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<title>TFPT — Zenodo description</title>
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<div style="max-width:820px; margin:0 auto; padding:18px 22px; font-family:Calibri, Arial, sans-serif; font-size:15px; line-height:1.55; color:#1a1a1a;">
<h1 style="font-size:22px; color:#1F4E79; margin:0 0 4px;">Topological Fixed-Point Theory (TFPT)</h1>
<p style="font-size:16px; color:#444; margin:0 0 10px;"><i>Version 5.4 — a two-input discrete compiler for the dimensionless structure of the Standard Model, the fine-structure constant, and cosmology, with a fully machine-checked verification stack (904 Python modules, Wolfram 116+588, Lean 4).</i></p>
<p style="margin:0 0 16px; padding:10px 12px; background:#f6f8fb; border:1px solid #dbe3ee; border-radius:6px; font-size:14px;">
<b>Project links:</b>
<a href="https://www.fixpoint-theory.com" style="color:#1F4E79;">Website & interactive verification (fixpoint-theory.com)</a>
· <a href="https://www.fixpoint-theory.com/orientation" style="color:#1F4E79;">Reading guide</a>
· <a href="https://www.fixpoint-theory.com/verification" style="color:#1F4E79;">Reproduce every claim in-browser</a>
· <a href="https://github.com/sthamann/tfpt" style="color:#1F4E79;">Source code (GitHub)</a>
<br><span style="color:#666; font-size:13px;">The physics theory TFPT — distinct from the Brouwer–Lefschetz fixed-point theory of mathematics.</span>
</p>
<p>TFPT models fundamental physics as a small, deterministic <b>compiler</b>. Two boundary inputs are fed in; an <span style="font-family:Consolas,'Courier New',monospace;">E₈</span> “audit hull” is built as an intermediate object; and the Standard-Model gauge structure, the fermion generations, the fine-structure constant, the flavour pattern, and the leading cosmological quantities emerge as <b>projections</b> — through a chain of exact identities and lattice/Lie theorems, not parameter fits. Every load-bearing statement is reproduced by an independent verification suite (Python, Wolfram, and a Lean 4 proof) and tracked in a versioned status ledger.</p>
<p>This release reframes the theory around its sharpest form: <b>not</b> “more numerical coincidences,” but a closed discrete compiler plus a small, explicitly typed set of physical anchors. The framework is deliberately <b>over-determined</b> — it predicts by exclusion, and it states honestly what is closed, what is conditional, and what remains open.</p>
<h2 style="font-size:18px; color:#1F4E79; margin:24px 0 6px;">The two inputs</h2>
<table style="border-collapse:collapse; width:100%; font-size:14px; margin:6px 0;">
<tr style="background:#1F4E79; color:#fff;"><th style="text-align:left;padding:6px 8px;">Input</th><th style="text-align:left;padding:6px 8px;">Symbol</th><th style="text-align:left;padding:6px 8px;">Value</th><th style="text-align:left;padding:6px 8px;">Role</th></tr>
<tr style="border-bottom:1px solid #ddd;"><td style="padding:6px 8px;">Seam normalisation (P1)</td><td style="padding:6px 8px;font-family:Consolas,monospace;">c₃</td><td style="padding:6px 8px;font-family:Consolas,monospace;">1/(8π)</td><td style="padding:6px 8px;">boundary / horizon constant</td></tr>
<tr style="border-bottom:1px solid #ddd; background:#f6f8fb;"><td style="padding:6px 8px;">Carrier rank (P2)</td><td style="padding:6px 8px;font-family:Consolas,monospace;">g_car</td><td style="padding:6px 8px;font-family:Consolas,monospace;">5</td><td style="padding:6px 8px;">the <span style="font-family:Consolas,monospace;">3+2</span> carrier interface</td></tr>
</table>
<p>These two collapse further: both are the elementary-symmetric data of the <b>parabolic anchor</b> <span style="font-family:Consolas,'Courier New',monospace;">a = (1,1,2)</span>, so the genuine input layer is <span style="font-family:Consolas,'Courier New',monospace;">a</span> plus the single transcendental <span style="font-family:Consolas,'Courier New',monospace;">π</span> (with <span style="font-family:Consolas,'Courier New',monospace;">c₃ = 1/(2·e₁(a)·π) = 1/(8π)</span>). The carrier value <span style="font-family:Consolas,'Courier New',monospace;">g_car = 5</span> is itself an <i>over-determined bootstrap fixed point</i>, forced three independent ways by the <span style="font-family:Consolas,'Courier New',monospace;">E₈</span> closure. On the dimensionless axis the theory therefore has <b>no free load-bearing number</b> — only <span style="font-family:Consolas,'Courier New',monospace;">π</span> is primitive.</p>
<h2 style="font-size:18px; color:#1F4E79; margin:24px 0 6px;">The E₈ audit hull (not a gauge group)</h2>
<p>The compiler builds the carrier <span style="font-family:Consolas,'Courier New',monospace;">D₅ ⊕ A₃ + μ₄</span> inside <span style="font-family:Consolas,'Courier New',monospace;">E₈</span>, realised as an explicit even unimodular lattice certificate (<span style="font-family:Consolas,'Courier New',monospace;">240</span> roots, glue index <span style="font-family:Consolas,'Courier New',monospace;">4 = |μ₄|</span>, <span style="font-family:Consolas,'Courier New',monospace;">dim E₈ = 248</span>, <span style="font-family:Consolas,'Courier New',monospace;">rank 8</span>). Crucially, <b><span style="font-family:Consolas,'Courier New',monospace;">E₈</span> is the unimodular audit / compiler hull, not an unbroken physical gauge group.</b> The Standard Model is a read-out <i>after projection</i>; Lorentz signature appears only after projection. This is exactly why the classical no-go results against literal <span style="font-family:Consolas,'Courier New',monospace;">E₈</span> world-formulas (Distler–Garibaldi; Coleman–Mandula) do not apply — TFPT makes no such claim.</p>
<h2 style="font-size:18px; color:#1F4E79; margin:24px 0 6px;">What the compiler derives</h2>
<p style="margin:6px 0;"><b>Gauge structure & carrier.</b> Admissibility fixes the minimal carrier algebra <span style="font-family:Consolas,'Courier New',monospace;">E = E₃ ⊕ E₂</span>, the Standard-Model gauge group <span style="font-family:Consolas,'Courier New',monospace;">(SU(3)×SU(2)×U(1)_Y)/ℤ₆</span>, and exactly one chiral family from the even exterior algebra <span style="font-family:Consolas,'Courier New',monospace;">S⁺ = Λ^{even}E</span>. The hypercharge is a carrier observable, <span style="font-family:Consolas,'Courier New',monospace;">Y = diag(−⅓,−⅓,−⅓,½,½)</span>, the exact root of <span style="font-family:Consolas,'Courier New',monospace;">6Y² − Y − 1 = 0</span> (anomaly-free; machine-formalised in Lean).</p>
<p style="margin:6px 0;"><b>Three generations.</b> <span style="font-family:Consolas,'Courier New',monospace;">N_fam = 3 = rank A₃ = dim H₁(ℙ¹∖μ₄)</span> — the family count is the first homology of the four-punctured sphere, not an input.</p>
<p style="margin:6px 0;"><b>The fine-structure constant as a fixed point.</b> <span style="font-family:Consolas,'Courier New',monospace;">α</span> is not inserted but <i>selected</i> as the unique positive root of the boundary <span style="font-family:Consolas,'Courier New',monospace;">U(1)</span> Ward identity
<br><span style="font-family:Consolas,'Courier New',monospace;"> α³ − 2c₃³α² − (4/5)c₃⁶·41·ln(1/φΣ(α)) = 0, c₃ = 1/(8π),</span>
<br>giving <span style="font-family:Consolas,'Courier New',monospace;">α⁻¹ = 137.0359992</span> (existence and uniqueness proved, with interval-arithmetic enclosure; deviation from CODATA-2022 <span style="font-family:Consolas,'Courier New',monospace;">≈ 3×10⁻¹⁰</span>). The budget <span style="font-family:Consolas,'Courier New',monospace;">41 = 10b₁</span> is forced, not fitted.</p>
<p style="margin:6px 0;"><b>Flavour.</b> Four integer lattice operators <span style="font-family:Consolas,'Courier New',monospace;">(Q,K,R,L)</span> on <span style="font-family:Consolas,'Courier New',monospace;">H₁(ℙ¹∖μ₄)=ℤ³</span> with determinants <span style="font-family:Consolas,'Courier New',monospace;">(3,4,8,20)</span>, product <span style="font-family:Consolas,'Courier New',monospace;">1920 = |W(D₅)|</span>. Masses follow one <span style="font-family:Consolas,'Courier New',monospace;">φ₀</span>-ladder (<span style="font-family:Consolas,'Courier New',monospace;">φ₀ = 1/(6π) + 48c₃⁴</span>); the charged-lepton coefficients are exactly <span style="font-family:Consolas,'Courier New',monospace;">(16/7, 4/3, 7/6)</span>; the quark mass <i>ratios</i> are integer Plücker read-outs (<span style="font-family:Consolas,'Courier New',monospace;">c_u/c_d = 55/117</span>, …) on a now-derived selector stratum — no transcendental solve. Mixing is carried by holonomy on the four-punctured sphere <span style="font-family:Consolas,'Courier New',monospace;">ℙ¹∖μ₄</span>.</p>
<p style="margin:6px 0;"><b>Neutrinos.</b> The frozen solar-angle prediction is <span style="font-family:Consolas,'Courier New',monospace;">sin²θ₁₂ = ⅓ − φ₀/2 = 0.306747</span> (conditional on the seam-misalignment lemma), with the reactor angle <span style="font-family:Consolas,'Courier New',monospace;">sin²θ₁₃ = φ₀·e^{−5/6}</span> (its exponent <span style="font-family:Consolas,monospace;">5/6 = tr_E Y²</span>, the carrier hypercharge trace). The full complex PMNS matrix assembles from these plus the <span style="font-family:Consolas,monospace;">μ₆/triality</span> CP phase <span style="font-family:Consolas,monospace;">δ = 240°</span>, giving a derived leptonic Jarlskog <span style="font-family:Consolas,monospace;">J_PMNS = −0.0297</span>. The absolute neutrino-mass scale reduces to one seesaw ratio (the same single dimensionful anchor as the amplitude normalisation), with a normal-ordering floor <span style="font-family:Consolas,monospace;">Σmₙ = 0.0586 eV</span> consistent with the cosmological bound.</p>
<p style="margin:6px 0;"><b>Higgs & scales.</b> A single Higgs doublet is selected by a bosonic index (<span style="font-family:Consolas,'Courier New',monospace;">Ind(B⁺E₂)=1, Ind(B⁺E₃)=0</span>); the strong-CP angle closes, <span style="font-family:Consolas,'Courier New',monospace;">θ_eff = 0</span>.</p>
<p style="margin:6px 0;"><b>Gravity & cosmology.</b> The same <span style="font-family:Consolas,'Courier New',monospace;">c₃ = 1/(8π)</span> is the Einstein/Jacobson coefficient. The induced <span style="font-family:Consolas,'Courier New',monospace;">R+R²</span> sector gives the Starobinsky scalaron mass <span style="font-family:Consolas,'Courier New',monospace;">M = c₃^{7/2}·M̅_Pl ≈ 3.06×10¹³</span> GeV; the cosmological constant is <span style="font-family:Consolas,'Courier New',monospace;">Λ ~ e^{−2α⁻¹}</span>; the baryon fraction is <span style="font-family:Consolas,'Courier New',monospace;">Ω_b = (1−1/4π)φ₀ ≈ 0.04894</span>; and the same seed predicts a cosmic-birefringence angle <span style="font-family:Consolas,'Courier New',monospace;">β = φ₀/(4π) ≈ 0.2424°</span>.</p>
<p style="margin:6px 0;"><b>Gravity is parameter-free (v5.3).</b> Beyond the induced <span style="font-family:Consolas,'Courier New',monospace;">R+R²</span> action, the classical metric-sector <i>field equation</i> is now supplied directly by the entanglement first law <span style="font-family:Consolas,'Courier New',monospace;">δS = δ⟨K⟩</span> (Jacobson; Faulkner et al.), run with the theory’s atoms: it gives the <b>full covariant Einstein equation</b> <span style="font-family:Consolas,'Courier New',monospace;">G_ab + Λ g_ab = c₃⁻¹ T_ab</span> with <b>both coefficients fixed</b> — <span style="font-family:Consolas,'Courier New',monospace;">c₃⁻¹ = 8π</span> (no free dimensionless Newton dial; the thermodynamic origin <span style="font-family:Consolas,'Courier New',monospace;">2π/η</span> equals the geometric one <span style="font-family:Consolas,'Courier New',monospace;">|ℤ₂|·2π·χ</span> iff <span style="font-family:Consolas,'Courier New',monospace;">|μ₄| = |ℤ₂|·χ(S²) = 4</span>, so <span style="font-family:Consolas,'Courier New',monospace;">c₃</span> is <b>triply over-determined</b> — anchor, geometry, thermodynamics, <span style="font-family:Consolas,monospace;">v358</span>) and <span style="font-family:Consolas,'Courier New',monospace;">Λ</span> from <span style="font-family:Consolas,'Courier New',monospace;">α</span> (<span style="font-family:Consolas,monospace;">v359</span>/<span style="font-family:Consolas,monospace;">v60</span>). The perturbative Stelle ghost is a Seeley–DeWitt truncation artefact; resummation of the KMS heat kernel pushes it to infinity (<span style="font-family:Consolas,monospace;">v380</span>). Only the equation-of-state interpretive fork and the one absolute scale <span style="font-family:Consolas,monospace;">v_geo</span> remain; an <b>external candidate</b> for that missing action level — Bianconi’s entropic action, <i>Gravity from entropy</i>, Phys. Rev. D 111, 066001 (2025) — is quantified in <span style="font-family:Consolas,monospace;">v473</span> (her free constant pinned exactly at <span style="font-family:Consolas,'Courier New',monospace;">β′_B = c₃/6 = 1/(48π)</span>; the <span style="font-family:Consolas,'Courier New',monospace;">R²</span> gap <span style="font-family:Consolas,'Courier New',monospace;">3(8π)⁹ ≈ 10¹³</span> pre-registered as kill test) without changing the typing.</p>
<h2 style="font-size:18px; color:#1F4E79; margin:24px 0 6px;">The boundary QFT as one relative object (Modular Spectral Closure)</h2>
<p>On top of the compiler the boundary quantum field theory is assembled and then collapsed to a <b>single relative object</b> <span style="font-family:Consolas,'Courier New',monospace;">TFPT_QFT = (AΣ, ωΣ, ΔΣ, ρ, A_F, H_F, D_F, J, γ, S_rel)</span>. The modular flow of the seam state is KMS at <span style="font-family:Consolas,monospace;">β=1</span> (Tomita–Takesaki); Osterwalder–Schrader reconstruction yields a positive Hamiltonian with mass gap <span style="font-family:Consolas,monospace;">Δ = 6·log(3/2)</span>; particles are the DHR superselection sectors of the carrier anyon category (Gauss–Milgram returns <span style="font-family:Consolas,monospace;">c=8</span>). The matter content is the carrier half-spinor — one anomaly-free Standard-Model generation with <span style="font-family:Consolas,monospace;">sin²θ_W = 3/8</span> — and the carrier-native Pati–Salam algebra <span style="font-family:Consolas,monospace;">A_F = ℍ_L ⊕ ℍ_R ⊕ M₄(ℂ)</span> gives the exact charges; the explicit <b>96-dimensional finite spectral triple</b> verifies reality, grading, KO-dimension 6, order-zero and the first-order condition (violated <i>exactly</i> by the Majorana — the Chamseddine–Connes–van Suijlekom <span style="font-family:Consolas,monospace;">σ</span> mechanism).</p>
<p>Three closures finish the layer. <b>(i)</b> The finite Dirac operator <span style="font-family:Consolas,monospace;">D_F</span> is not posited but the <b>modular/covariance induction</b> of the seam state: with covariance <span style="font-family:Consolas,monospace;">C = (1+e^H)⁻¹</span> the one-particle modular Hamiltonian <span style="font-family:Consolas,monospace;">log((1−C)C⁻¹) = H</span> exactly, so <span style="font-family:Consolas,monospace;">[D_F] = [DΣ] ⊗ [K_car]</span> and the Yukawas are a read-out of the boundary two-point function, not an input. <b>(ii)</b> The spectral-action <b>cutoff is that same KMS weight</b>, so the moment ratio <span style="font-family:Consolas,monospace;">f₂/f₀ = 1</span> exactly and <span style="font-family:Consolas,monospace;">κ</span> reduces to a finite-triple trace ratio (the last open scheme freedom removed). <b>(iii)</b> The seam (pillowcase), the carrier-16 (the 16 Kummer nodes <span style="font-family:Consolas,monospace;">= dim S⁺</span>) and <span style="font-family:Consolas,monospace;">E₈</span> (the intersection form <span style="font-family:Consolas,monospace;">H²(K3) = U³ ⊕ E₈(−1)²</span>) are facets of <b>one Kummer/K3 surface</b>. An assembly certificate pins the cross-consistency — one number <span style="font-family:Consolas,monospace;">4 = [B:A] = |μ₄| = 2χ = |(ℤ/2)²|</span> (index = marks = fixed points = glue order), one carrier-16, one gap <span style="font-family:Consolas,monospace;">6·log(3/2)</span>. The honest sense of completeness: the boundary QFT is <b>closed as one relative object modulo the single named keystone</b> <span style="font-family:Consolas,monospace;">SEAM.EQUIV.01</span> (the raw reflection-positive seam state is the holomorphic <span style="font-family:Consolas,monospace;">(E₈)₁</span> net at <span style="font-family:Consolas,monospace;">τ=i</span>; its conformal-deck face <span style="font-family:Consolas,monospace;">QGEO.SYM.01</span> is downstream), with the ambient quantum-gravity measure gap-decoupled and held separate by design — not a diffuse list of open interfaces.</p>
<p><b>The 4D perturbative S-matrix is constructible.</b> On top of the boundary object, the 4D scattering layer is typed as three distinct objects — the 2D DHR braiding, the 4D Epstein–Glaser S-matrix of the spectral action <span style="font-family:Consolas,monospace;">S_pert</span>, and the LSZ object on the reconstructed Wightman functions. Because the spectral-action interaction is power-counting renormalizable, the perturbative S-matrix exists order by order (Epstein–Glaser causal perturbation theory; one logarithmic counterterm per coupling, loop factor <span style="font-family:Consolas,monospace;">1/(16π²)</span>), and the same mechanism returns the SM one-loop β-coefficients <span style="font-family:Consolas,monospace;">(b₁,b₂,b₃) = (41/10, −19/6, −7)</span> from the carrier content. The matter+gauge sector now closes <i>to all orders</i> as a typed Epstein–Glaser/BRST contract (<span style="font-family:Consolas,monospace;">v381</span>, <span style="font-family:Consolas,monospace;">QFT4D.EG.ALLORDER.01</span>): dimension-4 power-counting ⇒ a finite counterterm space, BRST nilpotency for <span style="font-family:Consolas,monospace;">su(3)×su(2)</span>, and the seam gap ⇒ the adiabatic limit, with the all-order <span style="font-family:Consolas,monospace;">Tₙ</span> existence and Slavnov–Taylor identity imported (gravity <span style="font-family:Consolas,monospace;">R²/Weyl²</span> fenced out as the resummed form factor). The complete complex PMNS matrix is assembled, with the leptonic Jarlskog (CP strength) a derived number <span style="font-family:Consolas,monospace;">J_PMNS = −0.0297</span> (data-consistent). The one genuine structural frontier — the <i>nonperturbative</i> ambient measure <span style="font-family:Consolas,monospace;">QG.AMB.01</span> — now carries an explicit roadmap (Tier A gap-decoupled, Tier B reduced to the holomorphic <span style="font-family:Consolas,monospace;">(E₈)₁</span> boundary net): reduced, not closed.</p>
<h2 style="font-size:18px; color:#1F4E79; margin:24px 0 6px;">The seam as a horizon & the central theorem</h2>
<p>The boundary “seam” is the <b>abstract boundary normaliser whose local gravitational realisation is a horizon</b> (not literally an event horizon). The integer <span style="font-family:Consolas,'Courier New',monospace;">8</span> in <span style="font-family:Consolas,'Courier New',monospace;">c₃=1/(8π)</span> is triply forced — geometry (<span style="font-family:Consolas,'Courier New',monospace;">2|μ₄|</span>, one-sided Gauss–Bonnet), lattice (<span style="font-family:Consolas,'Courier New',monospace;">rank E₈ = h(D₅) = φ(30)</span>), and gravity (Hawking/Einstein <span style="font-family:Consolas,'Courier New',monospace;">8π</span>). The single remaining <b>central theorem target</b> is to derive the <span style="font-family:Consolas,'Courier New',monospace;">1/(8π)</span> area-law coefficient from the replica variation of the seam determinant. Its <i>structure</i> is closed — by the Fursaev–Solodukhin conical method, <span style="font-family:Consolas,'Courier New',monospace;">S = 2πc₃A = ¼A ⇔ c₃ = 1/(8π)</span> uniquely — the replica chain is now exercised <i>numerically on the discretized collar with the seam's own kernel</i> (real replica sheets, BFK/Calderón conically clean, the transfer masses on the EH line, the attractor mode's IR divergence regulated by the recovery gap; <span style="font-family:Consolas,'Courier New',monospace;">v471</span>), and the residual is the one irreducible dimensionful anchor (<span style="font-family:Consolas,'Courier New',monospace;">1/G</span> is UV-sensitive, Sakharov-type induced gravity) plus the continuum scaling limit (the same MMST-class statement as the <span style="font-family:Consolas,'Courier New',monospace;">SEAM.EQUIV.01</span> residual), not a diffuse gap. That single anchor is moreover <b>over-determined</b>: Newton’s <span style="font-family:Consolas,monospace;">G</span> and the compiler’s dark-energy prediction <span style="font-family:Consolas,monospace;">ρΛ/M̅⁴ = (3/4π²)e^{−2α⁻¹}</span> with the measured dark-energy scale give the <i>same</i> reduced Planck mass to <span style="font-family:Consolas,monospace;">0.11%</span>. Because the seam is a conformal <span style="font-family:Consolas,monospace;">c=8</span> CFT (scale-invariant by construction), the absence of a derivable absolute scale is a <i>theorem</i>, not a gap: the theory is scale-complete up to one over-determined anchor — the gravitational unit.</p>
<h2 style="font-size:18px; color:#1F4E79; margin:24px 0 6px;">Parameter-freeness as a theorem</h2>
<p>The boundary transport is gapped (<span style="font-family:Consolas,'Courier New',monospace;">Δ = 6·log(3/2) > 0</span>), so by Perron–Frobenius its iteration has a <b>unique attractor</b> at geometric rate <span style="font-family:Consolas,'Courier New',monospace;">(2/3)⁶</span>: the realised constants are <i>selected, not tuned</i>. The hull carries a literal order-<span style="font-family:Consolas,'Courier New',monospace;">30 = 2·3·5</span> Coxeter cycle whose eight live eigenphases are the <span style="font-family:Consolas,'Courier New',monospace;">φ(30) = 8 = rank E₈</span> totatives of 30.</p>
<h2 style="font-size:18px; color:#1F4E79; margin:24px 0 6px;">Honest status — four layers</h2>
<table style="border-collapse:collapse; width:100%; font-size:14px; margin:6px 0;">
<tr style="background:#1F4E79; color:#fff;"><th style="text-align:left;padding:6px 8px;">Layer</th><th style="text-align:left;padding:6px 8px;">Content</th><th style="text-align:left;padding:6px 8px;">Status</th></tr>
<tr style="border-bottom:1px solid #ddd;"><td style="padding:6px 8px;"><b>1. Closed compiler</b></td><td style="padding:6px 8px;"><span style="font-family:Consolas,monospace;">E₈</span> glue, carrier, <span style="font-family:Consolas,monospace;">α⁻¹</span>, <span style="font-family:Consolas,monospace;">(R,K,Q,L)</span>, lepton/quark ratios</td><td style="padding:6px 8px;font-family:Consolas,monospace;">[E]</td></tr>
<tr style="border-bottom:1px solid #ddd; background:#f6f8fb;"><td style="padding:6px 8px;"><b>2. Protected IR physics</b></td><td style="padding:6px 8px;"><span style="font-family:Consolas,monospace;">R+R²</span>; admissible gapped transfer sector, OS-reconstructed <i>under RP/gap hypotheses</i>; the boundary QFT as one relative object (Modular Spectral Closure: Dirac = covariance induction, cutoff = KMS weight, seam/carrier/<span style="font-family:Consolas,monospace;">E₈</span> on one K3)</td><td style="padding:6px 8px;font-family:Consolas,monospace;">[E]/[C]</td></tr>
<tr style="border-bottom:1px solid #ddd;"><td style="padding:6px 8px;"><b>3. Anchors</b></td><td style="padding:6px 8px;"><span style="font-family:Consolas,monospace;">π</span>, one dimensionful induced-gravity scale, the absolute amplitude normalisation</td><td style="padding:6px 8px;font-family:Consolas,monospace;">[O]</td></tr>
<tr style="border-bottom:1px solid #ddd; background:#f6f8fb;"><td style="padding:6px 8px;"><b>4. Interfaces</b></td><td style="padding:6px 8px;"><span style="font-family:Consolas,monospace;">m_p/m_e</span>, <span style="font-family:Consolas,monospace;">η_B</span> (leptogenesis), Koide, axion relic, full ambient QG measure (<span style="font-family:Consolas,monospace;">QG.AMB.01</span>)</td><td style="padding:6px 8px;font-family:Consolas,monospace;">[C]/[O]</td></tr>
</table>
<p><b>This release does not claim a certified strict Theory of Everything.</b> No dimensionful quantity is claimed as a derivation from pure numbers; Newton’s constant is a metrology read-out after selecting the physical <span style="font-family:Consolas,monospace;">Λ</span> branch and fixing one dimensionful anchor, not a free input.</p>
<h2 style="font-size:18px; color:#1F4E79; margin:24px 0 6px;">Reproducibility (the distinguishing feature)</h2>
<p>The deposit is fully machine-checkable:</p>
<ul style="margin:6px 0; padding-left:22px;">
<li style="margin-bottom:3px;"><b>Python suite</b> <span style="font-family:Consolas,monospace;">v1–v913</span> (one file per claim cluster; 906 modules, highest ID v913) → <span style="font-family:Consolas,monospace;">ALL CHECKS PASSED</span>.</li>
<li style="margin-bottom:3px;"><b>Independent Wolfram path</b> → <span style="font-family:Consolas,monospace;">116/116</span> base checks plus the <span style="font-family:Consolas,monospace;">588/588</span> extension mirroring the exact algebraic/identity/lattice results.</li>
<li style="margin-bottom:3px;"><b>Lean 4 proofs</b> of the carrier algebra (hypercharge, anomaly-freedom, integer rigidity) and the seam equivalence chain (<span style="font-family:Consolas,monospace;">FORM.SEAMEQUIV.01</span>, <span style="font-family:Consolas,monospace;">FORM.SEAM.MMST.01</span>), now with the Borchers/Wiesbrock standard-pair relations, the applicability-ledger count, the rigidity forcing converse (the entrywise forcing iff, uniform in N, with the exact commutant dimension and order discriminator) and the edge central-charge arithmetic (the Chern integers, the bulk–edge channel count, the assembly <span style="font-family:Consolas,monospace;">c₋=8=g_car+N_fam</span>, holomorphy <span style="font-family:Consolas,monospace;">c≡0 (mod 8)</span> and the order-3 modular <span style="font-family:Consolas,monospace;">T</span>-phase) kernel-checked axiom-free (<span style="font-family:Consolas,monospace;">FORM.SEAM.BW.HSMI.01</span>, <span style="font-family:Consolas,monospace;">FORM.SEAM.APPLICABILITY.01</span>, <span style="font-family:Consolas,monospace;">FORM.SEAM.RIGIDITY.FORCING.01</span>, <span style="font-family:Consolas,monospace;">FORM.SEAM.EDGE.CHERN.01</span>), and the post-F G-block residual reduced to one named realisation axiom plus one combined cited theorem (<span style="font-family:Consolas,monospace;">FORM.SEAM.RESIDUAL.01</span>: the one-sided count <span style="font-family:Consolas,monospace;">8=|ℤ/2|·(∫K/π)</span>, the reflection <span style="font-family:Consolas,monospace;">C→−C</span>, <span style="font-family:Consolas,monospace;">248=8+240=120+128</span>, <span style="font-family:Consolas,monospace;">det K</span> <span style="font-family:Consolas,monospace;">1</span> vs <span style="font-family:Consolas,monospace;">4</span>, the Wannier/Wilson winding <span style="font-family:Consolas,monospace;">=|C|=1</span> strict-locality obstruction, the finite-Fock spinor counts <span style="font-family:Consolas,monospace;">256=128+128</span> and the <span style="font-family:Consolas,monospace;">c=8</span> holomorphy selector (three level-1 candidates <span style="font-family:Consolas,monospace;">A8/D8/E8</span> each <span style="font-family:Consolas,monospace;">dim=8(1+h∨)</span>, the forced <span style="font-family:Consolas,monospace;">dim V₁=248=E8</span>) all by <span style="font-family:Consolas,monospace;">decide</span>; the former <span style="font-family:Consolas,monospace;">mmst_existence</span> and <span style="font-family:Consolas,monospace;">agt_lattice_extension</span> merged into one external axiom, so <span style="font-family:Consolas,monospace;">#print axioms</span> drops from six to four) → <span style="font-family:Consolas,monospace;">AUDIT: PASS</span>.</li>
<li style="margin-bottom:3px;"><b>Versioned status ledger</b> (<span style="font-family:Consolas,monospace;">status_ledger.csv</span>): every claim carries an id, status, dependency, verification script, and <span style="font-family:Consolas,monospace;">active/canonical_status/supersedes</span> fields.</li>
<li style="margin-bottom:3px;"><b>Content manifests</b> (<span style="font-family:Consolas,monospace;">SHA-256</span>) so the shipped package verifies literally.</li>
</ul>
<p>Status markers used throughout (four display classes): <span style="font-family:Consolas,monospace;">[E]</span> exact / proven (identity, Lie/lattice theorem, Lean-formalised, or numerical fixed point), <span style="font-family:Consolas,monospace;">[C]</span> conditional (physical / under named hypotheses), <span style="font-family:Consolas,monospace;">[O]</span> open / axiom / anchor, <span style="font-family:Consolas,monospace;">[X]</span> falsifiable kill test. The status ledger keeps the finer per-claim type (Axiom / Formal / Lattice / Numerical / Identity / Physical).</p>
<h2 style="font-size:18px; color:#1F4E79; margin:24px 0 6px;">Falsifiability</h2>
<p>The framework predicts by exclusion and lists explicit kill criteria:</p>
<ul style="margin:6px 0; padding-left:22px;">
<li style="margin-bottom:3px;"><b>[core]</b> a fourth chiral generation (breaks <span style="font-family:Consolas,monospace;">N_fam = 3</span>); a genuinely free fundamental constant that is not an <span style="font-family:Consolas,monospace;">E₈</span>-closure fixed point; a seam denominator <span style="font-family:Consolas,monospace;">≠ 8</span>; <span style="font-family:Consolas,monospace;">α⁻¹</span> away from the fixed-point root; a non-zero strong-CP angle; loss of Higgs uniqueness.</li>
<li style="margin-bottom:3px;"><b>[obs]</b> a measured <span style="font-family:Consolas,monospace;">v_GW ≠ c</span> or native photon dispersion; cosmic birefringence converging far from <span style="font-family:Consolas,monospace;">0.2424°</span> at <span style="font-family:Consolas,monospace;">≥ 3σ</span>; a JUNO solar-angle central value clearly away from <span style="font-family:Consolas,monospace;">0.307</span>; a cosmological <span style="font-family:Consolas,monospace;">Σmₙ < 0.0586 eV</span> (excluding the normal-ordering floor); a proton-decay non-observation beyond the Hyper-Kamiokande reach (for the optional Pati–Salam UV branch).</li>
</ul>
<p>Downstream tests include rare-kaon channels, the neutrino sector, and CMB observables.</p>
<h2 style="font-size:18px; color:#1F4E79; margin:24px 0 6px;">Positioning</h2>
<p>TFPT is <b>over-determined rather than under-constrained</b>, <b>topological/algebraic rather than perturbative-first</b>, and <b>predictive through exclusion rather than parameter fitting</b>. No free continuous parameters are introduced beyond the two boundary inputs (themselves reducible to <span style="font-family:Consolas,monospace;">a=(1,1,2)+π</span>), one dimensionful scale, and the explicitly typed interface data.</p>
<h2 style="font-size:18px; color:#1F4E79; margin:24px 0 6px;">Scope of this version</h2>
<p><b>Established:</b> the discrete compiler closure; the electromagnetic fixed-point equation; the carrier, family and Higgs structure; the flavour operator ladder and quark/lepton ratios; the self-consistency attractor; the induced <span style="font-family:Consolas,monospace;">R+R²</span> gravitational sector and the leading cosmological read-outs; the <b>parameter-free full covariant Einstein equation</b> (entanglement equilibrium, <span style="font-family:Consolas,monospace;">v358</span>/<span style="font-family:Consolas,monospace;">v359</span>); the cyclotomic/Galois arithmetic capstone (<span style="font-family:Consolas,monospace;">v313</span>–<span style="font-family:Consolas,monospace;">v321</span>, zero dimensionless free parameters); the S3 closure stack pinning the <span style="font-family:Consolas,monospace;">(E₈)₁</span> target at every computable level (<span style="font-family:Consolas,monospace;">v376</span>–<span style="font-family:Consolas,monospace;">v379</span>); the prediction observatory with live data scorecard (<span style="font-family:Consolas,monospace;">v375</span>); the <b>universal spectral-gap principle</b> (every sector is a gapped unique-attractor, so parameter-freeness is one theorem, not many coincidences, <span style="font-family:Consolas,monospace;">v383</span>); the all-order Epstein–Glaser/BRST contract for the perturbative 4D S-matrix (<span style="font-family:Consolas,monospace;">v381</span>) and the finite, UV-softened, tree-unitary graviton-exchange amplitude (<span style="font-family:Consolas,monospace;">v386</span>); and the gap-driven correction calculus (the same gap that forces parameter-freeness sizes each sector's first correction, <span style="font-family:Consolas,monospace;">v387</span>).</p>
<p><b>Open / conditional (explicitly typed):</b> the absolute amplitude normalisation (<span style="font-family:Consolas,monospace;">v_geo</span>, the one metrology unit by the No-Unit Theorem; its interface is structurally closed as an R<sub>+</sub> scale torsor in calibration form, <span style="font-family:Consolas,monospace;">v725</span> — no scale derivation); the frontier transfer interfaces (<span style="font-family:Consolas,monospace;">m_p/m_e</span>, <span style="font-family:Consolas,monospace;">η_B</span>, Koide, axion relic) as typed <span style="font-family:Consolas,monospace;">F_transfer</span> solvers (<span style="font-family:Consolas,monospace;">v371</span>–<span style="font-family:Consolas,monospace;">v374</span>, never compiler outputs; both thermal-time routes for internalizing the clocks are machine-killed, <span style="font-family:Consolas,monospace;">v723</span>/<span style="font-family:Consolas,monospace;">v724</span>, and the frozen external-clock contract is executed on its expected K1 kill, <span style="font-family:Consolas,monospace;">v777</span> — no common continuous clock exists; the fibered functor with the constant seam obstruction cocycle survives). On the metric sector, net existence and full-cone reflection positivity are <b>discharged to a theorem</b> (<span style="font-family:Consolas,monospace;">v175</span>), and the <span style="font-family:Consolas,monospace;">(E₈)₁</span> net is an assembled, verified certificate. The seam structural theorem <span style="font-family:Consolas,monospace;">SEAM.EQUIV.01</span> is now, on its MMST route <span style="font-family:Consolas,monospace;">SEAM.EQUIV.MMST.01</span>, <b>closed modulo cited theorems</b> (route split 2026-07-22, no status change in substance; the twistor route <span style="font-family:Consolas,monospace;">SEAM.EQUIV.TWISTOR.01</span> and the unconditional parent stay [O]): an explicit gapped lattice model (<span style="font-family:Consolas,monospace;">v367</span>/<span style="font-family:Consolas,monospace;">v368</span>) plus the S3 stack pin central charge, character, genus-1 count and reflection positivity; Lean <span style="font-family:Consolas,monospace;">FORM.SEAM.MMST.01</span> formalises the composition with MMST and OS reconstruction as named cited axioms. The <em>only</em> residual is the abstract continuum scaling-limit existence (the published MMST theorem, <span style="font-family:Consolas,monospace;">v336</span>). That residual’s intrinsic Bisognano–Wichmann face is further reduced (<span style="font-family:Consolas,monospace;">v424</span>) to the recent commuting-projector theorem of Naaijkens–Penneys–Wallick (<span style="font-family:Consolas,monospace;">arXiv:2605.10693</span>) — whose reflection-positivity axiom is the modular-conjugation condition <span style="font-family:Consolas,monospace;">uΘ=J</span>, distinct from clock-invariance — modulo two explicitly-named open sub-steps (realising the raw seam as a <span style="font-family:Consolas,monospace;">ℤ/2</span>-reflection commuting-projector model, and extending the axiom to the invertible KMS case): a reduction, not a closure. Sub-step (ii) is now constructively exhibited (<span style="font-family:Consolas,monospace;">v426</span>): a gapped reflection-symmetric <span style="font-family:Consolas,monospace;">μ₄</span>-even <span style="font-family:Consolas,monospace;">β=1</span> KMS collar satisfies <span style="font-family:Consolas,monospace;">ΘKΘ=−K</span> (<span style="font-family:Consolas,monospace;">uΘ=J</span>) and <span style="font-family:Consolas,monospace;">[ρ,K]=0</span>, so the axiom holds there by direct Tomita–Takesaki — the invertible-KMS corner NPW26 leave open — with the continuum sub-step (i) still the only residual. The chiral <span style="font-family:Consolas,monospace;">edge</span> half of that residual is independently reinforced: its central charge <span style="font-family:Consolas,monospace;">c₋=8</span> is read three disjoint ways — the correlator scaling limit (<span style="font-family:Consolas,monospace;">v444</span>), the integer bulk Chern number plus bulk–edge correspondence (<span style="font-family:Consolas,monospace;">v447</span>) and the Calabrese–Cardy entanglement law (<span style="font-family:Consolas,monospace;">v450</span>); the edge is <i>named</i> as the chiral Ising/Majorana model by its operator tower <span style="font-family:Consolas,monospace;">{h_σ,h_ε}={1/16,1/2}</span> (<span style="font-family:Consolas,monospace;">v451</span>); the <span style="font-family:Consolas,monospace;">(E₈)₁</span> identity is pinned on the torus by its modular data (<span style="font-family:Consolas,monospace;">S</span>-invariant, <span style="font-family:Consolas,monospace;">T</span>-phase <span style="font-family:Consolas,monospace;">e^{−2πi/3}</span>, <span style="font-family:Consolas,monospace;">v452</span>); the external MMST fact is pinned at four-point and uniform-in-<span style="font-family:Consolas,monospace;">N</span> order (<span style="font-family:Consolas,monospace;">v448</span>/<span style="font-family:Consolas,monospace;">v449</span>); and the last structural premise <span style="font-family:Consolas,monospace;">QGEO.SYM.01</span> is <i>derived</i> from the four marks being <span style="font-family:Consolas,monospace;">μ₄</span> (<span style="font-family:Consolas,monospace;">v453</span>) — a reduction, not a closure. A post-F <b>G-block</b> reduces the residual on ten more fronts: the lattice current algebra carries the level-1 Sugawara <span style="font-family:Consolas,monospace;">c=8</span> (<span style="font-family:Consolas,monospace;">v454</span>); the edge chirality <span style="font-family:Consolas,monospace;">c₋≠0</span> is <i>forced</i> by the one-sidedness defining <span style="font-family:Consolas,monospace;">c₃=1/(8π)</span> (<span style="font-family:Consolas,monospace;">v456</span>, so <span style="font-family:Consolas,monospace;">S3</span> follows from axiom <span style="font-family:Consolas,monospace;">P₁</span>); an <span style="font-family:Consolas,monospace;">(E₈)₁</span>-vs-<span style="font-family:Consolas,monospace;">SO(16)₁</span> character/sector kill test passes (<span style="font-family:Consolas,monospace;">v457</span>, <span style="font-family:Consolas,monospace;">248=120+128</span>, <span style="font-family:Consolas,monospace;">det K</span> <span style="font-family:Consolas,monospace;">1</span> vs <span style="font-family:Consolas,monospace;">4</span>); an exact MMST citation audit (<span style="font-family:Consolas,monospace;">v458</span>) isolates the single open piece to the <span style="font-family:Consolas,monospace;">128</span>-spinor extension, which the complementary lattice-VOA route <span style="font-family:Consolas,monospace;">A_{E₈}</span> then <i>constructs</i> (<span style="font-family:Consolas,monospace;">v459</span>); the strict locality of that realisation is shown to be <i>topologically forbidden</i> rather than a missing premise (<span style="font-family:Consolas,monospace;">v461</span>: the Wilson-loop/Wannier winding <span style="font-family:Consolas,monospace;">=|C|=1≠0</span>, so Kapustin–Fidkowski forbids any strictly finite-range commuting projector — the realisation is necessarily the quasi-local NPW26 net); the <span style="font-family:Consolas,monospace;">128</span>-spinor extension is exhibited at character level and as a finite-<span style="font-family:Consolas,monospace;">L</span>→continuum convergence (<span style="font-family:Consolas,monospace;">v462</span>: the Jacobi/E₈ identity <span style="font-family:Consolas,monospace;">θ₂⁸+θ₃⁸+θ₄⁸=2E₄</span> makes <span style="font-family:Consolas,monospace;">χ_{(E₈)₁}=χ_o+χ_s</span>, <span style="font-family:Consolas,monospace;">248=120+128</span>, with the lattice ring converging <span style="font-family:Consolas,monospace;">c₋→8</span>); the <i>identification</i> is made classification-forced (<span style="font-family:Consolas,monospace;">v463</span>: <span style="font-family:Consolas,monospace;">c=8</span> has <i>three</i> level-1 candidates <span style="font-family:Consolas,monospace;">A8/D8/E8</span>, but holomorphy forces <span style="font-family:Consolas,monospace;">dim V₁=E₄/η⁸</span> <span style="font-family:Consolas,monospace;">q¹</span> coeff <span style="font-family:Consolas,monospace;">=248</span>, so only <span style="font-family:Consolas,monospace;">E₈</span> survives — Dong–Mason/Schellekens give the holomorphic <span style="font-family:Consolas,monospace;">c=8</span> VOA unique <span style="font-family:Consolas,monospace;">=V_{E₈}</span>); the <i>realisation</i> input <span style="font-family:Consolas,monospace;">R₁</span> is reduced to its one-particle data (<span style="font-family:Consolas,monospace;">v464</span>: the seam being quasi-free makes its symbol <span style="font-family:Consolas,monospace;">P</span> a unique idempotent whose scaling limit is exhibited — Cauchy kernel, entanglement <span style="font-family:Consolas,monospace;">c→1</span>, <span style="font-family:Consolas,monospace;">c₋=8</span> — so by Araki/Shale–Stinespring it is the unique quasi-free realisation modulo the cited CAR functor); and a uniform-in-<span style="font-family:Consolas,monospace;">N</span> Tomita–Takesaki tower (<span style="font-family:Consolas,monospace;">v455</span>) lifts the intrinsic Bisognano–Wichmann condition — the whole G-block now Lean-hardened to <i>one</i> realisation axiom plus <i>one</i> combined cited theorem (<span style="font-family:Consolas,monospace;">#print axioms</span> six→four), the residual now <i>entirely certification</i> (a named, hypothesis-audited package — MMST, AGT/AMT, Dong–Mason, Araki, Shale–Stinespring — with no open internal mechanism); still a reduction, not a closure. The v5.4 closure-route round (<span style="font-family:Consolas,monospace;">v469</span>) <b>re-founds both halves on peer-reviewed ground</b>: the <span style="font-family:Consolas,monospace;">128</span>-spinor extension is the <i>local</i> <span style="font-family:Consolas,monospace;">ℤ₂</span> simple-current crossed product — the locality integer <span style="font-family:Consolas,monospace;">h_s=16/16=1∈ℤ</span> is exactly the Longo–Rehren criterion (Longo–Rehren 1995; Böckenhauer 1996; Böckenhauer–Evans 1998; KLM <span style="font-family:Consolas,monospace;">μ=4/2²=1</span> ⇒ holomorphic), so the extension leg now rests on <b>1995–2001 peer-reviewed subfactor theory</b> with the AGT/AMT preprint route demoted to an independent second witness (the index-4 <span style="font-family:Consolas,monospace;">μ₄</span> glue runs on the same integer, <span style="font-family:Consolas,monospace;">h(J^k)={1,1,1}</span>); and the realisation axiom is reduced from model fiat to <i>invariants</i> (R1′: quasi-free + gap + class D + <span style="font-family:Consolas,monospace;">c₋=8</span> from P₁, computed: FHS <span style="font-family:Consolas,monospace;">|C|=1</span>, <span style="font-family:Consolas,monospace;">ν=16</span> — the Kitaev sixteen-fold-way class whose edge <i>is</i> the bosonic <span style="font-family:Consolas,monospace;">(E₈)₁</span> state); Lean carries the parallel derivation <span style="font-family:Consolas,monospace;">seamResidualClosed'</span> with the locality/μ/sixteen-fold joints as kernel facts. Its conformal-deck face <span style="font-family:Consolas,monospace;">QGEO.SYM.01</span> is its downstream corollary (<span style="font-family:Consolas,monospace;">v335</span>). The ambient quantum-gravity measure <span style="font-family:Consolas,monospace;">QG.AMB.01</span> is no longer an open structural item: it is a <span style="font-family:Consolas,monospace;">[C]</span> <b>redundancy</b> (<span style="font-family:Consolas,monospace;">v369</span>) — a certification object rather than missing dynamics, conditional on <span style="font-family:Consolas,monospace;">SEAM.EQUIV.01</span> and Bisognano–Wichmann, with TFPT rigorously gap-decoupled from the general Euclidean-QG conformal-factor problem (margin <span style="font-family:Consolas,monospace;">1.648 > 0</span>). A dependency audit (<span style="font-family:Consolas,monospace;">v423</span>) makes this a machine-checked DAG/script fact: no frozen readout is computed from <span style="font-family:Consolas,monospace;">QG.AMB.01</span> (its only predictive link is the architectural 4D-QFT contract, not a numerical input). Perturbative graviton unitarity holds via the KMS Entire Hessian (<span style="font-family:Consolas,monospace;">v380</span>): the Stelle ghost is a truncation artefact, not a physical pole. The EM-Ward functional origin (“why <i>this</i> <span style="font-family:Consolas,monospace;">F_U(1)</span>”) is named as the tracked target <span style="font-family:Consolas,monospace;">ALPHA.QUILLEN.EXACT.01</span> (<span style="font-family:Consolas,monospace;">v382</span>) — a face of <span style="font-family:Consolas,monospace;">SEAM.EQUIV.01</span>, never the <span style="font-family:Consolas,monospace;">α</span> value (which stays <span style="font-family:Consolas,monospace;">[E]</span>). The v5.4 round (<span style="font-family:Consolas,monospace;">v470</span>) upgrades its two leftovers: the <span style="font-family:Consolas,monospace;">α³</span> level is no longer “the unit level by minimality” but <b>equals the computed bulk Chern invariant</b> <span style="font-family:Consolas,monospace;">|C|=1</span> of the same collar model that realises S3 (TKNN / Avron–Seiler–Simon quantisation + Callan–Harvey inflow + the APS/Witten <span style="font-family:Consolas,monospace;">η</span>=CS reading of <span style="font-family:Consolas,monospace;">δ log det</span>), and the seam <span style="font-family:Consolas,monospace;">F</span>-normalisation is retyped as the <b>affine embedding index</b> <span style="font-family:Consolas,monospace;">k_Y=5/3</span> (Ginsparg 1987; <span style="font-family:Consolas,monospace;">(3/5)·(41/6)=41/10=b₁</span> exactly) — level-1 current-algebra rigidity, zero independent content; one invertible phase feeds both named targets (<span style="font-family:Consolas,monospace;">c₋=8</span> gravitational, <span style="font-family:Consolas,monospace;">C=1</span> electromagnetic). Both targets stay <span style="font-family:Consolas,monospace;">[O]</span>. The honest residual is therefore <span style="font-family:Consolas,monospace;">v_geo</span> plus the typed <span style="font-family:Consolas,monospace;">F_transfer</span> interfaces, above the cited-theorem ceiling on the seam. A ledger audit (<span style="font-family:Consolas,monospace;">v384</span>) makes the shape explicit: the whole residual is <b>certification, not construction</b> — every open item is an external math proof, theorem-forbidden (the unit), or external physics, with <b>zero open internal mechanisms</b>. The optional carrier-Pati–Salam UV branch is proton-safe on the all-order footing (<span style="font-family:Consolas,monospace;">v385</span>): minimal <span style="font-family:Consolas,monospace;">SU(4)</span> leptoquarks mediate rare LFV, not <span style="font-family:Consolas,monospace;">p→e⁺π⁰</span>, so <span style="font-family:Consolas,monospace;">M_PS∼3×10¹³</span> GeV clears the binding bound by <span style="font-family:Consolas,monospace;">∼10⁷</span> (no fake proton-lifetime window).</p>
<p><b>Frontier firewall (v5.3).</b> The four frontier interfaces are typed as one transfer functor — <span style="font-family:Consolas,monospace;">F_pole</span> (Koide), <span style="font-family:Consolas,monospace;">F_Boltzmann</span> (η_B), <span style="font-family:Consolas,monospace;">F_relic</span> (axion), <span style="font-family:Consolas,monospace;">F_QCD</span> (<span style="font-family:Consolas,monospace;">m_p/m_e</span>) — now promoted to typed runnable solvers (<span style="font-family:Consolas,monospace;">v371</span>–<span style="font-family:Consolas,monospace;">v374</span>) with kill tests, guarded by <span style="font-family:Consolas,monospace;">v187</span> (ledger-enforced: never promoted to primitive compiler outputs) and <span style="font-family:Consolas,monospace;">v188</span> (prose sentinel). A live prediction scorecard (<span style="font-family:Consolas,monospace;">v375</span>) records JUNO/NuFIT/ACT/BK18 compatibility; <span style="font-family:Consolas,monospace;">θ₁₃</span> is flagged at 2.0σ tension. The Galois-locked CP prediction <span style="font-family:Consolas,monospace;">δ_PMNS = δ_CKM,lead + π = 240°</span> (<span style="font-family:Consolas,monospace;">v320</span>) is a sharp kill test at DUNE/Hyper-K.</p>
<p><b>Safeguards companion (new) & the single-flow reduction.</b> A dedicated methodology paper now collects, in one place, every mechanism by which TFPT defends a claim against coincidence and numerology: the four-class status calculus + single-source ledger + sync audit; the no-free-pattern rule and the reverse audit (only <span style="font-family:Consolas,monospace;">3/8</span> of <span style="font-family:Consolas,monospace;">E₈</span>’s Casimir degrees feed a readout, the other <span style="font-family:Consolas,monospace;">5/8</span> are published overhead); the <b>over-determination map</b> (<span style="font-family:Consolas,monospace;">v427</span>) with its honest self-correction (<span style="font-family:Consolas,monospace;">v428</span>): the framework counts evidence as <i>multiplying</i> only across genuinely disjoint grammars, and applying it to TFPT’s own seven arithmetic witnesses — Gauss, Eisenstein, cyclotomy, Galois, lattice, Pascal, Coxeter — shows (by the Brieskorn classification, <span style="font-family:Consolas,monospace;">v236</span>) that they are facets of <i>one</i> <span style="font-family:Consolas,monospace;">(2,3,5)/E₈</span> object: they <i>compress</i>, like the anchor, not multiply. The genuine multiplication is the input forced four independent ways (the “8” in <span style="font-family:Consolas,monospace;">c₃</span> from rank <span style="font-family:Consolas,monospace;">E₈</span>, <span style="font-family:Consolas,monospace;">h(D₅)</span>, <span style="font-family:Consolas,monospace;">φ(30)</span>, the Milnor number) plus the foreign witness <span style="font-family:Consolas,monospace;">α⁻¹≈137</span>; the <span style="font-family:Consolas,monospace;">F_transfer</span> firewall and the No-Unit theorem; the frozen registry with a Monte-Carlo null model (joint formula-fishing <span style="font-family:Consolas,monospace;">P ≤ 10⁻³⁰·⁷</span>, ∼102 bits) and the live scorecard; the two independent reproduction paths (Wolfram 116+584, Lean 4); and the red team. The four frontier transfers are further unified as <b>one native recovery flow</b> (<span style="font-family:Consolas,monospace;">v425</span>, the single-flow reduction): their <i>dynamics</i> is the seam recovery semigroup (gap <span style="font-family:Consolas,monospace;">6 ln(3/2)</span>, rate <span style="font-family:Consolas,monospace;">(2/3)⁶</span>), and only the anchors stay external — a reduction that respects, not relaxes, the firewall.</p>
<p><b>Working notes (new).</b> Two standalone, machine-checked working notes join the deposit. <i>The Gaussian code bridge: E₈ over ℤ[i], the extended Hamming code, and a four-bit information layer</i> proves that Construction A over the extended Hamming code <span style="font-family:Consolas,monospace;">[8,4,4]</span>, placed μ₄-equivariantly, makes <span style="font-family:Consolas,monospace;">E₈</span> a unimodular Hermitian <span style="font-family:Consolas,monospace;">ℤ[i]</span>-lattice whose reduction at the ramified prime <span style="font-family:Consolas,monospace;">1+i</span> is a canonical four-bit quotient <span style="font-family:Consolas,monospace;">L/(1+i)L ≅ F₂⁴</span> — the 240 roots distribute exactly <span style="font-family:Consolas,monospace;">15×16</span> over the nonzero classes and the code that builds the lattice returns as its <i>message space</i> (exact-arithmetic probes 26/26 + 22/22, promoted as <span style="font-family:Consolas,monospace;">v689</span>/<span style="font-family:Consolas,monospace;">v690</span>; 65 kernel-checked Lean 4 theorems; no claim beyond the stated algebra). <i>A computable, zeta-free truncation family for the Weil measure: measurements on a Hilbert–Pólya candidate</i> documents the measurement programme on the Gaussian-<span style="font-family:Consolas,monospace;">E₈</span> Hecke tower (<span style="font-family:Consolas,monospace;">v714</span>, <span style="font-family:Consolas,monospace;">v716</span>–<span style="font-family:Consolas,monospace;">v721</span>, <span style="font-family:Consolas,monospace;">v727</span>–<span style="font-family:Consolas,monospace;">v734</span>): SHA-256-frozen truncation spectra hit 100% of the first 377 zeta zeros at tolerance 0.25 with no prime table and no zero data anywhere in the construction path, and the one remaining statement (Weil positivity in the limit) is localized in four machine-verified equivalent languages — with the explicit no-proof fence: <b>no theorem about the Riemann zeta function and no RH claim</b>.</p>
<p style="margin:18px 0 4px; color:#555; font-size:13.5px;"><i>Claim discipline: nothing in this deposit is marked closed that is not machine-verified, and no dimensionful constant is claimed as a derivation from pure numbers. The versioned status ledger is the authoritative, per-claim source of truth.</i></p>
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