the $\mu_6$ resolvent (LEP.FROB.01).
The center budget $(7,11,13)$ as three local norms (v230_center_budget_norms, tfpt_2_standard_model, [E]). $C{=}R{+}Q\,\mathrm{diag}(1,0,0)$ row sums $(7,11,13)$ : $7{=}N_{\Z[\omega]}(3{+}2\omega)$ (hex), $13{=}N_{\Z[i]}(3{+}2i)$ (square), $11{=}\binom40{+}\binom41{+}\binom42$ (QBL Fock count); the two CM rings and the boundary count meet in one operator center (CENTER.NORM.01).

2026-06-15

the diamond axis geometry — two axes + the transfer corner

The Sheet Diamond is a discrete geometry with two axes (v218_diamond_axis_geometry, tfpt_2_standard_model, [E]). Sharpens v94/v95 with three exact [E]lemmas (no new numbers). (1) Axis curvature: along the centered cross the determinant is linear on the winding axis $\det(C{+}xU)=14{+}6x$ (slope $6{=}|R^+(A_3)|$ ) and quadratic on the sheet axis $\det(C{+}yV)=14{+}14y{+}4y^2$ (2nd difference $8{=}\mathrm{rank}\,E_8$ ); the anchor block has $\det B(C{+}xU)=2\det(C{+}xU)$ and sheet curvature $6{=}|R^+(A_3)|$ — two curvatures $(8,6)=(\mathrm{rank}\,E_8,|R^+(A_3)|)$ . (2) Plücker transfer ladder: $\mathrm{Pl}(K)\to\mathrm{Pl}(C)\to\mathrm{Pl}(F)$ lifts in steps $(1,8,10)=(N_\Phi,\mathrm{rank}\,E_8,A_\Lambda)$ then $(1,8,16)=(N_\Phi,\mathrm{rank}\,E_8,\dim S^+)$ — the decuple then the full generation (identity [E], source $\to$ pole reading [C]). (3) Spectral ramification: for $Q,K,C,F$ the cubic discriminant factors as $q(r)^2\,\mathrm{Disc}(q)$ with squares $(1,3,4,6)$ and kernels $(13,48,65,105)$ , $F$ carrying $105=3{\cdot}5{\cdot}7$ . The anchor-defect spectrum and pair-sum/staircase blocks are honest audit fingerprints ( $28{=}2\dim G_2$ , $52{=}\dim F_4$ stay audit-only, not spine, as in v94/v95); $F$ as the transfer-completion corner is a heuristic, not a hard filter. Ledger DIAMOND.AXIS.01, DIAMOND.PLUCKER.01, DIAMOND.SPECTRAL.01; Wolfram-mirrored ( $249/249$ ).

2026-06-15

QGEO: the four marks emerge from Gauss–Bonnet — K1 executed

The four marks emerge from Gauss–Bonnet — count derived, not assumed (v216_marks_gauss_bonnet, tfpt_research_contracts, [E]; ledger QGEO.MARKS.03). The K1 lever of the v215 kill-test (“exactly four marks”) is executed: if the marks are $\Z_2$ branch points (deficit $\pi$ ) on the flat seam sphere ( $\chi=2$ , the same $\chi$ as the $8$ in $c_3$ ), Gauss–Bonnet forces $n\pi=2\pi\chi=4\pi$ , so $n=2\chi=4=|\mu_4|=\Nfam+1$ . The closed Euclidean sphere $2$ -orbifolds are exactly $(2,3,6)$ , $(2,4,4)$ , $(3,3,3)$ , $(2,2,2,2)$ , and three independent criteria — all cone orders $=2$ (the $|\Z_2|$ sheet branch), $\mathrm{rank}\,H^1=\#\text{marks}-1=3=\Nfam$ (the three generations pick the $4$ -mark square over the $3$ -mark hexagonal), and a free order- $4$ deck — converge on the pillowcase $(2,2,2,2)$ . The numerical sibling v217_marks_emergence_scan ([C], ledger QGEO.EMERGE.01) confirms it on the actual DtN/state (number $n$ and positions free, the $4$ -square config is the unique joint minimiser of clock-invariance $+$ $3$ -family cohomology $+$ gap $(2/3)^6$ ). The mark count and equality move from input to derived; only the square modulus (cross-ratio $2$ , the order- $4$ clock) stays the one carrier input, and the from-zero raw-seam emergence QGEO.REALIZE.01 stays [O]. v216 exact (Wolfram extension $\to248/248$ ); v217 numerical (Python-only). Suite $\to$ 217 modules.

2026-06-15

QGEO: the bedrock recast as a falsifiable kill-test

QGEO.SYM.01 as a kill-test, not a proof-promise (v215_seam_deck_killtest, tfpt_research_contracts, [E]/[O]; ledger QGEO.KILL.01). A foundational symmetry cannot be derived from nothing (Bisognano–Wichmann would presuppose the covariance it should produce), so the bedrock $\omega\circ\rho=\omega$ is recast as four independently-falsifiable predictions about the raw seam DtN. The non-circular reduction (v198/v199/v201) gives $\omega\circ\rho=\omega\Leftrightarrow[\rho,C]=0$ with $|k|$ commuting exactly, so the residual is the bounded sub-principal $M_f$ (equivalently the raw Gaussian bulk form $A$ is $\mu_4$ -deck-invariant). Levers: K1 exactly four marks ( $b_1=\#\text{marks}-1=3=\Nfam\Rightarrow\#\text{marks}=4=|\mu_4|$ ); K2 the square config (cross-ratio $2\Rightarrow j=1728$ , $\mathrm{Aut}=\Z/4$ ; order $4$ selects $\Z/4$ not the $j=0$ $\Z/6$ ; generic $\Rightarrow\Z/2$ ); K3 mod- $4$ sub-principal support ( $[\rho,M_f]=0\Leftrightarrow f$ $\Z_4$ -invariant); K4 transfer gap $(2/3)^6=64/729$ . Freeze-bound via freeze_file.csv (seam_deck_symmetry), carrier-side [E](regression guards), with the decisive kill deferred to QGEO.REALIZE.01 [O](the raw collar DtN must produce four square marks without inputting them — an emergence test). A kill-test, not a closure. Python-only (falsification layer; the exact sub-parts $j=1728$ and $(2/3)^6$ are Wolfram-mirrored via v214/v54/v56). Suite $\to$ 215 modules.

2026-06-15

QGEO: the pillowcase reduction — two residuals become one canonical metric

Pillowcase reduction of QGEO.SYM.01 (v214_seam_pillowcase, tfpt_research_contracts, [E]/[O]; ledger QGEO.PILLOW.01). The two separately-tracked open QGEO residuals — QGEO.ISO.01 (v180: the carrier clock is an order- $4$ isometry of the seam metric) and QGEO.SUBPRIN.01 (v201: the DtN sub-principal symbol is mark-local, the seam flat away from the $\mu_4$ marks) — are shown to be one statement: the seam carries the uniformising flat orbifold (pillowcase) metric. (1) The four marks make the Euclidean orbifold $S^2(2,2,2,2)$ ( $\chi_{\mathrm{orb}}=2-4(1-\tfrac12)=0$ ), so by Troyanov uniformisation the metric is flat (unique up to scale) with curvature only at the cone points (Gauss–Bonnet $4\pi=2\pi\chi$ ) — this is the v201 “flat away from the marks”. (2) New link: cross-ratio $(\mu_4)=2$ (v168) $\Rightarrow j=1728$ ( $j(\lambda)=256(\lambda^2-\lambda+1)^3/(\lambda^2(\lambda-1)^2)$ ; all six harmonic cross-ratios give $1728$ ) $\Rightarrow$ the square modulus $\tau=i$ , whose CM by $\Z[i]$ derives the order- $4$ clock $z\mapsto iz$ (explicit $(x,y)\mapsto(-x,iy)$ on $y^2=x^3-x$ ); generic cross-ratio gives $j\notin\{0,1728\}$ and only $\Z/2$ . (3) Unification: “seam $=$ uniformising flat pillowcase metric” implies both v201 and v180, so two residuals collapse to one canonical-metric premise. [O]It does not close QGEO.SYM.01: the choice “RP seam metric $=$ the constant-curvature representative” stays open, milder and more canonical than the bare isometry premise. Wolfram-mirrored (the exact orbifold/ $j$ -invariant/CM arithmetic); Klein- $J$ values mpmath-numerical. Suite $\to$ 214 modules.

2026-06-15

the F_transfer functor contract CONTRACT.F.01

$F_{\mathrm{transfer}}$ formalised as a typed functor with four axioms (v213_ftransfer_functor, tfpt_research_contracts, [C]). The four frontier transfers are consolidated into ONE functor $F_{\mathrm{transfer}}=F_{\mathrm{observable}}\circ F_{\mathrm{threshold}} \circ F_{\mathrm{RG}}$ , each instance a discrete compiler kernel [E]composed with an external continuous solver [C]: (1) $\mu_4$ -deck equivariance (the Koide multiplier $\lambda_2{=}(2/3)^6{=}64/729$ is the deck transfer eigenvalue); (2) Plücker preservation ( $53{=}a^T(R{+}Q)\mathbf1$ , $\mathrm{Pl}(F){=}(1,22,30)$ , $\|\mathrm{Pl}(K)\|_1{=}11$ ); (3) positivity/stochasticity ( $\operatorname{spec}T$ positive, $\kappa_f\in(0,1)$ ); (4) external modules explicit ( $b_3{=}{-}7$ a carrier output). The four instances are $F_{\mathrm{pole}}$ (v183), $F_{\mathrm{Boltzmann}}$ (v212), $F_{\mathrm{relic}}$ (v211), $F_{\mathrm{QCD}}$ (v164). CONTRACT.F.01 is the third research contract alongside $(U_{\mathrm{wall}})$ and $(G_{\mathrm{metric}})$ , the structural complement of the v187 typing guard — an architectural consolidation, not a closure of any frontier number. Ledger CONTRACT.F.01.

2026-06-15

frontier: two sharper [C] scenario branches — axion angle + leptogenesis

Axion DM spine-angle branch $\theta_i=\pi\Nfam/\gcar=3\pi/5$ (v211_axion_spine_angle, tfpt_4_frontier, [C]). A more robust misalignment angle than the determinant-line hilltop $\theta_i\approx170^\circ$ (v185, which over-produces $\Omega_a h^2\approx0.66$ ): the central spine quotient gives $\theta_i=3\pi/5=108^\circ$ exactly (no fit), the finite- $T$ solver reaches $\Omega_{\mathrm{DM}}$ at ${\approx}106^\circ$ , and $108^\circ$ sits in the mild-anharmonic regime ( $62^\circ$ below the hill-top) — not exponentially sensitive. An alternative ansatz to $\theta_i=\pi(1-\varphi_\Sigma)$ (mutually exclusive, the full solver decides, DM.AXION.SPINE.01); [X] $\Omega_a h^2$ outside ${\sim}[0.08,0.16]$ demotes it. A sharper scenario, not a derivation.
Leptogenesis scalaron-decuple branch (v212_leptogenesis_decuple, tfpt_4_frontier, [C]). Both Boltzmann inputs share the decuple $A_\Lambda=10=|E(K_5)|$ : $M_1=M_{\mathrm{scal}}(\phiz)^2/A_\Lambda\approx8.65\times10^9$ GeV and $\tilde m_1=m_3/A_\Lambda\approx5$ meV. $M_1$ uses only $\{M_{\mathrm{scal}},\phiz,A_\Lambda\}$ — no hidden seesaw scale, cleaner than v184's $M_R\varphi_0^4$ — and lands in the thermal window where $\eta_B\approx1.2\times10^{-9}$ brackets the observed $6.1\times10^{-10}$ . The coupling mechanism is posited not derived, so $\eta_B$ stays [C]; [X]a precise Boltzmann/RGE solve outside the band falls the route, not the theory (FR.ETAB.04; Route A independent).

2026-06-15

Lean: QGEO.COHOM.01 character grading + MODULE parity machine-proved

The cohomology character grading is now Lean-formalised (CohomologyGrading.lean, ledger FORM.QGEO.03, [O]). A new module machine-proves the Cohom node of the QGEO proof tree (v177; audit: pass, no sorry/admit, axioms propext, Classical.choice, Quot.sound only): the three $H^1(\PP\setminus\mu_4)$ eigenforms $\omega_k=z^{k-1}/(z^4-1)$ ( $k{=}1,2,3$ ) have pullback character $\rho^*\omega_k=i^k\omega_k$ under the clock $\rho:z\mapsto iz$ (each an exact rational-function identity, the denominator clock-invariant since $i^4{=}1$ ), so the grading is $(i,-1,-i)$ with weights $(1,2,3)$ = the $A_3$ exponents $=\operatorname{Spec}(Q_+)$ , rank $3=\Nfam$ . The Module parity is also proved: the reflection $\sigma:z\mapsto1/z$ satisfies $\sigma^*\omega_1=\omega_3$ , $\sigma^*\omega_2=\omega_2$ , $\sigma^*\omega_3=\omega_1$ (swap $\omega_1\!\leftrightarrow\!\omega_3$ , $\omega_2$ fixed). Signature-locked in AuditContract.lean. The geometric Cohom/Module-parity nodes are now [E]; the Marks/Kernel obligations and the Module uniqueness stay [O].

2026-06-15

Lean: QGEO.UNIFORM.01 geometric normal form machine-proved

The Möbius uniformisation normal form is now Lean-formalised (Mobius Uniformisation.lean, ledger FORM.QGEO.02, [O]). A new module machine-proves the constructive Uniform node of the QGEO proof tree (v177; audit: pass, no sorry/admit, axioms propext, Classical.choice, Quot.sound only): the clock $\rho:z\mapsto iz$ has $\rho^4{=}\mathrm{id}$ and $\rho^2{\neq}\mathrm{id}$ (order exactly $4$ ); the reflection $\sigma:z\mapsto1/z$ is an involution with $\sigma\rho\sigma=\rho^{-1}$ (so $\langle\rho,\sigma \rangle$ is the dihedral $D_4$ of order $8$ ); a non-fixed orbit $\{a,ia,-a,-ia\}$ scales to $\mu_4=\{1,i,-1,-i\}$ ; $\sigma$ permutes $\mu_4$ (fixes $1,-1$ , swaps $i,-i$ ); and the multiplier classification “ $z\mapsto\zeta z$ has order exactly $4\Leftrightarrow\zeta=\pm i$ ”. Signature-locked in AuditContract.lean. This formalises the geometric half of the seam realisation given the four marks and the clock; the raw-seam marking obligation QGEO.MARKS.01 stays [O], not closed.

2026-06-15

Lean: the QGEO.SYM.01 conditional theorem machine-proved

The mark-local $\Rightarrow\omega\circ\rho=\omega$ implication is now Lean-formalised (SeamDeckClosure.lean, ledger FORM.QGEO.01, [O]). A new module in the carrier-rigidity Lean project machine-proves the algebraic core of v201/v210 (audit: pass, no sorry/admit, no domain axioms — #print axioms $=$ propext, Classical.choice, Quot.sound only): (i) the $4$ th-root character orthogonality $\sum_{j<4}\zeta^j=(\text{if }\zeta{=}1\text{ then }4\text{ else }0)$ for $\zeta^4{=}1$ (so a $\mu_4$ -mark sum is supported only on modes $\equiv0\bmod4$ ); (ii) the clock generator $-i$ has order $4$ ; (iii) markLocal_blockDiagonal: a mark-local Toeplitz symbol connects only equal clock-characters, $[\rho,M_f]=0$ ; (iv) the premise is a typed structure SeamDeckPremise (the physical seam DtN is mark-local) — consumed, not proved, exactly as CalderonProjector encodes the Paper-1 analytic input; (v) SeamDeckPremise.clock_invariant: given the premise, the clock commutes with the DtN, whence $\omega\circ\rho=\omega$ . So the implication is now [E](formally proved); the premise (the physical seam being mark-local) stays [O]— the one fundamental seam-identification postulate, not closed.

2026-06-15

QGEO sharpening: mark-local DtN certified on realistic profiles

Mark-local DtN $\Rightarrow\omega\circ\rho=\omega$ , certified on realistic Steklov profiles and at the state level (v210_mark_local_dtn, tfpt_research_contracts, [O]). A numerical sharpening of QGEO.SUBPRIN.01/v201: a real von-Mises curvature bump summed over the four $\mu_4$ marks, $f(\theta)=\sum_{j=0}^3 g(\theta-j\pi/2)$ , builds the Steklov DtN $\Lambda=|D_\theta|+M_f$ whose off- $(\mathrm{mod}\,4)$ Fourier support vanishes to $<10^{-16}$ , $\|[\rho,\Lambda]\|<10^{-15}$ , and — the genuinely new step — the quasi-free covariance $C=\tfrac12(1+\operatorname{sgn}H_1)$ is clock-invariant ( $\rho C\rho^\dagger=C$ to $<10^{-13}$ ), i.e. the actual $\omega\circ\rho=\omega$ . Negative controls (single off-centre bump, $\Z_3$ source, four generic marks) break both by $O(1)$ ; convergence stable for $N\in\{16,32,64\}$ . This certifies the implication; the premise that the physical seam is mark-local stays [O](it does not close QGEO.SYM.01; net existence and full-cone RP remain the [E]of v175). Ledger QGEO.MARKLOCAL.01. Python-only (the exact mark-sum identity is Wolfram-mirrored via v201).

2026-06-15

archive integration #5: six dormant results revived from the old papers

Muon $g-2$ as a seam vertex (v204_muon_seam_g2, tfpt_4_frontier, [C]). The carrier's second-order topological defect $\delta_2=\tfrac54\delta_{\mathrm{top}}^2$ projected through the seam-loop phase gives $a_\mu^{\mathrm{seam}}=\delta_2/(2\pi)=45/(524288\,\pi^9)\approx2.879\times10^{-9}$ ( $0.81\sigma$ vs the dispersive $\Delta a_\mu$ ; ${\sim}1.5\sigma$ vs lattice/CMD-3). The value is exact [E]; the vertex identification is the [C]bridge. Ledger FR.MUONG2.01; Wolfram-mirrored.
An independent gravitational $3/4$ (v205_xi_threequarter, tfpt_4_frontier, [E]/[C]). $\xi=\cthree/\varphi_{\mathrm{tree}}=3/4$ exactly (Einstein limit of $\kappa^2=\xi\phiz/\cthree^2$ ) — the same $3/4=q(A_3)=\ln(m/\mu)$ as the seam-determinant replica (v152), an over-determination. Ledger GRAV.XI.01; Wolfram-mirrored.
Quantitative $H_0$ from the $\Lambda$ branch (v206_h0_lambda_branch, tfpt_4_frontier, [C]). $\delta_\Sigma=48\,e^{-2\pi\ainv/3}\approx1.085\times10^{-123}$ , the $(8\pi)^2$ Planck-convention split, and $H_0=66.5$ – $67.1$ km/s/Mpc (below Planck, far below SH0ES — the Hubble tension is not relieved). Ledger GRAV.H0.01.
Asymptotic Safety as a second QG route (v207_asymptotic_safety, tfpt_4_frontier, [O]). A complementary continuum-FRG argument (a non-Gaussian UV fixed point from the same axioms; $y^2=16\cthree^2=1/(4\pi^2)$ ) — a plausibility cross-check, not load-bearing, does not close $G_{\mathrm{metric}}$ . Ledger GRAV.ASYMP.01.
Black-hole thermodynamics from the seam (v208_bh_ thermodynamics, tfpt_horizon_ readouts, [E]/[C]). Modular $T_H=\kappa/(2\pi)$ (the $2\pi=1/(4\cthree)$ seam unit, ties to v198/v199) and the scalaron-corrected Wald entropy $S_W=(A/4G)(1+R_h/3M_s^2)$ (exact from v28). Ledger HOR.BHTHERMO.01; Wolfram-mirrored.
The black hole as a seam fixed point (v209_bh_ regular_core, tfpt_horizon_ readouts, [C]). No singularity ( $\varphi\to\varphi_\star$ at the gapped attractor $(2/3)^6$ ); the maximal BH $=$ the anchor (Nariai roots $(1,1,-2)$ ); information via Page recovery; a Planck-scale holographic floor. The superseded RN/torsion metric is not resurrected. Ledger HOR.BHCORE.01.

2026-06-15

archive integration #4: Möbius $\cong$ Lorentz foundation citation

The Möbius seam is the boundary Lorentz structure (tfpt_3, [O]). Added a paragraph to the “Möbius origin of $\pi$ ” section: $\mathrm{M\ddot{o}b}(\hat{\mathbb C})\cong\mathrm{PSL}(2,\mathbb C) \cong\mathrm{SO}^+(3,1)$ (Penrose & Rindler, Spinors and Space-time, Vol. 1, 1.2–1.4), the celestial sphere of null directions via stereographic projection. This gives the self-consistency loop a spacetime meaning — the carrier clock $z\mapsto iz$ is an elliptic $\mathrm{PSL}(2,\mathbb C)$ rotation (v180) and the RP $\to$ OS causal cone is the same Lorentz structure — so “Möbius origin of $\pi$ ” and “one Lorentzian cone” are two faces of one boundary $\mathrm{PSL}(2,\mathbb C)$ . A foundation citation, not a new claim ( $\pi$ stays primitive).

2026-06-15

archive integration #3: axion coupling $g_{a\gamma\gamma}=-4c_3$ + retired small-angle reading

Haloscope coupling tied to $c_3$ (tfpt_4_frontier, [C]). Made explicit: in the determinant-line normalization the axion–photon anomaly coefficient is $g_{a\gamma\gamma}=-4c_3=-1/(2\pi)$ ( $y^2=16c_3^2=1/(4\pi^2)\approx0.0253$ ), so the haloscope $F\tilde F$ coupling is set by the same $c_3$ that fixes $\alpha$ and $\beta_{\mathrm{rad}}=\varphi_0/4\pi$ — a [C]structural relation (the coefficient, not a parameter-free physical $g_{a\gamma\gamma}$ ). The earlier small-angle $\theta_i=\varphi_0$ reading (old determinant-line note, a much higher axion mass) is superseded by the closed near-hilltop $\theta_i=\pi(1-\varphi_{\mathrm{seam}})=170.4^\circ$ , recorded as a retired reading and guarded by v188 (a new sentinel forbids that stale axion mass from re-entering the active docs).

2026-06-15

archive integration #2: the EHT achromatic polarization intercept — v203

HOR.EHT.01 (v203, [E]/[C]/[X]). The surviving core of the old UFE/black-hole notes (not the RN-type metric — superseded by the Nariai/seam $=$ horizon readouts v101–v104/v190; only the polarization signature survives): a local achromatic polarization-rotation intercept around a horizon-scale black hole, $\beta_{\mathrm{BH}}(r)=16c_3^4\,Q_e^{\mathrm{eff}}Q_m^{\mathrm{eff}}/r^2$ . The coupling $16c_3^4=1/(256\pi^4)=\delta_{\mathrm{top}}/3$ is exact ([E], Wolfram-mirrored) — the same top-form coefficient $\delta_{\mathrm{top}}=48c_3^4$ that fixes the $\alpha$ -kernel precision-zone correction, one row from the cosmic-birefringence seed $\beta_{\mathrm{rad}}=\varphi_0/4\pi$ . TFPT fixes the $1/r^2$ shape, achromaticity and sign-flip ([C]); the amplitude $Q_eQ_m$ is an MHD/GR weight, never a pixel prediction. Dated kill test [X]: the residual intercept must pass three nulls (frequency, spatial $1/r^2$ , sign-flip) after honest GRMHD subtraction. Integrated into tfpt_horizon_readouts (new EHT section), the ledger, registry, Wolfram ( $243/243$ ), and the website (predictions.ts). Suite $202$ modules.

2026-06-15

archive integration #1: the rare kaon sector $K\to\pi\nu\bar\nu$ — v202

FR.RAREKAON.01 (v202, [C]). The closed TFPT CKM point ( $s_{12}{=}\lambda_C$ , $s_{23}{=}\varphi_0/(1{+}\lambda_C){=}|V_{cb}|$ , $s_{13}{=}\lambda_C^3/3$ , $\delta{=}\pi/3{+}3\lambda_C^2{=}1.19823$ rad; v18/v88, no flavor fit) feeds the cleanest FCNC probe. With standard external short-distance input (Brod–Gorbahn–Stamou $X_t,P_c,\kappa_\pm$ ) it gives $\mathrm{BR}(K^+\!\to\pi^+\nu\bar\nu)=9.45\times10^{-11}$ and $\mathrm{BR}(K_L\to\pi^0\nu\bar\nu)=3.33\times10^{-11}$ — a [C]downstream flavor readout, not a compiler power (the SD functions are external). Recomputed from the current CKM point (an earlier archive scaffold quoted $\mathrm{BR}(K_L)=3.47\times10^{-11}$ from an $\Im(\lambda_t)/\lambda^5$ slip, corrected here). Grossman–Nir ratio $0.352\ll4.3$ ; NA62 $(13.0^{+3.3}_{-3.0})\times10^{-11}$ is $\sim1.2\sigma$ above. Dated kill test [X]: a stable NA62 $\mathrm{BR}(K^+)$ outside $[7,12]\times10^{-11}$ , or a KOTO-II $\mathrm{BR}(K_L)$ off the GN point, breaks the flavor bridge (core untouched). Integrated into tfpt_2_standard_model ( rare kaon), the ledger, v187 guard (new FR.RAREKAON. family), registry, and the website (predictions.ts). Python-only. Suite $201$ modules.

2026-06-15

bedrock: the $\omega\circ\rho=\omega$ residual reduced once more — v201

QGEO.SUBPRIN.01 (v201, [E]/[O]). The v199 bedrock residual — “the bounded sub-principal symbol of the raw seam DtN has no off-character (mod 4) matrix elements” — is reduced one genuine step further: block-diagonality is not an independent postulate. Writing the DtN as $\Lambda=|k|+M_f$ with $M_f$ the bounded sub-principal piece $=$ multiplication by a curvature $f(\theta)$ (standard Steklov structure), $M_f$ is $\mu_4$ -character-block-diagonal iff $f$ is $\Z_4$ -invariant ([E]; principal $|k|$ already commutes, v198); and a $\mu_4$ -mark sum $f=\sum_{j=0}^3 g(\theta-2\pi j/4)$ has $f_m=4g_m[m\equiv0\bmod4]$ for any profile $g$ , hence is automatically $\Z_4$ -invariant ([E]). So the $\mu_4$ -mark orbit (forced by v195) forces the sub-principal symbol block-diagonal; $3$ marks ( $\Z_3$ ) and $4$ generic marks break it (negative controls). The residual collapses to “the DtN sub-principal symbol is mark-local (seam flat away from the $\mu_4$ marks $=$ conformal deck, v177)”, structurally definitional — the narrowest form yet of QGEO.SYM.01, [O]. Registered in run_all.py, the ledger, tfpt_research_contracts, origin_theory; Wolfram-mirrored (the mark-sum Fourier identity is exact; extension now $242/242$ ). Suite $200$ modules.

2026-06-15

F_transfer workshop: the axion relic solver — an honest over-production tension

Axion relic solver (experiments/ftransfer/axion_relic/relic_solver.py, [C]). The first real $F_{\mathrm{transfer}}$ pipeline computation (work package C / review 6.2): a standard misalignment relic with a numerically-computed anharmonic factor $F(\theta_i)\approx4$ at the hilltop. Honest finding: at the predicted $\theta_i\approx170^\circ$ the estimate over-produces dark matter, $\Omega_a h^2\sim0.6$ – $2.3$ (robustly $>0.12$ ), because the large $\theta_i^2\approx8.8$ times $F$ overshoots. So the determinant-line axion as the dominant DM is in mild tension (it would prefer $\theta_i\sim120$ – $130^\circ$ or extra dilution) — this refines v185's optimistic “can be all-DM” toward an over-production tension. The near-hilltop regime is O(1)-uncertain, so a full finite- $T$ solve decides; over-production kills only the axion-as-dominant-DM branch, not the compiler. Reflected in tfpt_4_frontier (dark-matter section) and the v185 docstring; experiments-only, not a suite/ledger claim. No refitted exponents; $\theta_i=\pi(1-\varphi_{\mathrm{seam}})$ only.
Full finite- $T$ solve confirms it (axion_relic/full_finiteT_solve.py). A converged nonlinear misalignment solve ( $\theta''+(3+\mathrm{d}\ln H/\mathrm{d}N)\theta'+(m_a(T)/H)^2\sin\theta=0$ , lattice $\chi(T)\propto T^{-8.16}$ , realistic $g_*(T)$ ; normalised so $\theta_i{=}1\to\Omega_a h^2\approx0.03$ , the standard value) gives $\Omega_a h^2\approx0.66$ at the predicted $\theta_i\approx170^\circ$ — $\sim$ 5.5 $\times$ above $\Omega_{\mathrm{DM}}=0.12$ , reached only at $\theta_i\approx106^\circ$ . The over-production is thus confirmed (not the optimistic “all-DM”); tfpt_4_frontier, v185 docstring and the website updated accordingly. Stays [C]; kills only the axion-as-dominant-DM branch.

2026-06-14

work packages A+B: attacking $\omega\circ\rho=\omega$ + the variational scan — v199, v200

v199_seam_state_invariance.py [E]/[O](claim QGEO.STATE.01, work package A). Attacking $\omega\circ\rho=\omega$ directly on the raw seam. (1) [E]the setup is non-circular: $\rho$ is the Coxeter element of $W(A_3)=S_4$ ( $\rho^4=1$ , v117), an automorphism of the raw CAR algebra (16 Majoranas) — both carrier-side, no seam geometry. (2) [E]for a quasi-free RP state $C_\Sigma=\tfrac12(1{+}\operatorname{sgn}H_1)$ , so $\omega\circ\rho=\omega\Leftrightarrow[\rho,H_1]=0$ . (3) [E] $[\rho,H_1]=0\Leftrightarrow H_1$ is block-diagonal in the four $\mu_4$ -character classes $\{n{=}r\bmod4\}$ (verified). (4) [O]the residual is sharpened to “the bounded sub-principal symbol has no off-character matrix elements” — a bounded, finite-character condition, not a diffuse geometry; not a closure. Cited in tfpt_research_contracts; Wolfram-mirrored.
v200_seam_variational_scan.py [C]/[O](claim QGEO.VARI.02, work package B). The discretised variational test: with the clock angle free, $E_{\mathrm{fail}}(\theta)$ has its unique minimum at $\theta=\pi/2$ (the $\mu_4$ clock $z\mapsto iz$ ) — order-4 and the three distinct characters $i,-1,-i$ = the $(1,2,3)$ grading; decoys ( $0,\pi,\pi/3,2\pi/3$ ) all lose. A numerical sign that the variational principle selects $\mu_4$ ; the full operator-valued minimisation stays the v199 residual [O]. Cited in tfpt_research_contracts.
Also (this pass, experiments/ only, not the ledger): the $F_{\mathrm{transfer}}$ four-pipeline scaffold (experiments/ftransfer/) with one CONTRACT per interface, and confirmation that the FRB preregistration (frb_tfpt_v1.yaml) and its status semantics already exist. Suite now 199 modules, highest ID v200; Wolfram extension $241/241$ .

2026-06-14

cracking the bedrock to a state-invariance: principal symbol $+$ Tomita–Takesaki — v198

v198_modular_commutator_reduction.py [O](claim QGEO.MODULAR.01). The decisive crack on the last residual. (1) [E]the DtN principal symbol $|k|=\sqrt{-\partial_\theta^2}=\mathrm{diag}(|n|)$ and the clock $\rho{:}z\mapsto iz=\mathrm{diag}(i^n)$ are both diagonal in the Fourier basis, so $[\rho,|k|]=0$ exactly on all of $L^2$ (verified on 33 modes) — the leading-order commutation is free on the whole boundary, never the open part. (2) [E]by Tomita–Takesaki the modular operator is intrinsic to $(M,\Omega)$ , so a state-preserving symmetry ( $\rho\Omega=\Omega$ ) commutes with $\log\Delta\sim\Lambda_\Sigma$ : hence $[\rho,\Lambda_\Sigma]=0$ follows from $\omega\circ\rho=\omega$ , using only the state $+$ reflection (RP) and no conformal covariance — which removes the v194 Bisognano–Wichmann circularity worry. (3) [E] the finite $H^1$ block is already $\mu_4$ -invariant (v177). So the entire residual collapses to the single state-invariance “the raw quasi-free seam state is $\mu_4$ -invariant” ( $\omega\circ\rho=\omega$ $\Leftarrow$ the Gaussian bulk measure is deck-invariant) — the maximally-operational, non-circular form of QGEO.SYM.01, [O]. Not a full closure (a foundational symmetry cannot be derived from nothing, like $c=\text{const}$ ), but the sharpest falsifiable form, with the circularity gone. Cited in tfpt_research_contracts; OpenGates updated. Suite now 197 modules, highest ID v198; Wolfram extension $240/240$ .

2026-06-14

three review levers: Marks-via-Lefschetz, E_fail functional, RR $\to$ D5 — v195–v197

v195_marks_lefschetz_character.py [E]/[O](claim QGEO.MARKS.02). The four seam marks are forced (not posited): $\rho{:}z\mapsto iz$ fixes only $\{0,\infty\}$ , $H^1= \chi_1{\oplus}\chi_2{\oplus}\chi_3$ (the $A_3$ exponents, $\operatorname{Tr}(\rho|H^1)=i{+}i^2{+}i^3={-}1$ ) has no trivial component $\Rightarrow$ no puncture at a fixed point, and $\operatorname{rank}H^1=n{-}1=3 \Rightarrow n=4 \Rightarrow$ a single free $\mu_4$ orbit (cross-ratio $2$ ). So Marks reduces from the geometric posit “ $D_4$ marks” to the milder premise “ $H^1$ carries the $A_3$ -exponent rep” — less circular, still [O]. Cited in tfpt_research_contracts.
v196_seam_energy_functional.py [E]/[O](claim QGEO.VARI.01). The failure functional $E_{\mathrm{fail}}=\|[\rho,\Lambda_\Sigma]\|^2_{HS}+\|\rho^4{-}1\|^2+\|\Theta\rho\Theta-\rho^{-1}\|^2$ , zero locus $=$ the QGEO.SYM.01 conditions; on the finite $H^1$ block it vanishes at the $\mu_4$ config [E]and is $>0$ for any $\mu_4$ -breaking perturbation, so $\mu_4$ is a true minimiser. The full-operator minimisation is the v194 Bisognano–Wichmann residual — a concrete discretisable target on the open bedrock, [O]. Cited in tfpt_research_contracts.
v197_rr_carrier_clifford_d5.py [E]/[C](claim ARCH.RRCAR.02). Hardens the Riemann–Roch carrier from $g_{\mathrm{car}}$ to $D_5$ itself: $\Lambda^{\mathrm{even}}(C_{\mathrm{car}}) =\binom50{+}\binom52{+}\binom54=16=2^{g_{\mathrm{car}}-1}=\dim S^+$ , the $\mathfrak{so}(10)=D_5$ half-spinor — so $D_5$ is the Clifford spinor of the $5$ -dim mode space, closing $\mu_4{\to}g_{\mathrm{car}}{\to}D_5$ . [E]arithmetic, [C]identification (as v189). Cited in origin_theory.
All three are validated external-review levers (the axion-hilltop “ $\pi-3\phi_0$ ” proposal was rejected as a $\pi\approx3$ coincidence, not built). Suite now 196 modules, highest ID v197; Wolfram extension $239/239$ .

2026-06-14

subclaim 2 of ENERGY.02 tackled: raw-seam-DtN RP-definability — v194

v194_raw_seam_dtn_rp.py [O](claim QGEO.DTN.01). The next hard lever — “is the raw RP-seam DtN definable from RP data alone?” (sub-claim 2 of QGEO.ENERGY.02) — was tackled, and the honest result is a reduction, not a closure. (1) [E]the commutator $[\rho,\Lambda_\Sigma]=0$ closes on the finite cohomology $H^1$ ( $\rho^*w_k=i^k w_k$ , distinct $\mu_4$ characters; v177). (2) [E]the hinge is met: the DtN/transfer operator is RP-canonical (Osterwalder–Schrader, v54) on a quasi-free seam state (v155), so $\Lambda_\Sigma$ is RP-definable without naming $\PP^1\!\setminus\!\mu_4$ . (3) [O]the residual relocates: the full- $L^2$ commutation $\Leftrightarrow$ Bisognano–Wichmann geometric modular flow of the quasi-free seam state (which must be intrinsic, else it re-circulates). So QGEO.SYM.01 reduces from a definitional postulate to “intrinsic BW geometric modular covariance” — one notch sharper, still [O]; the last structural fog point sharpens, it does not close to [E]. Cited in tfpt_research_contracts; OpenGates updated. Suite now 193 modules, highest ID v194.

2026-06-14

QGEO.ENERGY.02 energy-commutator + QFT-wording hardening — v193

v193_qgeo_energy_commutator.py [O](claim QGEO.ENERGY.02). The non-circular sharpening of QGEO.ENERGY.01: the energy commutator $[\rho,\Lambda_\Sigma]=0$ on the rank- $8$ Calderón polarisation, with three sub-claims — (1) [E] $\rho$ is carrier-defined (Coxeter of $W(A_3){=}S_4$ , v117), not imported from the seam; (2) [O] the non-circularity hinge: $\Lambda_\Sigma$ must be the raw RP-seam DtN, not the $\mu_4$ normal form; (3) [E]the commutator forces the $(1,2,3)$ grading on $H^1$ (QGEO.COHOM.01). Exact [E] rider (Wolfram-mirrored): the induced EH coefficient $k=(\ln m)/(12\pi)$ (v150) reproduces $c_3/2$ iff $\ln m=q(A_3)=\tfrac34$ (family), not $q(D_5)=\tfrac54$ (carrier, off by $5/3$ ) — gravity is family-geometry-induced. A proof target; if sub-claim (2) holds, QGEO.SYM.01 becomes an energy-rigidity theorem. Cited in tfpt_research_contracts. Suite now 192 modules, highest ID v193; Wolfram extension $236/236$ .
QFT-wording hardening (review point 7). tfpt_2_standard_model (4) was retitled to “Constructive QFT closure of the admissible physical sector”, and its standalone opening over-claim replaced by an explicitly scoped sentence (the unprojected ambient metric measure is not constructed; $G_{\mathrm{metric}}$ frontier). The two superseded standalone phrasings were added to the v188 prose guard so a frozen release cannot re-introduce them.

2026-06-14

geometry round: Riemann-Roch carrier, Nariai bound, branch line, energy clock — v189–v192

v189_riemann_roch_carrier.py [E]/[C](claim ARCH.RRCAR.01). The pair $(\gcar,\Nfam)=(5,3)$ are the two canonical invariants of one object, the four-point seam divisor $D=\mu_4$ on $\PP^1$ : the cycle side $\operatorname{rank}H_1(\PP^1\!\setminus\!\mu_4)=\deg{-}1=3=\Nfam$ (already QGEO.COHOM.01) and the function side $h^0(\PP^1,\mathcal O(\mu_4))=\deg{+}1=5=\gcar$ , matched by $\operatorname{rank}(D_5)=5$ . The carrier-as-mode-space reading is [C](geometric, does not displace the over-determined $\gcar=5$ ). Cited in origin_theory; Wolfram-mirrored.
v190_nariai_entropy_bound.py [E](claim HOR.NARIAI.02). A variation-free one-line proof of the SdS entropy floor: $3(x^2{+}1)-2\Phi_3(x)=(x{-}1)^2\ge0$ , so $S_{\mathrm{tot}}\ge\tfrac23 S_{dS}$ with equality iff $x=1$ (the Nariai merge). Cited in tfpt_horizon_readouts; Wolfram-mirrored.
v191_universal_branch_line.py [C](claim HOR.BRANCHLINE.01). The affine map $q=\tfrac72+\tfrac{\Nfam^2}{2}m$ carries the SdS branch points ${\pm}1/\Nfam$ onto the flavor labels $\{2,5\}$ . Honestly typed [C] — an exact relabeling, not a theorem (a decoy pair $\{3,4\}$ admits an equally exact map; the shared content is the known $2/3$ ramification). Cited in tfpt_horizon_readouts; Wolfram-mirrored.
v192_qgeo_energy_clock.py [O](claim QGEO.ENERGY.01). An operator-checkable restatement of the bedrock: $\rho^*\Lambda_\Sigma\rho=\Lambda_\Sigma$ (the clock preserves the DtN energy form). Honestly typed: it relocates QGEO.SYM.01 to a more falsifiable surface but does not eliminate it (plausibly equivalent unless $\rho$ is independently defined and the invariance proven). Cited in tfpt_research_contracts. Suite now 191 modules, highest ID v192 (v186 skipped).
All four are validated external-review proposals (problem_b); each is built with the honest typing determined on review — the branch line is recorded as an alignment, not a theorem, and the energy clock as a relocation, not a closure.

2026-06-14

Zenodo release 5.1 (rev 120) — F_transfer firewall, v184–v188

Published to Zenodo. Version 5.1 (rev 120) of the ten-PDF document set was published as a new version of the TFPT deposit — record 20687564, DOI 10.5281/zenodo.20687564. This version carries the F_transfer-firewall round (v184–v188): the honest $\eta_B$ anchored-Boltzmann test (sharper scenario, not a closure), the axion hilltop-relic typing, the ledger v187 and prose v188 guards, and the Route B/Koide/dark-matter wording fixes plus the P1/P2-vs-QGEO.SYM.01 two-layer clarification. The uploader's DEFAULT_RECORD_ID was advanced to the new record for the next release. Suite 187 modules (highest ID v188; v186 skipped). run_all.py green, audit clean, website built.

2026-06-14

F_transfer round: eta_B honest test v184, axion relic v185, discipline guard v187

v184_etaB_anchored_boltzmann.py [C](claim FR.ETAB.03). An honest test of the external-review $\eta_B$ proposal ( $M_1=M_R\varphi_0^4$ , $\tilde m_1=m_3/A_\Lambda$ ). Firewall verdict: sharper scenario, not a closure. The washout anchors plausibly ( $\tilde m_1=m_3/10\approx5$ meV, $A_\Lambda=10$ atom, in the strong-washout window) [C]; but $M_1$ does not — $M_R$ is the seesaw scale $\sim v^2/m_3$ and the nearest clean TFPT powers of $\bar M_{\mathrm{Pl}}$ both miss it ( $c_3$ -/ $\varphi_0$ -powers off ${\sim}75\%$ / ${\sim}40\%$ ), so $M_1=M_R\varphi_0^4$ merely relocates the free input. $\eta_B$ stays [C], the route viable but with one (not zero) free input. Cited in tfpt_4_frontier.
v185_axion_relic_solver.py [C](claim FR.DM.03). Honest misalignment estimate: the determinant-line axion $f_a=M_{\mathrm{scal}}/128\approx2.39{\times}10^{11}$ GeV ( $m_a\approx23.8\,\mu$ eV) CAN be all dark matter, but the harmonic misalignment under-produces ( ${\sim}21\%$ at $\theta\sim O(1)$ ), so the $\theta_i\approx170^\circ$ hilltop anharmonic enhancement is required — where the relic is exponentially sensitive. Hence a [C]scenario, not a sharp prediction; the relic contract is a kill test for the BRANCH, not the theory. Cited in tfpt_4_frontier.
v187_ftransfer_laws.py [E](claim FR.TRANSFER.01). A CI-style firewall guard: the four continuous-transfer frontier observables (Koide, $\eta_B$ , axion, $m_p/m_e$ ) are read from the ledger and required to carry a [C]/[O]marker — never a primitive [E]compiler prediction (exact sub-parts like the Koide $53/54$ factor or $b_3=-7$ may be [E], the physical prediction never is). Records the four interfaces $F_{\mathrm{pole}}/F_{\mathrm{Boltzmann}}/ F_{\mathrm{relic}}/F_{\mathrm{QCD}}$ ; prevents any future edit from quietly promoting a frontier number to a closed output. Cited in tfpt_4_frontier.
v188_frontier_wording_guard.py [E](claim AUDIT.WORDING.01). A prose sentinel (no new physics): v187 protects the ledger typing, this guard protects the prose. It scans the 10 active documents and forbids five stale phrasings whose semantics earlier rounds superseded (the old [E]-typed Route B leptogenesis claim and its heavy-scale wording $\to$ v184 [C]; the old “open relic scale” dark-matter line $\to$ v185; the old “near, not exact” Koide line $\to$ v183; and the module-count/ID conflation), so a frozen Zenodo release can never re-introduce wording that was true yesterday and is half-true today. The same pass updated the tfpt_4_frontier Route B (to [C]), the Koide and dark-matter summary lines, and added the P1/P2-vs-QGEO.SYM.01 two-layer clarification to the introduction. Suite now has 187 modules, highest verification ID v188 (v186 was intentionally skipped as redundant — $m_p/m_e$ is already typed [O]as a QCD matching contract, QCD.LAMBDA.01).
Review framing points (P1/P2 as projections of the seam-deck postulate, $v_{\mathrm{geo}}$ as unit gauge, $G_{\mathrm{net}}$ a corollary of QGEO.SYM.01, grammar tuning $=$ data) were validated as already implemented in the prior rounds; $m_p/m_e$ is already typed [O]as a QCD matching contract (QCD.LAMBDA.01), so no redundant module was added.

2026-06-14

operator origin of the Koide 53/54 factor: the missing Sheet-Diamond corner, v183

v183_koide_f_corner_transfer.py [E]/[C](claim FR.KOIDE.07). An external-review proposal, validated exactly: the Koide source $\to$ pole factor $\tfrac{53}{54}$ is not a bare arithmetic guess but an operator identity on the carrier, $u_{\mathrm{pole}}/u_{\mathrm{source}} = a^T(R+Q)\mathbf1 / (2\,\mathbf1^T R a) = 53/(2{\cdot}27) = \tfrac{53}{54}$ . Here $\mathbf1^T R a = 27$ is the $E_6{\times}A_2$ cubic family block ( $248 = \dim E_6 + \det R + 2(\mathbf1^T R a)\Nfam = 78+8+2{\cdot}27{\cdot}3$ ) and $a^T(R+Q)\mathbf1 = 53 = 52+1$ , where $F = R+Q$ is the missing Sheet-Diamond corner with $\det B_F = 52 = \dim F_4$ (v80). Hard negative control: $a^T M\mathbf1$ for $M\in\{R,Q,K,L\}$ is $\{32,21,35,56\}$ — only the absent corner $F$ gives $53$ . This upgrades FR.KOIDE.03 from “near miss $+$ conjecture” to “operator-sourced source $\to$ pole transfer”: the factor is [E](exact, mirrored in Wolfram, $232/232$ ); the mechanism (the leptonic source $\to$ pole transfer reads the $F$ corner) stays [C], an $F_{\mathrm{transfer}}$ special case. The prediction itself stays [C]. Cited in tfpt_4_frontier (Koide section). Suite now 183 modules.
Review point 2 noted as already-present: the claim that flavor and Nariai share one double-cover ClockFunctor (flavor rate $(2/3)^{2\Nfam}$ vs gravity curvature $(2/3)^{\Nfam}$ , exponent ratio $|\Z_2|$ , “one clock, two geometries”) is exactly HOR.TRISECT.01/v103 — a rediscovery of an existing result, no new module.

2026-06-14

review recommendations 1/3/4 + the four concerns A–D mapped to the named residuals

v182_reviewer_residual_map.py [E]/[C](claim REVIEW.MAP.01). A careful external review raised four concerns (A mapping $2D\!\to\!4D$ , B UV-gravity abstractness, C grammar-tuning/meta-look-elsewhere, D Koide Möbius flow). This module shows three of them reduce, by the same discipline as v175–v181, onto the two already-named residuals $\{\texttt{QGEO.SYM.01},F_{\mathrm{transfer}}\}$ : A (Plücker- $11$ $=$ QBL boundary count v174 $+$ holographic reduction), B ( $\equiv$ QGEO.SYM.01), D (Möbius forced by $\mathrm{Aut}(\PP)=\mathrm{PSL}(2,\mathbb C)$ on the deck; the missing generator $=F_{\mathrm{transfer}}$ ). Only C is genuinely experiment-only (frozen $+$ minimal $+$ over-determined grammar; residual falls to JUNO/CMB-S4). A unification of the concern structure, not a closure. Cited in tfpt_5_redteam. Suite now 182 modules.
Review recommendation #3 — a “Rosetta” translation lexicon (website RosettaLexicon): TFPT's compiler-speak (seam, deck, readout, microcode, audit hull, gap, anchor, $F_{\mathrm{transfer}}$ , $v_{\mathrm{geo}}$ , QGEO.SYM.01) mapped onto standard QFT / mathematical-physics language (Wilsonian boundary CFT, orbifold deck, index/intersection number, RG irrelevance rate, renormalization condition, fundamental postulate) — a reading aid for mainstream physicists, not a new claim.
Review recommendation #1 — kill-tests up front (website TrustContract): the frozen pre-data predictions (sin $^2\theta_{12}=0.3067$ , JUNO; $r\approx0.004$ , CMB-S4) and the null model ( $P\le10^{-30.7}$ ) are now a prominent strip directly under the hero.
Review recommendation #4 — the bedrock as a postulate. QGEO.SYM.01 is now framed confidently as TFPT's one fundamental postulate (the role “ $c=$ const” plays in relativity), not a gap — in the tfpt_research_contracts box and the website “what is open” card; the achievement is that the whole theory is compressed onto exactly one sharply-located, falsifiable premise.

2026-06-14

external-review response: CSV fix, G_net 3-level, QGEO.SYM.01 page, claim detox

Ledger CSV bug fixed + guarded. Three rows (AX.P1.01, AX.P2.01, QGEO.ISO.01) had unquoted commas in a status/external field (e.g. “a=(1,1,2)”, “PSL(2,C)”), so a strict CSV parser read 11–12 columns instead of 10 — a real machine-readability defect in the single source of truth. All offending fields are now quoted (every row parses to exactly 10 columns), and audit_sync.py gained a check_csv_wellformed guard (ledger, registry, clusters, freeze must all parse to constant width) so it cannot regress.
$G_{\mathrm{net}}$ typed in three explicit levels (website “What is open” card): (1) algebra [E] $(D_5)_1{\otimes}(A_3)_1{\rtimes}\langle(1,1)\rangle\cong(E_8)_1$ ; (2) AQFT machinery [E](net existence $+$ full-cone RP, CAR functor, v175); (3) seam instantiation [O](QGEO.SYM.01). The target object's mathematics is closed; only the physical coupling of the raw seam is open.
QGEO.SYM.01 now has its own one-page box in tfpt_research_contracts: what is identified, why it is weaker than CONF/ISO, what follows automatically (the conditional theorem), and what would falsify it (genus $>0$ double; non-deck transport; $\Nfam\neq3$ ); with the explicit conditional framing “given QGEO.SYM.01, the closure follows” rather than “the theory derives the seam geometry”.
Claim-language detox. “no free fundamental number” softened to “no free dimensionless compiler dial beyond the anchor and $\pi$ (dimensionful scale $+$ transfer physics stay typed)” (origin_theory, introduction, website); the site title softened from “the Standard Model Derived” to “the Standard-Model Skeleton Derived”.
External-reviewer map added to the website verification page: four boxes (exact kernel [E], conditional physics [C], open premises [O], kill tests [X]) so a reviewer sees the attack surface without reading 181 scripts. Suite unchanged at 181.

2026-06-14

Zenodo release 5.1 (rev 114) — v175–v181 bedrock + figures + P1/P2

Published to Zenodo. Version 5.1 (rev 114) of the ten-PDF document set was published as a new version of the TFPT deposit — record 20686284, DOI 10.5281/zenodo.20686284. This version carries the AQFT-closure-to-bedrock chain (v175–v181, the structural residual reduced to the single definitional premise QGEO.SYM.01), the two overview figures (residual_chain, script_timeline), and the P1/P2 anchor-reduction provenance on the axiom surfaces. The README and the Zenodo description were refreshed (181 modules), and the uploader's DEFAULT_RECORD_ID was advanced to the new record for the next release.

2026-06-14

overview figures + P1/P2 reduction reflected on the axiom surfaces

Two overview figures (make_figures.py; PDF $+$ website PNG). (i) residual_chain — the structural-residual reduction chain v175–v181 as a descending staircase from “build a quantum-gravity measure” to the single definitional bedrock QGEO.SYM.01; embedded in tfpt_research_contracts. (ii) script_timeline — the eight-phase journey of the $\sim$ 181 scripts (foundations $\to$ SM readouts $\to$ seam $=$ horizon $\to$ horizon/flavor geometry $\to$ R1–R5/premise-(A) $\to$ PyR@TE cross-checks $\to$ AQFT bridges $\to$ AQFT closure), what each did mathematically and physically; embedded in introduction ahead of the master script index, and both shown on the website verification page.
P1/P2 reduction now reflected on the axiom surfaces. The reduction of the two axioms to the single parabolic anchor $a=(1,1,2)$ plus $\pi$ (with $g_{\mathrm{car}}=5$ an over-determined bootstrap fixed point — forced three ways, v6, Pascal-unique and Lean-formalised, FORM.LADDER.01) was already established (ANCHOR.GEN.01/v23, ARCH.CORE.01/v53) and stated in the papers/glossary, but the axiom surfaces still read as bare “declared inputs”. Fixed: the ledger rows AX.P1.01/AX.P2.01 now carry the anchor/bootstrap reduction and point to it, and the website dependency-graph nodes P1/P2 now show the anchor input ( $c_3=1/(2e_1(a)\pi)$ ; $g_{\mathrm{car}}=e_2(a)$ , bootstrap-forced) rather than “declared axiom”. No marker change (still declared inputs), only honest provenance.
Manifests refreshed (two new figures added to the FIG list). Suite unchanged at 181.

2026-06-14

the final reduction to bedrock v181 + full non-changelog status sweep

v181_clock_is_conformal_symmetry.py [E]/[O](claim QGEO.SYM.01). The isometry premise QGEO.ISO.01 (v180) is weakened one more genuine step — to a conformal-symmetry premise — via equivariant uniformisation (Nielsen realisation; for cyclic groups Kerékjártó $+$ uniformisation): a conformal automorphism (strictly weaker than an isometry — every isometry is conformal, conformal allows any positive scale) already suffices to put the order- $4$ clock in the form $z\mapsto iz$ . Since the clock is the Coxeter element of $W(A_3)=S_4$ (v117), the $\mu_4$ deck, and a deck transformation preserves the pulled-back conformal structure by definition, the residual collapses to the definitional identification QGEO.SYM.01: “the seam's conformal structure is the $\mu_4$ -deck structure of the carrier clock”. This is bedrock — a physical/definitional statement tying P2 to the seam's conformal geometry, not a finite computation and not reducible further without relabeling. The chain REALIZE(v175) $\to\dots\to$ SYM.01(v181) ends here; we stop honestly. Python-only. Suite now 181 modules.
Full non-changelog status sweep. The current bedrock framing was propagated to every live status surface (not just the changelog): the introduction “latest reductions” prose, tfpt_5_redteam Target A, the tfpt_research_contracts central-theorem keybox, origin_theory; and on the website OpenGates, VerificationDag, papers.ts (Target A $\times2$ , $G_{\mathrm{net}}$ ), the glossary $G_{\mathrm{net}}$ entry and the faq live-residual answer — all now end at QGEO.SYM.01.

2026-06-14

the conformal premise reduces to a milder isometry premise v180

v180_clock_is_mobius.py [E]/[O](claim QGEO.ISO.01). Cracks QGEO.CONF.01 one level further: the conformal-realisation premise is replaced, via three classical theorems, by a strictly milder, non-circular premise. (1) Uniformisation (Poincaré–Koebe): a genus- $0$ Riemann surface is conformally $\PP$ , so the genus- $0$ seam double (P1, v179) with its RP-metric conformal structure is $\PP$ — the target is produced, not assumed; (2) Kerékjártó (1919; Constantin–Kolev 2003): a finite-order orientation-preserving homeomorphism of $S^2$ is conjugate to a rotation, so the order- $4$ clock ( $h(A_3){=}4$ ) is topologically $z\mapsto iz$ ; (3) isometry $\Rightarrow$ conformal $\Rightarrow$ Möbius: an orientation-preserving isometry of a Riemannian surface is holomorphic, $\mathrm{Aut}(\PP)=\mathrm{PSL}(2,\mathbb C)$ ; (4) an order- $4$ Möbius map is $z\mapsto iz$ (verified: projective order $4$ , fixed $\{0,\infty\}$ , multiplier $i$ , free orbit $\mu_4$ ). Hence QGEO.CONF.01 is implied by the milder premise QGEO.ISO.01: “the carrier clock is an order- $4$ orientation-preserving isometry of the RP seam metric” — which does not name $\PP/\mu_4$ (uniformisation produces them) and is the natural statement that the seam transport is metric-compatible (a holonomy preserving the RP inner product). That milder premise is the single, now milder, structural residual of the whole theory; its surface realisation from the raw seam stays honestly [O]. Cited in tfpt_research_contracts; Python-only. Suite now 180 modules.

2026-06-14

the two obligations collapse to ONE geometric premise v179

v179_conformal_realisation.py [E]/[O](claim QGEO.CONF.01). Investigating the two residual premises left by v178 shows they are not independent — they collapse onto a single geometric premise (honest unification; the premise itself stays [O]). Marks's residual is not three independent assumptions: (1) genus- $0$ is P1 — the one-sided Gauss–Bonnet $c_3=1/(|\Z_2|\,2\pi\,\chi(S^2))=1/(8\pi)$ uses $\chi(S^2)=2$ and $\chi=2-2g\Rightarrow g=0$ , so “genus- $0$ ” is the same $\chi=2$ that gives the “ $8$ ” in $c_3$ (v58/v73); (2) the order- $4$ clock is the carrier — the Coxeter element of $W(A_3)=S_4$ (v117), order $h(A_3)=4=|\mu_4|$ ; (3) marks $=$ one orbit is forced (the parabolic marks are not the two elliptic fixed points, a free order- $4$ orbit has exactly $4=e_1(a)$ points). Kernel then follows from the same geometry (DtN symbol $|k|$ , Lee–Uhlmann v156; $c=8$ rigidity v158; the cusped-surface residual $=H^1=\mathbb C^3=\Nfam$ ). So the entire structural residual of the theory is the single geometric premise QGEO.CONF.01: “the raw RP seam normal double is conformally $(\PP,\mu_4)$ with the carrier clock as the order- $4$ Möbius automorphism”. The two doors of v177/v178 are one geometric realisation, left honestly [O]. Cited in tfpt_research_contracts; Python-only. Suite now 179 modules.

2026-06-14

an honest attempt at the two obligations v178 — deeper reduction, not closure

v178_marks_kernel_attempt.py [E]/[O](claim QGEO.REDUCE.01). An honest attempt at QGEO.MARKS.01 and QGEO.KERNEL.01. These are genuine constructive-geometry/AQFT statements, not finite computations — neither is closed. What the module does is push each as far as computation allows: it closes the finite [E]core of each and reduces each to one sharper premise. Marks core [E]: given a genus- $0$ double with an order- $4$ clock $\rho$ (fixed points $\{0,\infty\}$ ) and reflection $\tau$ , the marks are forced to be a generic $\rho$ -orbit $\{1,i,-1,-i\}=\mu_4$ (not the fixed points), distinct iff $b_1=4-1=3=\Nfam$ (any collision drops $b_1$ ), with $\tau\rho\tau=\rho^{-1}$ giving a faithful $D_4$ of order $8$ — so Marks reduces to the single topological/clock premise. Kernel core [E]: on the $3$ -dim multiplicity-free $H^1$ the $\mu_4$ characters $(1,2,3)$ are distinct, so by Schur a $\mu_4$ -equivariant operator is forced diagonal and completely determined by its eigenvalue per character; two such with the forced transfer spectrum $\{1,(2/3)^6,(1/3)^6\}$ (v162) and the unique residue-normalised basis (v177) are equal as operators, not merely isospectral — the spectrum-vs-operator worry vanishes on the finite block. So Kernel reduces to the single full-operator-reduction premise (principal symbol $|k|$ , Lee–Uhlmann/v156; no drift v158). Net: neither obligation closed; both sharpened to milder premises with their finite cores [E]. Cited in tfpt_research_contracts; Python-only (Möbius/Schur symbolic $+$ numeric). Suite now 178 modules.

2026-06-14

QGEO proof tree v177 — the residual sharpened into two named obligations

v177_seam_marking_kernel.py [E]/[O](claims QGEO.TREE.01, QGEO.MARKS.01, QGEO.KERNEL.01). A second external residual-class audit pointed out that the v176 statement takes the marks/ $D_4$ as a hypothesis — a near-circular trap. This module factors the central theorem honestly as $\textsc{Realize}=\textsc{Marks}\cdot\textsc{Uniform}\cdot\textsc{Cohom}\cdot\textsc{Module}\cdot \textsc{Kernel}\cdot\textsc{Net}$ and closes four nodes constructively (all validated symbolically before adoption): Uniform [E]— an order- $4$ Möbius map conjugates to $z\mapsto iz$ , a non-fixed orbit scales to $\mu_4$ , and $\sigma\rho\sigma=\rho^{-1}$ for $\sigma:z\mapsto1/z$ gives a faithful $D_4$ (order $8$ ), so a genus- $0$ four-marked faithful- $D_4$ boundary is $(\PP,\mu_4)$ (strengthening v168's cross-ratio to the full uniformisation); Cohom [E]— $\rho^*\omega_k=i^k\omega_k$ , grading $(1,2,3)=A_3$ exponents; Module [E]— a unique $\mu_4$ -equivariant iso (multiplicity-free $+$ residue normalisation; reflection $\omega_1\!\leftrightarrow\!\omega_3$ , $\omega_2$ fixed); Net [E](v154/v175). The structural residual is thereby sharpened from one diffuse premise into exactly two named open obligations, neither a finite computation: QGEO.MARKS.01 (the raw RP seam collar canonically produces the genus- $0$ four-marked $D_4$ boundary) and QGEO.KERNEL.01 (the raw seam Calderón operator is the $\mu_4$ -equivariant free gapped contraction, as an operator). Cited in tfpt_research_contracts (the central-theorem keybox); Python-only (Möbius/cohomology symbolic; numbers mirrored via v168/v137/v162/v154/v175). Suite now 177 modules.

2026-06-13

Seam Collar Realisation Theorem v176 — the one central proof obligation

v176_seam_collar_realisation.py [E]/[O](claim QGEO.REALIZE.02). Following an external residual-class audit, the single remaining structural item is formulated as one central theorem and certified as a reduction (not a fabricated proof). Theorem: given an oriented one-sided RP seam collar with a sheet-odd Calderón involution, faithful $D_4$ marks, four parabolic marks with $\mu_4$ decomposition and admissible $c{=}8$ data, its conformal boundary is Möbius-equivalent to $\PP\setminus\mu_4$ with $H^1$ grading $(1,2,3)$ , the Calderón contraction is the rank- $8$ $K_\Sigma$ polarisation and the index- $4$ extension is $(E_8)_1$ . The proof decomposes into six steps, five already [E]: geometry/uniformisation (v168), Calderón DtN symbol $|k|$ (v156), $H^1$ character $=$ generation grading $(1,2,3)=A_3$ exponents (v137/v168), $\mu_4$ -equivariant contraction with gap $(2/3)^6$ (v162), AQFT closure $(D_5)_1{\otimes}(A_3)_1{\rtimes}\mu_4=(E_8)_1$ $+$ full-cone RP all $m$ (v154/v175). The whole structural residual thus reduces to the one open premise QGEO.REALIZE.01: that the physical seam collar's boundary is this $\PP\setminus\mu_4$ — a constructive-geometry statement, left honestly [O]. Cited in tfpt_research_contracts (the central theorem keybox); assembly/reduction certificate, Python-only (its exact identities are mirrored via v168/v156/v162/v154/% v175). Suite now 176 modules. Audit note: the metrology residual the same review flags is already discharged — v153 (No-Unit Theorem) is the metrology-line typing ( $v_{\mathrm{geo}}\mapsto\lambda^{-1}v_{\mathrm{geo}}$ , $1/G\mapsto v_{\mathrm{geo}}^2$ , dimensionless data invariant), and the Koide $u\to\tfrac{53}{54}u$ source $\to$ pole transfer is already typed [C](FR.KOIDE.03); neither is re-derived.

2026-06-13

Zenodo release 5.1 (rev 105) — v174 + v175 + doc refresh

Published to Zenodo. Version 5.1 (rev 105) of the ten-PDF document set (introduction, origin_theory, tfpt_1–5, horizon, research_contracts, changelog) was published as a new version of the TFPT deposit — record 20681451, DOI 10.5281/zenodo.20681451. This version carries the AQFT closure round (v170–v175): the seam Fock-space readings and the heavy-artillery discharge of net existence $+$ full-cone reflection positivity to [E]. The README and the Zenodo description were refreshed to the current state (175 modules, Wolfram $116/116 + 231/231$ ), and the uploader's DEFAULT_RECORD_ID was advanced to the new record for the next release.

2026-06-13

the heavy artillery v175: net existence + full-cone RP discharged to [E]

v175_net_existence_full_cone.py [E]/[O](claim QFT.NETRP.01). The two structural residuals that the premise-(A) chain had relocated to already-open items — $A_2$ net existence and full-cone reflection positivity — are now discharged to a theorem, leaving the seam realisation as the single irreducible open premise (nothing fabricated). (1) Full-cone RP for all $m$ : the CAR second-quantisation functor $\Gamma(t)=\bigoplus_m\Lambda^m(t)$ lifts the one-particle seam contraction $t$ to the complete Fock space $\Lambda^\bullet(\mathbb R^{16})$ ( $\dim 2^{16}=65536$ ); by the exterior-power spectrum theorem every eigenvalue is a subset product of $\mathrm{spec}(t)$ , so all $2^{16}$ products lie in $[0,1]$ (a contraction $=$ full-cone RP), with eigenvalue- $1$ multiplicity $2^8=256$ (wedges of the rank- $8$ $K_\Sigma$ polarisation) and sub-leading $=$ the one-particle gap $(2/3)^6$ — so full-cone RP reduces for every $m$ (not only $m\le6$ , v161) to the one-particle contraction (Shale–Stinespring), discharging the v160 scope premise. (2) $A_2$ assembled $+$ verified: the $(E_8)_1$ character $E_4/\eta^8=1+248q+4124q^2+34752q^3+213126q^4+1057504q^5$ (level- $1=248$ , extends the order-4 v156 check by one order), the embedding $248=120+128$ , and the $E_8$ Cartan matrix even with $\det 1$ (the unique rank- $8$ even unimodular lattice, v83); the net exists by cited theorems (free-fermion net, lattice VOA, index- $4$ Q-system, v125). (3) Both then need the same input — the seam realisation QGEO.REALIZE.01 (finite half proven, v168) — which is a constructive-geometry/AQFT statement, not closeable by a finite computation, and is left honestly [O]. Net: net existence and full-cone RP become [E]; the one irreducible structural premise is the seam realisation. Cited in tfpt_research_contracts (premise (A) closure) and tfpt_5_redteam (Target A); the exact parts (Cartan unimodular, character order 5, functoriality integers) mirrored in the Wolfram extension (231/231). Suite now 175 modules.

2026-06-13

seam Fock-space readings v174: CAR cone, Witten index, g-theorem

v174_seam_fock_readings.py [E](claim QFT.FOCK.01). Three more exact audit bridges from the same source note. (1) CAR cone compression: the even CAR algebra of the 16 seam Majoranas has $\dim\Lambda^{\mathrm{even}}(\mathbb R^{16})=2^{15}=32768$ directions, but a quasi-free Bogoliubov transport reduces the whole cone to a $16$ -dim one-particle problem ( $2^{15}/16=2^{11}$ ) — the explicit count behind v161. (2) Witten index $=$ the Plücker norm $11$ : the four $\mu_4$ -corner fermions span a $2^4=16=\dim S^+$ Fock space; QBL ( $\deg\le2$ ) keeps $\sum_{k\le2}\binom4k=11=\dim S^+-\gcar$ , so $c_u/c_d=55/117$ reads a topological state-space dimension. (3) Affleck–Ludwig $g$ -theorem: $c_{UV}=5+3=8=c_{IR}((E_8)_1)$ , so $\Delta c=0$ forces an exact isometry — the boundary-entropy form of the v157/v158 rigid fixed point. Cited in tfpt_2 (Exterior Leg Lemma); mirrored in the Wolfram extension (230/230). Suite now 174 modules. (The categorical reframings in the source note remain framing, not asserted claims.)

2026-06-13

CFT/QFT bridges: slice compression v170, OS moment v171, trace-anomaly seed v172, Pfaffian CP v173

v170_diamond_slice_compression.py [E](claim E8.SLICE.01). E8 Slice Compression Lemma: the seven $E_8$ audit slices are one projection of two alphabets — anchor power sums $P=(3,4,6,10)$ ( $p_n=2+2^n$ ) and Sheet-Diamond determinants $(3,4,8,14,20,32)$ summing to $81=N_{\mathrm{fam}}^4$ . All seven $248$ -slices, the $K_4$ edge graph, and the row-budget cross $(7,11,13)+s(3,3,3)+t(1,2,3)$ follow; $78=\dim E_6=p_2(p_0+p_3)$ . Cited in tfpt_3 (slice atlas). Exact; reading is audit (anti-numerology).
v171_os_moment_cluster.py [E]/[C](claim QFT.OSMOMENT.01). Atomic OS Moment Lemma: $\operatorname{spec}(T)=\{1,64/729,1/729\}$ makes every correlator a positive moment sequence, so the OS Hankel matrices factorise as Vandermonde Grams (a clean RP certificate); cluster $729/665$ , $\xi=0.4111$ . Sugawara Gap Safety: $31=1+h^\vee(E_8)$ , $c((E_8)_1)=248/31=8$ , $\Delta_{\mathrm{eff}}=6\log\tfrac32-31/(4\pi^2)>0$ . Cited in tfpt_research_contracts (G5).
v172_trace_anomaly_seed.py [E](claim SEED.ANOMALY.01). The seed prefactor $\tfrac43$ is the halved $(E_8)_1$ Weyl anomaly: over the seam $S^2$ ( $\chi=2$ ) the $c=8$ trace anomaly is $c\chi/6=\tfrac83$ , halved by the one-sided $|\Z_2|$ to $\tfrac43=16/12$ . Plus QCD $b_3=7=$ scalaron exponent $48-41$ (confinement $\leftrightarrow$ inflation), and the Volkov–Wipf $-98/45=-2\cdot7^2/\dim(D_5)$ factorisation. Cited in tfpt_2 (seed).
v173_pfaffian_cp_car.py [E](claim FLAV.STRONGCP.02). Strong CP $\theta_{\mathrm{eff}}=0$ as Pfaffian reality in the self-dual $16$ -Majorana CAR model: $\{D,\Sigma\}=0$ pairs the spectrum, $\gamma_5$ -Hermiticity makes the Pfaffian real, and RP picks the positive branch. Cited in tfpt_2 (Strong CP section).
All four validated computationally before adoption; the exact identities (v170/v171/v172) are mirrored in the Wolfram extension (229/229). Suite now 173 modules. (The categorical reframings in the source note — compiler-as-single-functor, $E_8=K_0$ , GIT/monadic/Langlands — are recorded as framing, not asserted as machine-checked claims.)

2026-06-13

Zenodo release 5.1 (rev 97)

Published to Zenodo. Version 5.1 (rev 97) of the ten-PDF document set (introduction, origin_theory, tfpt_1–5, horizon, research_contracts, changelog) was published as a new version of the TFPT deposit — record 20678568, DOI 10.5281/zenodo.20678568. The uploader's DEFAULT_RECORD_ID was advanced to the new record for the next release. Also fixed build.sh zenodo on macOS bash 3.2 (empty-array expansion under set -u).

2026-06-13

QGEO rigidity theorem v168 + $\eta_B$ leptogenesis interface v169

v168_qgeo_rigidity.py [E]/[C]{} (claims QGEO.RIGID.01, QGEO.REALIZE.01). Hardens the finite half of the one remaining Tier-1 hinge GATE.QGEO (the seam $=$ flavour $=$ horizon identification). Exact, machine-checked: $\mu_4=\{1,i,-1,-i\}$ has cross-ratio $2$ and a faithful Möbius stabiliser of order $8=|D_4|$ ; $H^1(\mathbb P^1\!\setminus\!\mu_4)$ has rank $4-1=N_{\mathrm{fam}}=3$ ; and the forms $\omega_k=z^{k-1}dz/(z^4-1)$ ( $k=1,2,3$ ) are $\mu_4$ -eigenforms with characters $\chi_1,\chi_2,\chi_3$ of weights $(1,2,3)=$ A $_3$ exponents $=\operatorname{Spec}(Q_+)$ . So a genus-0 boundary with faithful $D_4$ , four parabolic marks and this $\mu_4$ -decomposition is Möbius-equivalent to $\mathbb P^1\!\setminus\!\mu_4$ — the QGEO Rigidity Theorem (QGEO.RIGID.01, [E]). The seam-collar realisation stays the one premise (QGEO.REALIZE.01, [C]). Mirrored in the Wolfram extension (226/226). Cited in tfpt_research_contracts (U0). Not a new structural class — it hardens the existing hinge (consistent with v167's completeness claim).
v169_etaB_boltzmann_interface.py [C]{} (claim FR.ETAB.02). Operationalises the Tier-3 $F_{\mathrm{transfer}}$ leptogenesis path. Type-I thermal leptogenesis $\eta_B\sim0.96\times10^{-2}\varepsilon_1\kappa_f$ (sphaleron $28/79$ ), fed by TFPT's normal-ordered neutrino spectrum and the predicted $\delta_{CP}=240^\circ$ . Over natural $M_1\in[3\times10^9,3\times10^{10}]$ GeV and washout, $\eta_B$ brackets the observed $6.1\times10^{-10}$ (a canonical point gives $6.0\times10^{-10}$ , untuned) — the route is viable. But $M_1$ /washout are scenario inputs, so $\eta_B$ stays [C]; if a precise solve excluded the window the leptogenesis route falls, not the theory (the downstream $\Omega_b$ readout is independent). Cited in tfpt_4_frontier (Route B). Python-only.

2026-06-13

Higgs quartic from the free seam: SM near-criticality explained, v166

v166_higgs_free_seam.py [E]/[C]{} (claim HIGGS.FREESEAM.01). A new prediction tying the Higgs mass to premise (A). The seam UV is the free chiral $c{=}8$ fixed point (v158, Gaussian, no relevant/marginal interactions), so the one marginal SM scalar coupling vanishes there: $\lambda(M_{\mathrm{seam}})=0$ and $\beta_\lambda(M_{\mathrm{seam}})=0$ — the Shaposhnikov–Wetterich double-criticality, here derived from the free seam, not assumed. Integrating the PyR@TE-confirmed two-loop SM RGEs from $M_Z$ up with the measured $(m_H,m_t)$ gives $\lambda(\bar M_{\mathrm{Pl}})\approx0.002$ and $\beta_\lambda(\bar M_{\mathrm{Pl}})\approx0$ : the famous SM near-criticality is a consequence of the free seam (2-loop sharpens $\lambda(\bar M_{\mathrm{Pl}})$ from ${\sim}0.022$ at one loop to ${\sim}0.002$ ). The double condition predicts $m_H\sim129$ – $134$ GeV; the same condition at the scalaron scale gives ${\sim}107$ GeV (too low), so the boundary condition lives at the reduced Planck scale (seam $=$ horizon $=$ Planck). Fills the Higgs-sector gap (was only $N_\Phi=1$ ); cited in tfpt_4_frontier.
PyR@TE-sourced: the reproducer's SM run supplies the two-loop $\beta_\lambda$ , reduced to top-only (verification/pyrate/sm_higgs_betas.txt). Suite now 166 modules. Python-only (numerical 2-loop ODE).

2026-06-13

PyR@TE $F_{\mathrm{transfer}}$ follow-ups: flavor scale-tagging v163, QCD scale v164

v163_rg_stability_flavor.py [E]/[C]{} (claim FLAV.RGSTAB.01). Scale-tagging of the flavor sector. The lepton-mixing seeds ( $\sin^2\theta_{12}=\tfrac13-\tfrac{\varphi_0}{2}=0.3067$ , $\sin^2\theta_{13}=\varphi_0 e^{-5/6}=0.0231$ ) are RG-stable: the PMNS running is $y_\tau^2$ -suppressed (the only mixing-rotating Yukawa term is $\tfrac32 Y_e Y_e^\dagger Y_e$ , PyR@TE SM RGEs), so $\kappa_\tau=y_\tau^2/(16\pi^2)\ln(M_{\mathrm{scal}}/M_Z)\sim1.8\times10^{-5}$ and $|\Delta\sin^2\theta_{ij}|\lesssim10^{-4}$ — two to three orders below precision. Seam value $=$ measured value; the $y_t^2$ -driven quark mass ratios ( $m_t/m_b\sim41$ ) by contrast carry a scale tag. Cited in tfpt_2 (solar/reactor angle box).
v164_qcd_scale.py [E]/[O]{} (claim QCD.LAMBDA.01). The QCD confinement scale is parameter-free from the carrier $b_3=-7$ (v159): running $\alpha_s(M_Z)=0.1179$ down (two-loop, $n_f$ thresholds) reproduces $\alpha_s(m_b)\simeq0.22$ , $\alpha_s(m_c)\simeq0.38$ and confinement at $\sim0.5$ GeV by dimensional transmutation — so the QCD-scale numerator of $m_p/m_e$ is independently sourced. The $O(1)$ proton/ $\Lambda$ factor is lattice, so $m_p/m_e=1836$ stays the honest “[O]— not forced” frontier ratio. Cited in tfpt_4_frontier.
Both are PyR@TE-backed (the reproducer now also extracts the SM Yukawa $\beta$ 's, verification/pyrate/sm_yukawa_betas.txt). Suite now 164 modules. Python-only (no Wolfram mirror: magnitude bound / numerical running).

2026-06-13

PyR@TE external cross-check of the $F_{\mathrm{transfer}}$ gauge inputs — v159

New module v159_pyrate_gauge_crosscheck.py [E]/[C]{} (claim EM.BUDGET.02). The one-loop gauge coefficients used by the transfer functor are confirmed by an independent third-party RGE generator. Feeding the carrier / Standard-Model field content into the textbook one-loop formula (GUT normalisation) gives $(b_1,b_2,b_3)=(\tfrac{41}{10},-\tfrac{19}{6},-7)$ , and PyR@TE 3 (arXiv:2007.12700, github.com/LSartore/pyrate) writes $\beta_{g_1}=(\tfrac{41}{10})g_1^3$ , $\beta_{g_2}=-\tfrac{19}{6}g_2^3$ , $\beta_{g_3}=-7g_3^3$ verbatim (plus the full standard 2-loop matrix). So $b_1=41/10$ is pinned three independent ways — carrier algebra $10b_1=\gcar 2^{\gcar-2}{+}1=41$ , the $U(1)$ hypercharge index $\sum\tfrac35 Y^2$ , and PyR@TE — and the split $10b_1=40_{\text{(ferm.)}}+1_{\text{(Higgs)}}=41$ reproduces the EM-budget Gate 1 of tfpt_2. Cited there with \veri; the gauge sector of $F_{\mathrm{transfer}}$ is thus not a free knob.
PyR@TE reproducer (not vendored). verification/pyrate/reproduce.sh clones PyR@TE on demand into experiments/pyrate (git-ignored), neutralises its interactive pdflatex end-command, runs the SM at one and two loops, and re-extracts the gauge $\beta$ functions; the committed evidence is verification/pyrate/sm_gauge_betas.txt. PyR@TE is the right external tool for the transfer/RGE gates (gauge running, and — with a seesaw model — the neutrino-Yukawa running behind $\eta_B$ ); it is not a tool for premise (A) (a 2d boundary-CFT question). Mirrored in the Wolfram extension; suite now 159 modules.

2026-06-13

terminal residual inventory: (A) no longer a structural class; one hinge + F_transfer + irreducible core, `v167`

New module v167_inventory_post_closure.py [E]/[C]. The terminal residual inventory (line v105 $\to$ v123 $\to$ v167), re-pinned after the (A)-chain. With (A) discharged (GATE.METRIC.16--19) the v123 five structural classes collapse: the seam clock (R1), the index- $4$ net (R2) and the $Q$ -realisation (R5) all merge into one Tier-1 hinge — the seam $=$ flavour $=$ horizon identification $=$ $A_2$ net existence (assembly of established net constructions) $+$ GATE.QGEO (seam boundary $=\PP\setminus\mu_4$ , cohomology $b_1{=}\Nfam{=}3$ ); the EH step (R3) folds into $v_{\mathrm{geo}}$ (v152) and the ambient measure into $G_{\mathrm{net}}$ (v76). Terminal structure: Tier 0 $=$ the irreducible core $\{\pi,v_{\mathrm{geo}}\}$ (a theorem, No-Unit v153); Tier 1 $=$ one hinge; Tier 2 $=$ folded; Tier 3 $=$ $F_{\mathrm{transfer}}$ , one functor with four typed conditional interfaces (Koide, $\eta_B$ , axion, $m_p/m_e$ ), $\eta_B$ carrying the most open computational room. Completeness: a sixth independent structural class — or a new irreducible — fails the script (ledger SYNTH.INVENTORY.03). A unification $+$ re-typing, NOT an unconditional proof. Python-only (reads the ledger).
Bookkeeping. Suite at $167$ modules, all green; Wolfram extension unchanged at $224/224$ ; origin_theory (residual-inventory keybox) and next.txt moved together.

2026-06-13

premise A maximal honest closure: A2 by assembly, R1 = GATE.QGEO, zero independent open gates, `v165`

New module v165_premise_a_closure.py [C]/[O]. Pins the two residual gates of the v160–v162 (A)-chain to their floor. $A_2$ (net existence) closes by assembly of established mathematics [C]: the $16$ free Majoranas give a free-fermion conformal net (Buchholz–Mack–Todorov), the holomorphic $c{=}8$ lattice net is $(E_8)_1$ (Frenkel–Kac–Segal / Dong–Xu / Kawahigashi–Longo), the $\mu_4$ extension is a Longo Q-system of index $4$ (v125), $\mu(B){=}16/16{=}1$ , $248{=}120{+}128$ , character $E_4/\eta^8{=}j^{1/3}$ (v156); the one TFPT-specific input (seam Calderón kernel $=$ free-fermion two-point function) is done via DtN $=|k|$ (v156/v157). $R_1$ (seam clock) reduces to GATE.QGEO [C]: a $\mu_4$ -equivariant flat gapped generator is unique ( $=A_0^\star$ , v115/v116), so the gap $(2/3)^6$ is forced and the residual is the one geometric identification “seam boundary $= \PP\setminus\mu_4$ ” $=$ GATE.QGEO (cohomology established, v137, $b_1{=}3{=}\Nfam$ ). Final accounting: by the No-Unit Theorem (v153) the irreducibles stay $\{\pi, v_{\mathrm{geo}}\}$ ; premise (A) $=$ ( $A_2$ assembly) $+$ ( $R_1{=}$ GATE.QGEO) $+$ the $\{\pi,v_{\mathrm{geo}}\}$ core, so it carries zero independent open gates and ceases to be its own gate — a unification and re-typing, not an unconditional proof (ledger GATE.METRIC.19). Python-only (numpy/sympy $+$ stdlib).
Bookkeeping. Suite at $165$ modules, all green; Wolfram extension unchanged at $224/224$ ; tfpt_research_contracts (premise-A keybox) and next.txt moved together.

2026-06-13

the final identification: premise A factors into the already-open A2 + R1, no new open content, `v162`

New module v162_seam_transport_identification.py [E]/[O]. Pushes the v161 residual as far as it rigorously goes and shows it carries no new open content. The one-particle symbol splits into a gap value $(\beta)$ and a fixed space $(\alpha)$ . $(\beta)$ is forced: a $\mu_4$ -equivariant generator is diagonal in the cusp basis (the deck average is the diagonal projection, $\sum_{k}U^kXU^{-k}=|\mu_4|\operatorname{diag}X$ for $U{=}\operatorname{diag}(1,i,-i)$ ; the commutant of $U$ is exactly the diagonal algebra), so its spectrum is the cusp weights $\operatorname{spec}(A_0^\star){=}\{0,\tfrac13,\tfrac23\}$ (v115) and the transfer eigenvalue $(1{-}\alpha)^{p_2}$ with $p_2{=}6{=}|R_+(A_3)|$ gives $\{1,(2/3)^6,(1/3)^6\}$ , gap $6\log\tfrac32$ — all carrier data; the lift to the $16$ Majoranas is the $A_3$ subnet grading (v137). $(\alpha)$ is the rank- $8$ Calderón polarisation of $\omega_k{=}|k|$ (v113/v156). Closure: with v160 $+$ v161, (A) closes given only $\mu_4$ -equivariance $+$ admissibility, whose two non-derived inputs are the already-open A2 (net existence, Kawahigashi–Longo) and R1 (seam clock, HOR.CLOCK). So premise (A) factors exactly into $A_2+R_1$ — it adds no independent open item and is closed conditionally on them (a unification, not an unconditional proof; ledger GATE.METRIC.18). Python-only (numpy/sympy $+$ stdlib).
Bookkeeping. Suite at $162$ modules, all green; Wolfram extension unchanged at $224/224$ ; tfpt_research_contracts (premise-A keybox) and next.txt moved together.

2026-06-13

the cone reduces to one particle: premise A's scope premise discharged to a 16-dim statement, `v161`

New module v161_one_particle_reduction.py [E]/[O]. Discharges the scope premise of v160 (“the transport is gapped on the full Schwinger cone”) via Bogoliubov second quantisation. A quasi-free transport is $T_\Sigma{=}\Gamma(t)$ , the second quantisation of a one-particle contraction $t$ on the $16$ -dim Majorana space; $\Gamma(t)$ acts on the degree- $m$ correlator sector as the exterior power $\Lambda^m(t)$ . Machine-checked: (1) $\operatorname{spec}(\Gamma(t)|_{\deg m}) ={}$ products of $m$ one-particle eigenvalues (compound-matrix theorem, all $m{=}0..6$ ); (2) the cone gap equals the one-particle gap — the sub-leading eigenvalue over the whole cone is $(2/3)^6$ exactly, so premise 5 on the cumulant space is premise 5 on the $16$ -dim space; (3) the eigenvalue- $1$ sector is $\Lambda^{*}$ of the fixed subspace (disconnected Wick powers), with uniqueness closed by v113 (one polarisation $\Leftrightarrow$ one vacuum); (4) quasi-freeness is forced — the $120{=}\dim\mathfrak{so}(16)$ chiral currents are the Bogoliubov generators and v158 makes every non-Gaussian deformation irrelevant. Consequence: v160's three full-cone premises collapse to ONE finite ( $16$ -dim) one-particle statement (seam symbol $=$ gapped Calderón Bogoliubov map, fixed $=$ rank- $8$ $K_\Sigma$ , gap $(2/3)^6$ ); all numbers supplied, only the physical identification (Kawahigashi–Longo class $=$ the A2 net residual) stays open — the infinite-dimensional cone is eliminated (ledger GATE.METRIC.17). Python-only (numpy $+$ stdlib).
Bookkeeping. Suite at $161$ modules, all green; Wolfram extension unchanged at $224/224$ ; tfpt_research_contracts (premise-A keybox) and next.txt moved together.

2026-06-13

premise A as a conditional fixed-point theorem; the load relocates to one scope premise, `v160`

New module v160_seam_gaussianity_from_pf.py [E]/[O]. Formalises the proposed closure of premise (A) (“the seam bulk is a reflection-positive free field”) as a fixed-point theorem and types it honestly. The exact parts: (1) a quasi-free state has all higher connected cumulants $\kappa_{2n}{=}0$ — verified by the signed set-partition/Pfaffian moment $\leftrightarrow$ % cumulant inversion on a concrete pure Majorana covariance (the v113 “one kernel $=$ net” property at the cumulant level); (2) a kernel-preserving transport fixes the whole quasi-free state by Wick functoriality; (3) the Perron–Frobenius dichotomy (a fixed $\kappa_{2n}$ is a second fixed ray $\Rightarrow$ breaks uniqueness; a non-fixed one decays by the gap) forces Gaussianity; (4) the qualitative claim needs only $\mathrm{gap}{>}0$ , the value $(2/3)^6$ only sets the rate. The honest residual: v56's gapped PF uniqueness lives on the three-dimensional scalar transfer spectrum $\{1,(2/3)^6,(1/3)^6\}$ , while the $16$ -Majorana seam already carries $\binom{16}{4}{=}1820$ and $\binom{16}{6}{=}8008$ higher-cumulant directions — so (A) reduces to the single internal, exact-testable statement “the admissible TFPT seam transport is primitive $+$ spectrally gapped on the full Schwinger cone, not only the readout spectrum of v56”, which the suite does not yet establish (ledger GATE.METRIC.16). Python-only (numpy $+$ stdlib); no new exact-identity content for the Wolfram mirror.
Bookkeeping. Suite at $160$ modules, all green; Wolfram extension unchanged at $224/224$ (v160 is numerical, Python-only); tfpt_research_contracts (the premise-A keybox) and next.txt moved together.

2026-06-13

changelog date-order audit + reorder pass

Changelog sort enforced. audit_sync.py now checks that every dated \subsection*{YYYY-MM-DD...} block in this file is non-increasing (newest first; range titles such as 2026-06-07 / 2026-06-08 sort by the later date). A manual prepend had left five 2026-06-12 entries above seven 2026-06-13 blocks — reordered; future mis-sorts fail build.sh audit as [B.changelog].

2026-06-13

premise A: the destination fixed point is provably stable, `v158`

The free chiral $c{=}8$ fixed point is provably stable (v158, exact dimension count). The finite core of (A)'s “reaches-the-fixed-point” residual: the chiral Majorana has $h{=}\tfrac12$ , the bilinear current $h{=}1$ , the quartic $h{=}2$ . The relevant window $0<h<1$ for bosonic deformations is empty, the $h{=}1$ currents are chiral (v157, not $(1,1)$ -marginal), and the lowest interaction (quartic, $h{=}2$ ) is irrelevant — so the fixed point is isolated and stable against all interactions. Premise (A) reduces to a basin-of-attraction statement with a proven stable target (ledger GATE.METRIC.15). Tooling note: PyR@TE (4d gauge-Yukawa RGEs) is the wrong tool for this 2d boundary-CFT residual, but the right tool for the $F_{\mathrm{transfer}}$ interfaces ( $\eta_B$ leptogenesis RGEs, gauge-coupling running, the $b_1{=}41/10$ cross-check).
Bookkeeping. Suite at $158$ modules, all green; Wolfram extension $224/224$ ; contracts / origin_theory / next.txt / website moved together.

2026-06-13

premise A reframed: freeness is a rigid boundary fixed point, `v157`

The free-bulk premise becomes a fixed-point property (v157, simplicity-first). Instead of postulating Gaussianity, three facts click: (i) the DtN/Calderón symbol is universally $|k|$ (Lee–Uhlmann — order- $1$ $\Psi$ DO, principal symbol $|\xi|_g$ ; interactions live in the irrelevant lower-order symbol), so the free dispersion is bulk-detail-independent; (ii) a holomorphic $c{=}8$ theory is rigid — every field has $\bar h{=}0$ , so no marginal $(1,1)$ field exists and the fixed point is isolated, with no knob for an interaction; (iii) the same $|\Z_2|$ that halves $8\pi$ in $\cthree=\tfrac1{8\pi}$ is the Ramond/GSO projection giving $\mu{=}1$ ( $248{=}120_{\mathrm{NS}}{+}128_{\mathrm R}$ ). With $(E_8)_1$ unique (v83), premise (A) shrinks from “prove the seam is Gaussian” to “the gapped ( $\Delta{=}6\log\tfrac32$ ) boundary flow reaches the holomorphic fixed point” — freeness then forced by rigidity, not fine-tuned (ledger GATE.METRIC.14).
Bookkeeping. Suite at $157$ modules, all green; Wolfram extension $223/223$ ; contracts / origin_theory / next.txt / website moved together.

2026-06-13

Route 3: the seam net constructed and $(E_8)_1$ verified, `v156`

The constructive route carried to its exact endpoint (v156). “ $B\cong(E_8)_1$ ” is no longer an assertion: the chiral seam net is built explicitly and the identification checked. (a) The Dirichlet-to-Neumann (Calderón) operator of the $2$ d Laplacian is the free chiral dispersion $\omega_k=|k|$ (harmonic extension $e^{ikx-|k|y}$ ); (b) $16$ free Majoranas give $c=8=5{+}3$ ; (c) the weight- $1$ currents are $248=120_{\mathrm{NS}}+128_{\mathrm R}$ ( $SO(16)$ bilinears $+$ Ramond spinor, Frenkel–Kac); (d) the holomorphic character $E_4/\eta^8=q^{-1/3}(1+248q+4124q^2+34752q^3+213126q^4) =j^{1/3}$ (verified by $q$ -series) — the $248$ at level $1$ is $\dim E_8$ , so the net is $(E_8)_1$ . Residual: exact given (i) the free-bulk premise (DtN $=|k|$ , v155) and (ii) the operator-algebraic existence of the net from the seam kernel (a Kawahigashi–Longo-type theorem, not a finite computation) — where TFPT meets constructive QFT, now sharply located (ledger GATE.METRIC.13).
Bookkeeping. Suite at $156$ modules, all green; Wolfram extension $222/222$ (the DtN $=|k|$ identity, the $(E_8)_1$ character $E_4/\eta^8=j^{1/3}$ and the $248{=}120{+}128$ split mirrored); contracts / redteam (Target A) / origin_theory / next.txt / website moved together.

2026-06-13

the seam-side identification reduced to one shared premise, `v155`

$G_{\mathrm{net}}$ 's last premise reduces to a single shared physical premise (v155, Python-only). The seam-side identification of the Simple-Current Extension Theorem (v154) splits (v110) into (a) “the Calderón involution is sheet-odd” (the double-cover deck, structural) and (b) “the seam $2$ -point kernel is quasi-free”. Part (b) is not independent: the boundary marginal of a reflection-positive Gaussian bulk is the compression $P\Gamma P$ of the covariance, and the compression of a contraction is a contraction — so the seam state is automatically quasi-free (Wick inherited). Hence (b) follows from “the seam bulk is a reflection-positive free field”, the same premise already load-bearing in the area law (v59) and the EH mechanism (v150/v151). The entire seam-side residual is therefore one physical premise, shared by $G_{\mathrm{net}}$ , the area law and R3 — not reducible by a finite computation, but no longer three separate items (ledger GATE.METRIC.12).
Bookkeeping. Suite at $155$ modules, all green; Wolfram unchanged at $221/221$ (v155 is numerical/numpy, Python-only); contracts / origin_theory / next.txt / website moved together.

2026-06-13

external review formalised: No-Unit Theorem + Simple-Current Extension Theorem, `v153`–`v154`

$v_{\mathrm{geo}}$ re-typed: the No-Unit Theorem (v153). Every load-bearing compiler datum is mass-dimension $0$ and invariant under a unit rescaling $L\mapsto\lambda L$ , whereas a mass / $1/G$ is not — so a dimensionless boundary compiler provably cannot select an absolute scale. $v_{\mathrm{geo}}$ is therefore an irreducible metrology primitive, not an open gap, and the three apparent residuals collapse onto it ( $U_{\mathrm{point}}\sim v_{\mathrm{geo}}$ , $1/G\sim v_{\mathrm{geo}}^2$ , $m/\mu=e^{3/4}$ a pure ratio); the irreducibles stay $\{$ one unit, $\pi\}$ (ledger ANCHOR.VGEO.02).
$G_{\mathrm{net}}$ stated as the central closing theorem (v154). The Simple-Current Extension Theorem: $A{=}(D_5)_1{\otimes}(A_3)_1$ extended by the isotropic glue $L{=}\langle(1,1)\rangle$ has $[B{:}A]{=}|L|{=}4$ , $c{=}5{+}3{=}8$ , $\mu(B){=}\mu(A)/|L|^2{=}16/16{=}1\Rightarrow$ holomorphic $\Rightarrow B\cong(E_8)_1$ ( $SO(16)_1$ excluded). Every algebraic ingredient is machine-checked (v89/v92/v125/% v143/v148); the only residue is the seam-side identification. Pulled to the front of tfpt_research_contracts, tfpt_5_redteam (Target A final form) and origin_theory (ledger GATE.METRIC.11).
Status surfaces re-typed (review): the canonical status card now reads $v_{\mathrm{geo}}$ as a metrology primitive, $G_{\mathrm{net}}$ as the simple-current extension $\cong(E_8)_1$ ([E]/[C]), and $F_{\mathrm{transfer}}$ as one functor with four typed interfaces — “not structural gaps”. The final one-line framing (dimensionless boundary compiler; irreducibles $\{\pi, v_{\mathrm{geo}}\}$ ; one seam-net theorem; frontier $=$ $F_{\mathrm{transfer}}$ ) is in origin_theory, the introduction, the README and next.txt.
Bookkeeping. Suite at $154$ modules, all green; Wolfram extension $221/221$ ; intro/README/origin_theory/contracts/redteam/status-card/website moved together.

2026-06-13

currency sweep: remaining old-series “Paper N” cross-references removed

No old-version framing left in the active docs. A consistency sweep found a residual layer of old-series “Paper N” attributions and removed them: four literal “Paper 6” references (tfpt_4_frontier leptogenesis/axion, tfpt_2 seam determinant), the old “Paper 4” (OS/admissibility) and “Paper 5” (APS/Hodge) references in tfpt_2, the old “Paper 3” transport-kernel attributions in tfpt_2, and the internal “Paper 1/2/4” cross-references in tfpt_3, tfpt_4 and tfpt_horizon_readouts — all rewritten as content-based phrasing (the flavor sector, the architecture document, the $E_8$ decoder, the anchor characteristic polynomial, etc.). The active documents now attribute results to the current documents / axioms / scripts only, as the workflow rule requires; the machine-checked sync (scripts $\leftrightarrow$ papers $\leftrightarrow$ ledger $\leftrightarrow$ website) was already current ( $152$ scripts, AUDIT OK).

2026-06-13

fifth round: the R3 normalisation is the dimensionful anchor, `v152`

R3: the $q(A_3)$ normalisation merges into the one anchor (v152). The replica EH coefficient is a log-ratio $k=\ln(m/\mu)/(12\pi)$ ( $\ln m$ alone is scale-ambiguous, only $m/\mu$ is physical); pinning $k=\cthree/2$ fixes the dimensionless ratio $m/\mu=e^{3/4}$ , and in $d{=}2$ that ratio is the induced Newton constant $1/G$ (v68). So $v_{\mathrm{geo}}$ (v78), $1/G$ (v68) and $m/\mu$ are one dimensionful anchor in three readings — the irreducibles stay $\{$ one scale, $\pi\}$ , and SEAM.THEOREM.01's residual reduces to the kernel-identification premise alone. Audit (not promoted): the log-ratio is numerically $\tfrac34=q(A_3)$ , the target value the anchor takes in seam units — not a derivation (ledger SEAM.EHMODEL.03).
Bookkeeping. Suite at $152$ modules, all green; Wolfram extension $219/219$ ; intro/README/origin_theory/next.txt/website moved together.

2026-06-12

Zenodo version label: semantic + git rev

Release version string. build.sh now writes tex-artefacts/release-version.txt as {TFPTversion} (rev {git count}) (matches \TFPTdatestamp without the date). scripts/zenodo_upload.py and build.sh zenodo/zenodo-publish use this label on Zenodo; cursor rules extended for when zenodo_description.html must move with deposit-facing changes.

2026-06-12

Zenodo API upload workflow

Automated Zenodo versioning. Added scripts/zenodo_upload.py and .github/workflows/ zenodo-release.yml: creates a new draft version of record 20579275 (DOI 10.5281/ zenodo. 20579275), uploads the ten active paper PDFs, refreshes zenodo_description.html, bumps the version from tex-artefacts/version.tex, and optionally publishes via GitHub Actions (ZENODO_TOKEN secret).

2026-06-12

Overleaf shadow mirror: tfpt5-shadow

One-way GitHub mirror for Overleaf sync. Added scripts/export-shadow.sh and .github/workflows/shadow-sync.yml: on every push to main, a filtered copy is pushed to sthamann/tfpt5-shadow (papers, tex-artefacts/, figures/, verification/, experiments/; excludes _archive/, website/, all *.pdf, .cursor/). $\sim$ 270 files / $\sim$ 3 MB — within Overleaf GitHub-sync limits.

2026-06-12

origin_theory style alignment + box reduction

Fewer boxes, embedded in text. origin_theory from $22$ to $16$ boxes: the narrative/interpretation callouts (“Why the interpretation is internally consistent”, “Dependency chain of the birefringence test”, “The precise reformulation”, “The three theses honestly graded”, “The whole story”, “One-line summary”) become run-in bold prose; the boxed reformulation becomes a keyeq. The exact result keyboxes (v53–v56, v101, v105, v113, …) and the master-principle / Seam–Horizon target boxes are kept.
Colour-marked module references + marker hygiene. \vref applied to the inline vN references; stale literal [A]/[I]/[L] markers in running text replaced by the 4-class [O]/[E].

2026-06-12

tfpt_5 / horizon / research-contracts pass + build hardening

Forked document-set box removed (horizon). tfpt_horizon_readouts carried a hand-written, stale copy of the document-set card (“five short documents”, missing tfpt_5) and the canonical \input{tex-artefacts/tfpt_docset}; the fork is deleted so the single-source card (all five papers $+$ three companions) appears once.
Fewer boxes, embedded in text. Narrative/result callouts converted to run-in bold prose (with the \veri{} citation moved out of the bold title into the body): tfpt_horizon_readouts from $22$ to $7$ boxes (the ten-box “clock” wall becomes prose); tfpt_research_contracts from $19$ to $10$ (the nine progress/result winboxes become prose, the named-theorem keyboxes kept); tfpt_5_redteam from $10$ to $9$ (the outcome summary; the per-target verdict boxes are kept as the structured red-team output).
Colour-marked module references + marker hygiene. \vref applied to the inline vN references in all three documents; the horizon “Scope/typing” marker line and a stale literal [A] in the research contracts updated to the 4-class markers.
Build hardening. build.sh now removes a document's .aux/.toc/% .out on failure, so a half-written cross-reference file from a crashed compile cannot poison the next build; artefacts are still kept on success.

2026-06-12

fourth round: the Calderón transfer answered — the BFK split, `v151`

R3: the Calderón/DtN kernel is conically clean (v151). Reflection doubling derives that the Kac corner constant is boundary-condition independent ( $C_N=C_D$ ), so by the Burghelea–Friedlander–Kappeler gluing ledger the conical deficit of the two-sided Calderón jump determinant vanishes identically ( $C_{\mathrm{cone}}(\gamma)-2C_D(\gamma/2)=0$ ): the seam-reduced effective action inherits the v150 EH form verbatim, with all of it localised in the local half-space determinants — the “Calderón version” demanded by v150 needs no separate derivation. SEAM.THEOREM.01 narrows to the $q(A_3)$ normalisation plus the standing kernel premise; the gate stays [O](ledger SEAM.EHMODEL.02).
Bookkeeping. Suite at $151$ modules, all green; Wolfram extension $218/218$ ; intro/README/origin_theory/next.txt moved together.

2026-06-12

third round: both normals anchor data; the R3 mechanism exists, `v149`–`v150`

R4 $'$ : both dual normals are anchor data (v149). In the cusp frame the torsion normal pairs to $(6,3,5)=(p_2,p_0,e_2)(a)$ — one anchor invariant per $Q_+$ line (the cusp matrix is unimodular, so this determines $n$ uniquely); with $d=\tfrac32a-2\cdot\mathbf1$ the dual normal pair is anchor data through and through. Equivalences to the $(2,8,121)$ frame data and the $w_0$ -lift exact. R4 $'$ residue $=$ one discrete assignment (ledger GATE.UWALL.14).
R3: the mechanism exists at the gapped-model level (v150) — the first movement on SEAM.THEOREM.01. The conical heat-trace deficit is exact and $t$ -independent (Cheeger image sum $(N^2{-}1)/(12N)$ ); for a gapped operator the $\zeta$ -regularised replica variation is finite and cutoff-independent, $\Delta\log\det'=2C(\gamma)\ln m$ , and its linearisation is the Einstein–Hilbert form $(\ln m/12\pi)\int\!\sqrt gR$ . The v73 normalisation becomes one exact target equation: $k=\cthree/2\Leftrightarrow\ln m=\tfrac34=q(A_3)$ (audit, not asserted). Remaining: the Calderón (boundary) version and that normalisation — the gate narrows but stays [O](ledger SEAM.EHMODEL.01).
Bookkeeping. Suite at $150$ modules, all green; Wolfram extension $217/217$ ; status surfaces (intro reductions $+$ card, origin_theory, contracts, next.txt, website) moved together.

2026-06-12

R1–R5 second round: every class at its floor, `v145`–`v148`

R4 $'$ : the pairing values are atom identities (v145). Reading the v139 lift structurally ( $n=w_0(\sigma)+|\mu_4|e_3$ , $w_0=$ the $A_3$ exponent duality), all three pairings become atom arithmetic — including the new closure $|\mu_4|+\gcar=\Nfam^2$ ( $4{+}5{=}9$ , $\sigma\perp w_0(a)$ ) and $\|\sigma\|^2=110=|\Z_2|\gcar\|\mathrm{Pl}(K)\|_1$ . R4 $'$ $=$ derive one map (ledger GATE.UWALL.13).
R5: the Möbius $D_4$ realisation (v146). The full dihedral symmetry $\langle z{\mapsto}iz,\,z{\mapsto}1/z\rangle$ of the seam curve acts on $H^1$ exactly as the integer model: $\iota^*$ is the exponent duality with parity $+1$ on the self-conjugate line ( $=T_A$ in the cusp basis, glue-swap parity), and $\Sigma$ is the $\delta\iota$ class — the premise reduces to the module identification itself (ledger FLAV.QGEO.07).
R1: the clock is a Gaussian zero-mode integral, and the bend is det $'$ -clean (v147). Variance ratio $(1-\alpha)$ (forced by norm $=$ area) gives the Born-squared ratio $(1-\alpha)^{p_2}$ , the $\ln$ series is the v127 ring sum; the two quantum weights share one Nariai geometry, so the bend $\log_{3/2}3$ carries no determinant correction — the v144 obstruction is localised to the $\alpha=0$ reference (ledger HOR.CLOCK.13).
R2: the NS/R sector census (v148). The untwisted (Neveu–Schwarz) module carries only the even discriminant classes (integer weights), so the odd $\mu_4$ simple currents have zero NS support — they are Ramond modules; the R zero-mode module ( $256$ ) splits $128{+}128$ into the odd sectors of the two Lagrangian glues: choosing the glue is choosing the R-projection ( $248=120_{\mathrm{NS}}{+}128_{\mathrm R}$ ); the one remaining net statement is irreducibly twisted-sector (ledger GATE.METRIC.10). Correction note (same day): the first version of v148 graded the Ramond labels by the sum $q_D{+}q_A$ (not the glue label) and called that module untwisted; the census was rewritten as above — conclusion unchanged, support corrected, the R-sector sheet split is new.
Bookkeeping. Suite at $148$ modules, all green; Wolfram extension $215/215$ (README $+$ GATE.WOLFRAM.02 $+$ website counter in lock-step); status surfaces (intro card, tfpt_1, origin_theory third update, next.txt) moved together.

2026-06-12

external review integrated: $\Lambda$ typing, marker migration, website parity

$\Lambda$ normalisation made unambiguous. The external review flagged the adjacent reduced/unreduced displays in origin_theory as a type trap (the formulas were individually correct — $\bar M_{\mathrm{Pl}}$ vs $M_{\mathrm{Pl}}$ — but easy to misread). Both normalisations are now shown explicitly side by side with their order counts ( $3/(4\pi^2)\Rightarrow120.147$ reduced; $3/(256\pi^4)\Rightarrow122.948=119.028+3.920$ unreduced) plus a typing note.
Stale references cleaned. “How each of the seven papers simplifies” $\to$ “How the legacy layers simplify (bridge map)” with the lead-in “(Paper 6)” reference replaced by the scalaron-reheating chain (v86); “(Paper6/7)” in the tfpt_3 bridge table reworded; the tfpt_1 “single remaining geometric input (H2)” passage and the tfpt_2 “single remaining input (U)” passage carry dated status updates pointing at the current decomposition (v118–v122, v139, v141, v142, v75).
Marker migration completed in the shared figures. The claim stack, anchor cockpit, $E_8$ glue, $2/3$ motif and $K_5$ figures (tex-artefacts/tfpt_figures.tex) now show the four public classes [E]/[C]/[O]instead of the legacy $[A]/[I]/[L]/[B]/[P]/[R]$ badges.
Red-team front table pulled to the final state. The Target-A residual column now states the one remaining statement (boundary-net holomorphy $+$ $c{=}8$ $\Leftrightarrow$ index- $4$ inclusion; v83/v87/v89, Lie-level realisation v143); the historical three-residual form is kept below, dated.
Website parity. The Red Team document is now a first-class entry (papers.ts number 5, slug redteam) and the changelog PDF a download row; Appendix H / Origin Theory / Research Contracts are labelled companions (never “Paper 5–7”); the marker system on every website surface migrated to $[E]/[C]/[O]/[X]$ (fine types named in prose; the script index keeps quoting the scripts' internal fine-grained typing); the verification page counters are live ( $144$ checks generated from the registry via lib/suite.ts, Wolfram $116/116+211/211$ — now guarded by the sync audit) and the reproduce block matches the current pipeline. The papers.ts section bodies of the affected papers carry the v141–v144 outcomes (sheet question: deck derived; $G_{net}$ : Lie-level realisation; resummed clock: in-family det-ratio cancellation; selector triangle: two line pairings).
Not adopted (recorded for transparency): the review's narrative reframings (anchor-algebra trilogy, “one seam clock” framing, one-page structure) and the front-matter/status-card layout changes are editorial decisions left to the authors; the claimed $\Lambda$ error was in fact a correct-but-treacherous notation switch (see above).

2026-06-12

R1–R5 attack round: four residual classes sharpened, `v141`–`v144`

R5 closed at the discrete level (v141, deck selection theorem). The v140 $\Z_3$ choice is derived: the established integer deck $G=T_A\Sigma$ (v97/v98) pairs the $Q_+{=}1$ cusp line with the self-conjugate character $2$ , so only the sheet-twisted assignment $(2,3,1)=\mathrm{chars}(-U)$ survives; the cusp exponential $i^{Q_+}$ is excluded (same spectrum, wrong grading pairing). Explicit conjugacy constructed; under $k\to-k$ only the established sheet $\Z_2$ flips. Consequence: Euler grading $=Q_+\!\circ\rho$ . GATE.QGEO keeps only its realisation premise — no discrete freedom left (ledger FLAV.QGEO.06).
R4 $'$ narrowed: three pairings $\to$ two (v142, frame integrality). Integer covectors in the $(\mathbf1,a,\sigma)$ dual frame form an index- $11$ sublattice ( $x-3y+z\equiv0$ mod $11$ ; the index is $\|\mathrm{Pl}(K)\|_1$ ); with $(x,y)=(|\Z_2|,\mathrm{rank}\,E_8)$ the $\sigma$ -pairing is forced $\equiv0$ mod $11$ , and primitivity forces the line parameter even. Cramer reductions for both line pairings recorded as restructuring (ledger GATE.UWALL.12).
R2 realised at the finite Lie level (v143, graded Frobenius). The $\Z_4$ -graded hull carries exact coset duality ( $-C_1=C_3$ ; Killing pairing nondegenerate per $g_k\times g_{-k}$ ), the glue average is exactly the carrier projector (index $4$ ), and each glue sector is one Weyl orbit (simple currents, fusion $=\mathbb C[\Z_4]$ ) — the v125 Q-system realised by the hull; residue $=$ one conformal-net statement (ledger GATE.METRIC.09).
R1's det-ratio step derived in-family (v144). $e_2$ -rigidity of the traceless SdS cubic gives $r_br_c=1-\Delta^2/3$ exactly; with the v132 anomaly the non-zero-mode determinant ratio is $(1-\Delta^2/3)^{4/3}$ — no first-order term in the horizon split (the v131 cancellation derived, not assumed); deficit coefficient $\tfrac{32}{27}=|\mu_4|(\tfrac23)^3$ (audit). Finite-weight absorption stays [C]with the $6\to\tfrac{14}3$ obstruction stated sharply (ledger HOR.CLOCK.12).
R3 attempted, honestly unchanged. No defensible computation landed for the seam-determinant $\to$ EH step (SEAM.THEOREM.01); the gate keeps its [O]typing untouched.
Wolfram mirror extended to v141–v144: extension file now $211/211$ (GATE.WOLFRAM.02 and the wolfram README updated in lock-step); Python suite at $144$ modules, all green.

2026-06-12

sync infrastructure: single-source script index, content maps, one audit

Single-source script index. The master script $\to$ check table (tex-artefacts/verification.tex) and the website ScriptIndex.tsx are now generated from one registry (script_registry.csv $+$ script_clusters.csv in verification/) by make_script_index.py; both targets carry a generated-file header and are never edited by hand.
Content maps without splitting the papers. verification/make_docs_map.py generates docs_map.csv (every paper section with line range, the vN scripts cited there, a content hash and a last-changed date) and website_map.csv (which website file mentions which scripts/documents) — the machine-readable enumeration of all sync surfaces.
One sync audit. verification/audit_sync.py bundles and extends the previous loose shell checks, now in both directions: suite $\leftrightarrow$ run_all.py $\leftrightarrow$ registry $\leftrightarrow$ ledger; every script cited in a paper body (the master index alone no longer counts); no stale \veri/\vref targets; every new module mentioned in this changelog; website mirror byte-identical (PDFs, scripts, release.ts hashes, version stamps); wolfram counts; overfull boxes. Frozen exceptions live in audit_baseline.json (remove-only).
Build pipeline. build.sh gains gen / website / audit / release steps; notes now regenerates the single-source surfaces first; website copies all active PDFs (now incl. tfpt_5_redteam.pdf and changelog.pdf, with new release.ts entries) and the vN scripts, and stamps version, date and git revision into website/lib/version.ts (shown in the site header) and release.ts.
Citation gaps closed. The audit immediately found three scripts cited only in the master index: v17 and v85 are now cited in their tfpt_2 sections (hexagonal resolvent; master cover), and two short \veri{v19} citations were expanded to the full script name. v91 (spine tetrahedron) had no paper section at all — it is now integrated: a keybox in tfpt_3 (“Three views of one spine”: anchor closure, edge/face products, volume $120$ , $K_6$ negative control, the tautology/sub-grammar caveats) and a closing note in the tfpt_1 Spine Quotient Lemma; the ARCH.SPINE.01 ledger location is corrected to tfpt_1;tfpt_3 and the baseline exception list is empty again.
Rules. .cursor/rules updated (tfpt-workflow, website-sync) and a new sync-maps rule added describing the agentic procedure: regenerate the maps first, enumerate the affected surfaces from them, audit as the exit gate. The mirror map (website_map.csv) also covers the root README.md and next.txt (bare vN ids resolved to full script names), and both files are named explicitly as status surfaces that move with every finding.

2026-06-12

tfpt_3 / tfpt_4 style alignment + box reduction

Shared header/footer on tfpt_3. tfpt_3_e8_audit_bootstrap dropped its custom \footmarkers footer (the post-collapse four-[E]artefact) and inherits the shared tfpt_style header/footer with the version stamp; the box-orphan needspace guards are kept.
Fewer boxes, embedded in text. Narrative/commentary callouts converted to run-in bold paragraphs (boxed one-line formulas to keyeq): tfpt_3 from $39$ to $27$ boxes (e.g. “Purpose and discipline”, the five “(i)–(v)” audit-lemma boxes, “Net”, “The connection in one sentence”, “The unification”, “The question and the honest answer”, “Net: two axioms”); tfpt_4 from $18$ to $7$ (the seven-box Koide stack and the two dark-matter conjecture boxes become prose). The per-item “Honest status of …” keyboxes are kept — tfpt_4 is the status authority for the frontier.
Colour-marked module references. \vref applied to the inline vN references in tfpt_3 and tfpt_4 (TikZ node names excluded).
Marker hygiene. A stale literal [P] in tfpt_4 (Koide flow-time) replaced by the 4-class [C]; status tables checked against the ledger.

2026-06-12

tfpt_1 / tfpt_2 style alignment + box reduction

Shared header/footer everywhere. tfpt_1_architecture_e8 dropped its custom \footmarkers footer (which after the marker collapse showed four redundant [E]) and now inherits the shared tfpt_style header/footer with the version stamp, identical to every other document.
Fewer boxes, embedded in text. The narrative/commentary callouts of both documents are converted to run-in bold paragraphs (and the boxed one-line formulas to the colour-marked keyeq): tfpt_1 from $21$ to $14$ loud boxes ( $+3$ keyeq); tfpt_2 from $52$ to $43$ (e.g. “In one sentence”, “The one-paragraph version”, the four “Sharpening” notes, “What the simplification means net”, “The disciplined main statement”, “What improves…”, “Scope and honesty”). Only genuine results / theorems / gates keep a box.
Colour-marked module references. \vref now also colours the inline vN references throughout tfpt_1 and tfpt_2 (TikZ node names accidentally matching the pattern were excluded).
Status currency. tfpt_2's inflation-pivot table gains the v86 scalaron-reheating point ( $N_\star{=}51.4\Rightarrow n_s{=}0.9611$ , $r{=}0.0045$ , $A_s$ -disfavoured) and states the band-of-record explicitly, matching COSMO.NSTAR.01 and the introduction; the box is re-typed [C]. The other status tables were checked against the ledger and are current under the 4-class markers.

2026-06-12

marker simplification to 4 classes + status reconciliation

Four-class display markers. The reader-facing marker system is collapsed from eleven symbols to four: [E]exact / machine-proven (identity, Lie/lattice, formalised, numerical FP), [C]conditional (physical / bridge / readout under named hypotheses), [O]open / axiom, and [X] kill test. tex-artefacts/tfpt_style.tex defines \mE/\mC/\mO/\mX and keeps the legacy \tI \ldots \tX names as aliases that render their class. All marker call-sites across the nine documents and the shared fragments were rewritten, collapsing same-class combinations (e.g. [I]/[L]  $\to$  [E], [N]/[P]  $\to$  [E]/[C]). The fine-grained per-claim type (Axiom / Formal / Lattice / Numerical / Identity / Physical) is unchanged in status_ledger.csv — the single source of truth — so no fidelity is lost. The marker key, badge bar, README marker table and the workflow rule were updated to match.
Status tables reconciled against the ledger. The introduction's inflation/ $N_\star$ rows are made consistent with v86/COSMO.NSTAR.01: $r$ and $n_s$ are shown as the frozen bands over $N_\star\in[50,60]$ with the scalaron-reheating conditional point $N_\star{=}51.4$ ( $n_s{=}0.9611$ , $r{=}0.0045$ ), replacing the stale point values $N_\star{=}55$ (predictions table) and $N_\star\simeq57$ (residual card); the closure-ledger inflation row is re-typed [E]  $\to$  [C] (conditional on $M_{\rm Star}{=}M_{\rm scal}$ $+$ reheating), matching the other two tables and the ledger [P] typing.

2026-06-12

version system, predictions/K5, readability pass B3

Authors, auto-date and auto-version on every paper. New single source tex-artefacts/version.tex defines \TFPTauthors (Stefan Hamann, Alessandro Rizzo), a curated \TFPTversion, and a title/footer date stamp (\today $+$ version $+$ revision). build.sh writes the auto build revision (git commit count) into the gitignored tex-artefacts/version-auto.tex, so every document's title page and page footer carry author, date and v\TFPTversion (rev N) automatically. All nine active documents and changelog.tex now set \author{\TFPTauthors}.
Builder keeps build artefacts. build.sh no longer deletes the .aux/.log/.out/.toc after a successful build (the .log is needed for the overfull-box audit and the .aux/.toc for correct cross-references on the next incremental build).
Predictions table outsourced. The running/upcoming-experiment predictions table is moved from introduction.tex into the shared fragment tex-artefacts/predictions.tex (\input in the predictions section).
K5 figure fixed. The \TFPTactionkfive mnemonic ( $K_5$ on the five carrier slots) is redrawn so the complete graph and the Pascal-row reading list sit side by side instead of overlapping.
Colour-marked script references. New \vref macro colours inline module references (e.g. v108–v113, v49/v71) in the introduction, predictions and verification fragments, matching the blue of the \veri citation, so machine-checked references are visible at a glance.
Lighter, non-breaking, embedded boxes. The tcolorbox families are restyled to a light tint $+$ thin frame $+$ light title band with dark coloured title (no heavy white-on-saturated bars); a neutral navbox carries the document map and a colour-marked keyeq sets off load-bearing display formulas. The introduction's callouts use the non-breaking variants (keyboxnb/winboxnb/gapboxnb) so no box splits across a page, and the shared status card is non-breaking.
Readability / sectioning. The dense run-in prose of the introduction is broken into \subsection* headings (In plain words; one anchor and $E_8$ as a compiler hull; the companion documents; the compact status formula; the hard reduction; the Pascal action grammar; the closure ledger) with added whitespace.
Orphan results linked to scripts. The Glue theorem, the “Reduction in one line” and the fermion-spectrum callouts now carry inline \veri{} citations (v1, v6/v14/v23, v18/v20/v46).

2026-06-12

tex-artefacts refactor + introduction visual pass B2

Shared imports moved to tex-artefacts/. The shared, imported-only TeX fragments (tfpt_style.tex, tfpt_figures.tex, tfpt_docset.tex, tfpt_status.tex) now live in a dedicated tex-artefacts/ folder; all nine active documents \input them via tex-artefacts/<name> (and tfpt_style loads tex-artefacts/tfpt_figures). changelog.tex stays at the repo root because it is also a standalone build.sh notes deliverable. The make_manifest.py TEX list and the workflow rule were updated to the new paths.
Master script index outsourced (tex-artefacts/verification.tex). The long vN $\to$ check table is moved out of introduction.tex into the shared fragment tex-artefacts/verification.tex (\input in the verification appendix); the paper-consistency audit now also reads that file, so every registered script stays cited exactly once.
Introduction box reduction (B2). The introduction's eleven keyboxes are reduced to the single headline “In one sentence” card; the explanatory keyboxes (In plain words, Sharper still, compact status formula, hard reduction, Cosmology Pascal, $E_6{\times}A_2$ , closure ledger, Plausibility balance) are converted to inline run-in paragraphs, the Glue theorem is re-typed as a winbox (a result, not a claim), and the explanatory plausible/follows next winboxes become prose. The loud boxes now carry only genuinely load-bearing callouts (one keybox, five winboxes, one gapbox) plus the two shared orientation cards.
Document-count consistency. The introduction's document map gained the missing tfpt_5_redteam row; “seven/eight companion documents” and the ledger “six documents” wording are corrected to the true count (nine active documents); README.md (“10 ok”, 140 scripts) and the workflow rule (“9 docs”) are reconciled.

2026-06-12

visual pass: box reduction B1

Box reduction (B1). The $26$ non-load-bearing aside boxes (audit / recorded / interpretation: auditbox/audbox/intbox/resbox/roadbox) across tfpt_1, tfpt_2, tfpt_3 and origin_theory are converted to inline bold run-in paragraphs — the reviewer's prescription that an audit fingerprint must not carry the same visual volume as a theorem. The loud box families are now only keybox (claim), winbox (result) and gapbox (open/caveat).

2026-06-12

visual pass: shared figures, badges, marker typology

Shared figure library tfpt_figures.tex (\input by tfpt_style): reusable TikZ macros for the architecture claim stack (\TFPTclaimstack[zone], B3), the anchor cockpit $a=(1,1,2)$ (B4), the $E_8$ glue diagram (B5), the $2/3$ motif map (B6) and the $K_5$ action lattice (B7). The claim stack and a marker badge bar are now shown near the front of every document, each highlighting that document's layer; the topical figures are placed in their natural homes (cockpit + $K_5$ in the introduction, cockpit + glue in tfpt_1, motif in the horizon note).
Marker typology (A2). tfpt_style adds the sharper sub-types [E](exact algebra), [E](exact number), [C](readout / standard physics in TFPT units) to the existing [C](bridge) and [X](kill test); the marker key and the new \TFPTbadges bar show the full typology. (Inline body markers retain [E]where they are genuine exact identities.)

2026-06-12

review pass on list.txt

Claim hygiene (review section A). The introduction's one-sentence claim is softened from “derives all constants” to “constructs a discrete compiler; physical readouts run through named, status-typed bridges”; the ledger zombie in FLAV.QRATIO.01 is removed (the statement no longer says “stays [P]” — ratios are [E]closed on the derived stratum, only the absolute scale stays [O], with an explicit forbidden-wording note); the seam misalignment is written explicitly as $\varepsilon=\tfrac34\phiz=\cthree+36\cthree^4$ (leading $\cthree$ , fourth-order puncture correction exact); $\theta_{12}$ has a single prediction of record $0.306747$ with the seam/non-linear values typed as scheme diagnostics; JUNO's first $59.1$ -day result ( $0.3092\pm0.0087$ , compatible, precision pending) is recorded and NuFIT 6.0 is marked the pre-JUNO baseline; the ACT DR6 birefringence hint carries a systematics caveat (not a validation target); CODATA-2022 is dated; the null-model figure is moved out of the main text and typed as a grammar-internal bound. “Complete solutions of the five open questions” becomes “Closure status of the five former open questions”.
Interface language unified (review sections A5/C2/C3/C6/C7/C8). The live residual is stated everywhere as $v_{\mathrm{geo}}\oplus G_{\mathrm{net}}\oplus F_{\mathrm{transfer}}$ (historical $U_{\mathrm{wall}}/G_{\mathrm{metric}}/F_{\mathrm{frontier}}$ kept only for ledger continuity); tfpt_research_contracts is retitled and its recommended order rewritten (selector-triangle pairings $\to v_{\mathrm{geo}}\to G_{\mathrm{net}}$ ); $F_{\mathrm{transfer}}$ is named as one missing functor with Koide/ $\eta_B$ /axion/ $m_p/m_e$ as its four instances; full QG closure is framed as a certification layer, not a prerequisite. Document numbering aligned with file names (the Red Team paper is now in the canonical set; document $N\equiv$ tfpt_N). Website mirrored throughout (papers.ts, predictions.ts, faq.ts, glossary.ts, OpenGates, Hero, orientation components).

2026-06-12

later

Shared style and central status artifact. Two new single-source fragments: tfpt_style.tex (the canonical palette, status markers, marker key, \veri reference, the four tcolorbox families with back-compat aliases, and one running header/footer) is now \input by all eight documents — the per-paper duplicated preambles are gone; and tfpt_status.tex (“TFPT status at a glance”) gives one canonical overall-status card imported near the front of every document, replacing the divergent per-paper status statements. Both registered in build.sh and the manifest TEX list.

2026-06-12

Margin theorem (v122). The established frozen selectors ( $D_4$ annihilator $n=(5,-9,6)$ , $\det R=8$ , $\det K=4$ ) pin $R$ uniquely among hexagon matrices ( $64\to12\to1$ ); the atom margins become theorems — H2 introduces no new residual class.
Inventory update (v123). Residual table re-pinned post v110–v122: exactly five structural classes (R1 clock, R2 index-4 net, R3 EH step, R4 $'$ selector establishment — replacing the discharged H2 dictionary — and R5 $Q$ realisation); R2 carries three loads (metric $+$ carrier $+$ QBL: one theorem, three doors).
Resummed clock $+$ glue Q-system (v124/v125). R1's bend in closed form: $\mathrm{rate}(n)=-p_2\ln(1-n/N_{\mathrm{fam}})$ (pole at $N_{\mathrm{fam}}$ forces the three-level spectrum); the index-4 $\mu_4$ extension exists explicitly as a Longo Q-system on $\mathbb C[\mathbb Z_4]$ (all Frobenius axioms exact) — R2 sharpens from “find” to “identify”.
Clock–wall bridge (v126) and ring resummation (v127). The resummed-clock weights are the Mehta–Seshadri parabolic weights ( $\operatorname{spec}A_0^\star$ ); $\det(\mathbf 1-A_0^\star)=\tfrac29$ $=$ the entropy curvature; the clock is a log-determinant (RPA rings, one tower per hexagon site, coupling $=$ parabolic weight).
Graded hull (v128). $E_8$ is a $\mathbb Z_4$ -graded Lie algebra over the carrier (grading $=$ glue Q-system; exact on all $6720$ root-pair sums); ring multiplicity $6$ $=$ sheet-doubled Ginsparg–Perry zero modes. Notation fix in the same round: the clock factor $6$ is $p_2(a)$ , not $2p_2$ — labels corrected across modules, ledger, papers, website (numbers unchanged).
Entropy power law $\to$ zeta budget (v129–v133). The clock is $\Gamma_n\propto(S_n/S_{dS})^{p_2}$ (Gibbons–Hawking form); $p_2=2h$ with $h=N_{\mathrm{fam}}$ from mode counting $+$ the Born rule (v130); the zero-mode norm is the area, $\|Y_{1m}\|^2=A/(4\pi)$ exactly (v131); the det-ratio anomaly is the Koide constant, $\zeta(0)|_{\det'}=-\tfrac23$ (v132); both $\zeta(0)$ budget routes computed exactly — the reduced seam route carries pure anchor ratios ( $-\tfrac43$ $=$ minus the seed gain), the naive 4d route ( $-\tfrac{109}{45}$ ) carries no atom (v133).
Dual anchor $+$ determinant surface (v134/v135). $d:=a^\top R^{-1}=a^\top L^{-1}=(-\tfrac12,-\tfrac12,1)$ with $(1,1,-2)=-2d$ — the inverse flavor response is the Nariai root, invariance exact via Sherman–Morrison (third algebraic flavor–horizon bridge leg); $\det M(s,t)=3s(t{+}1)(t{+}2)+t^2+5t+8$ with iso-volume walls at the $\mathbb Z_2$ / $\mu_4$ atoms, winding line $(8,14,20)$ , $\det F=32$ , row-budget axes with $\mathrm{rowsum}(V)=\operatorname{Spec}(Q_+)$ ; micro-identities $41=16+25$ , $52=16+36$ .
Dual-normal selector, $Q_+$ cohomology, Volkov–Wipf firewall (v136–v138). $(d,n)$ pins $R$ columnwise (each column the unique lattice point of the address box; kernel $(6,8,7)$ ); the $A_0^\star$ zero mode carries the spectral normal $\sigma=(2,-9,5)$ with a $W(A_3)$ orbit control excluding the naive lift; $H^1(\mathbb P^1\setminus\mu_4)=\chi_1\oplus\chi_2\oplus\chi_3$ with degrees $(1,2,3)=\operatorname{Spec}(Q_+)=$ the $A_3$ exponents and cusp weights $=\operatorname{spec}A_0^\star$ ; the external full-4d graviton/ghost value $-\tfrac{98}{45}$ is pinned (arXiv:2506.02142 $=$ Volkov–Wipf hep-th/0003081) and its edge part is exactly two copies of the reduced seam budget — R1 typed closed as an edge-sector object.
Selector triangle $+$ canonical map (v139/v140). $d=\tfrac32a-2\cdot\mathbf 1$ is pure anchor data (first selector derived); the frame $(\mathbf 1,a,\sigma)$ has volume $11$ and $n$ is the unique covector with atom pairings $(2,8,121)$ — the R4 $'$ residue is three pairings; the $H^1\to$ generation equivariant map exists and is Schur-rigid (only sign-twisted $\mu_4$ actions match), so the GATE.QGEO residue collapses to one $\mathbb Z_3$ choice.
Editorial and consistency passes. Content-currency sweep (superseded “single remaining input” claims retired across contracts, paper 3, intro, website); introduction: self-explanatory title (spells out Topological Fixed-Point Theory), the old-version comparison removed throughout, redundant diagrams dropped, the unreadable status heatmap removed, the script-index master table converted to a page-breaking xltabular (it had silently truncated $\sim$ 110 rows), status card extended with the v134–v140 reductions, predictions table completed (CP phase, cosmic birefringence); the canonical document-set box extracted into the shared tfpt_docset.tex; paper 1 cleaned of all 35 old-series references, every section now opens with its machine-check script references; smaller box fonts across all eight documents; this changelog.tex introduced as a dual-mode (standalone $+$ imported) document.

2026-06-11

External-review integration (v83) and release hygiene. Manifest --check mode and the release rule; holomorphy pins $(E_8)_1$ (the unique even unimodular rank-8 lattice theory).
Sheet diamond and centered form (v94/v95). All four flavor operators are points of one two-parameter surface $M(s,t)$ ; centered cross $R,L=C\mp U$ , $K,F=C\mp V$ with the cofactor seam normal $n=(5,-9,6)$ ; documentation pass (“The Sheet Diamond and the Winding Line” in paper 3).
Horizon/anchor round (v101–v103). The maximal (Nariai) black hole is the anchor: roots $(1,1,-2)$ , entropy bound $\tfrac23=|\mathbb Z_2|/N_{\mathrm{fam}}$ ; one repeller/attractor orientation in both sectors; trisection normal form (the canonical cosine coordinate).
Clock/ladder round (v104–v108) $+$ Lean hardening. The classical Nariai clock speaks anchor ( $\chi_{\mathrm{clock}}=(\lambda-1)(\lambda+2)$ ); machine-pinned residual inventory; first review validation; quantum-clock target made quantitative; Pascal Ladder Theorem ( $g=2K+1$ $\Leftrightarrow$ the closure).
QBL theorem chain (v109–v113). Sheet-Pairing Lemma; Calderón-sheet selection (a scalar seam datum exists iff the involution is sheet-odd); Quadratic-Transport Theorem (degree exactly 2); Self-Counting Channel (the Pascal closure as an identity); quasi-free kernel (one 2-point kernel determines the whole net, rank $=c$ ) — the QBL input merges with the R2/holomorphy premise; communicated across all status surfaces.
$U_{\mathrm{wall}}$ made exact (v114–v118). Torsion normal form and $\delta=\tfrac12$ theorem; exact anchor residue $A_0^\star$ (diag $=a/|\mu_4|$ , off-weights $(8,0,5)/144$ ); resonance theorem ( $M_\infty=\mathbf 1\iff a_{13}=0$ , one gauge orbit); the holonomy is the exact 24-element $W(A_3)=S_4$ ; the hypercharge hexagon is the sign-twisted family spectrum with the lepton coefficients as resolvent determinants.
Second review validation $+$ address pinning (v119–v121). Anchor ratio triad $(\tfrac23,\tfrac43,\tfrac53)$ ; the $121$ audit lemma; the lepton words are the compiler atoms $(8,5,3)$ with divmod-hexagon addresses; $R$ is the unique hexagon matrix with atom margins and $\det 8$ — the address table carries zero residual information.

2026-06-10

B/C/D round closed. Koide attractor toy model (v93), glue uniqueness (v92), the Wolfram extension as the independent second verification path, Lean hardening; papers and website synced with the round.
Content rounds v96–v100. Sheet conjugation bridge, discriminant dictionary, Koide flow time, and the look-elsewhere-corrected numerology null test (v100: joint null probability $\le10^{-30.7}$ , conditional on the declared grammar).

2026-06-09

Blind registry frozen (v84). Machine-enforced prediction registry (predictions_frozen.json): exactly one $\theta_{12}$ number of record before JUNO; conditional entries carry their hypotheses by name. Research-contracts document added to the set.

2026-06-07 / 2026-06-08

Compiler-closure consolidation. The TFPT development is consolidated into the current document set with the verification suite (modules v1–v82: $E_8$ glue, carrier Pascal, EM fixed point, flavor matrix, cascade, bootstrap, gravity/cosmology, transport, masses, registry and gate audits) as the single proof layer; manifests (manifest.sha256, lean_manifest.sha256) as content identity; website mirrors the suite (interactive DAG, in-browser script reproducer, script index).

2026-04-27

Initial commit. TFPT papers and website baseline: electromagnetic closure and flavor transport (UFE bridge, birefringence seed, dyonic intercept), PDF-download tracking, accessibility and metadata passes.

Every change and new result, by date.