TFPT is built like a compiler, and verified like one. Nothing is marked closed that is not re-derived from the two axioms by an independent script, and no dimensionful quantity is claimed as a derivation from pure numbers. The graph below shows exactly how each result is computed, on which inputs it depends, and which scripts check it — including the self-consistency loop that fixes the inputs themselves. Every script is runnable live in your browser — click one to execute the real Python (via Pyodide / WebAssembly) and watch the checks pass, step by step.
A claim is only as strong as the way it is checked. The dimensionless skeleton is verified three independent ways and typed in a single versioned ledger, so the papers, the suite and the ledger stay in lock-step.
One file per claim cluster; run_all.py ends ALL CHECKS PASSED. Exact sympy where possible, mpmath/numpy otherwise.
An independent second path for the exact algebraic / identity / lattice results, on the Wolfram Engine: the verified base file plus the v84+ extension file.
The P2 carrier algebra — hypercharge, anomaly-freedom, integer rigidity — formalised in Lean 4 with only kernel axioms.
status_ledger.csv types every claim (id, status, location, dependency, script) and is versioned. If the text and the ledger disagree, the ledger wins.
What is exact, what is conditional, what is an open premise, and how to kill it — so a reviewer can decide where to push without reading 523 scripts first. Nothing here is hidden: the exact kernel stands on its own; the conditional and open layers are explicitly typed.
The honest one-line claim is conditional, not messianic: a two-input discrete compiler whose algebraic kernel derives the Standard-Model skeleton and several dimensionless readouts, with every physical transfer layer explicitly typed — and the keystone SEAM.EQUIV.01 (the raw RP seam = the holomorphic (E₈)₁ net at τ=i) is closed modulo cited theorems: the target net is pinned at every computable level (lattice v367/v368 + S3 stack v376–v379, ground-state witnesses v489/v490) and Lean-pinned (FORM.SEAM.MMST.01) to the published MMST/Adamo theorems, so the AQFT closure to (E₈)₁ follows modulo the cited continuum-existence residual (v336; extension leg on the peer-reviewed crossed-product package, realisation at invariant level, v469; stays [O]); its conformal-deck face QGEO.SYM.01 is a corollary.
The bridge between the static (lattice/spectrum) data and the dynamic (recovery/relaxation) data is not a map but a clock — the order-30 Coxeter element — and, because gcd(5,6)=1, it factorizes into two coprime hands: a static carrier ring ℤ/5 = g_car (golden √5, no rate) and a dynamic family ring ℤ/6 = 2·N_fam (the recovery rate (2/3)⁶, exponent 6). The dynamic hand runs 0,1,2,3,4,5 — position 0 is the conserved law (the attractor, rate 0), 1..5 the live phases; the static hand runs 1,2,3,4,5. So '0,1,2,3,4,5' is the law-inclusive reading and '1,2,3,4,5' the live-only reading of the same clock (v319).
Every TFPT sector is the same object: a gapped operator with a unique attractor (the physics) and a spectral gap (the reason there is no free parameter). The same gap also sizes each sector's first correction — a typed budget, not a uniform band — and the gap rate is the prime-3 (2/3)⁶ or prime-5 golden facet of the order-30 Coxeter clock. Watch the sectors race to their attractor; the gapless r=1 track never forgets its start (the Lean theorem). Beside it: the entire-form-factor graviton (finite, ghost-free, UV-soft) and the residual matrix that is certification, not construction (v383–v391).
The renormalization-group running that carries the boundary data to the observables, computed at two loops. The gauge β-functions are reproduced verbatim by the third-party generator PyR@TE 3 (v159); the strong coupling reaches confinement at Λ_QCD ≈ 0.4 GeV (v164); and the Higgs quartic falls to ≈0 with β_λ ≈ 0 at the Planck scale — the free-seam near-criticality that ties the Higgs mass to the boundary fixed point (v166).
The seven maximal E₈ slices (each a way of cutting 248) are not seven separate hits: every block is built from just two typed alphabets — the anchor power sums P = (3,4,6,10) and the Sheet-Diamond operator determinants (3,4,8,14,20,32), which sum to 81 = N_fam⁴. The atlas is therefore a closed grammar over admissible invariants, exactly what the No-Free-Pattern discipline demands (v170).
The verification suite grew in phases — foundations, the Standard-Model readouts, the seam=horizon geometry, the reductions and external cross-checks, the AQFT closure, the icosahedral capstone, the seam-equivalence closing arc and the certification round (523 scripts today). The closure arc drives the whole remaining structural question down, step by machine-checked step, to a target pinned at every computable level — closed modulo a cited published theorem (MMST/Adamo), not solved. Both views below are live HTML, not images: every script chip runs the real Python in your browser.
Carrier D₅+A₃+μ₄, the E₈ glue, the α⁻¹ fixed point; the anchor a = (1,1,2) to which {c₃, g_car} reduce — the two axioms become {a, π}.
The φ₀ mass ladder, the flavor operators (Q, K, R, L), lepton/quark ratios, hypercharge, the compiler core (5,3).
One-sided Gauss–Bonnet c₃ = 1/(8π), the Coxeter-30 cycle, the gapped attractor (2/3)⁶, the frozen registry + look-elsewhere null-MC.
Nariai = anchor, monodromy = W(A₃) = S₄, cusp weights {0, 1/3, 2/3}, H¹ cohomology, the canonical map.
Deck selection, the EH mechanism, the No-Unit Theorem, the simple-current (E₈)₁, the free c = 8 fixed point isolated and stable.
SM gauge/Yukawa/Higgs RGEs confirmed by an independent third-party generator (b₁ = 41/10), Λ_QCD, m_H near-criticality, η_B leptogenesis.
E₈ slice compression, OS moment/Sugawara, the trace-anomaly seed 4/3, the strong-CP Pfaffian, the Fock readings.
Net existence + full-cone reflection positivity [E]; the residual collapses to one premise: the carrier μ₄ clock is the seam's conformal deck.
The reviewer residual map; F_transfer as one typed functor (Koide, η_B, axion, m_p/m_e) + the machine wording guard.
The QGEO pillowcase (cross-ratio 2 ⇒ j = 1728), the four marks from Gauss–Bonnet, the Sheet-Diamond axis geometry.
McKay: why {2,3,5}; the CM norms 41/7, CP triality, the Kleinian seam, det K = 1 = the Kitaev E₈ phase — the (2,3,5) Brieskorn singularity generates ALL.
The 96-dim spectral triple, Dirac = covariance induction, cutoff = KMS weight; seam, carrier and E₈ on one K3: one relative object.
F_QCD m_p/m_e, the M_ν seesaw, S_pert (Epstein–Glaser, 1-loop + gauge betas), scale over-determination, the QG.AMB roadmap.
Seam = (E₈)₁ at τ=i named as ONE theorem; both routes reduced to one shared input (Flat-Away), the heat a₂ proved + Lean (v295/v296).
Flat-Away hard-pinned from the (E₈)₁ Steklov data (v300); Route A invertible via free fermions (v301); the gap = derived 6 ln(3/2) > 0 (v302).
Typed F_transfer solvers (Koide/η_B/m_p-m_e/axion, v371–v375/v402); the parameter-free Einstein equation, full nonlinear (v359); QG.AMB a [C] redundancy (v369).
The α-Quillen residual narrowed to the continuum ζ-det face (computed inflow level |C| = 1, det-line moduli; v470/v472); the sheet/deck complement + degree-ladder audits (v430/v431); the entropic-action bridge typed and bounded (v473–v478); the Kronheimer quiver bridge (v479), the four-interval μ₄ geometry (v480), the seesaw carrier-ladder candidate (v481).
The two axioms c₃ = 1/(8π) and g_car = 5 are not free knobs: they reduce to the single parabolic anchor a = (1,1,2) plus π, and g_car = 5 is a bootstrap fixed point (forced three ways, Lean-formalised). The full script→check map follows in the index below.
The whole “quantum gravity” question collapses, one machine-checked step at a time, to one falsifiable physical statement: is the raw seam (E₈)₁ at τ=i?
“build a quantum-gravity measure”
discharged to [E] (the CAR functor)
QGEO.SYM.01: the carrier μ₄ clock = the seam's conformal deck
state-invariance ω∘ρ = ω; the DtN map mark-local (ℤ₄)
no abelian sector ⇔ det K = 1 (the Kitaev E₈ tower)
flat τ=i ⇒ [ρ,H] = 0 to ALL orders (FORM.QGEO.03)
χ_E8(i) = 12: the flat τ=i geometry = (E₈)₁ holomorphy
RP-uniqueness 5/6 + condensation 3/4; the open lemmas coincide
import firewall (v286); Route A 4/5 (v287); Route B proves the full-L² ℤ₄ lift (v288)
heat a₂ closed + Lean (v292/v295/v296), spectral Hessian PD (v293), Troyanov (v294); Route A citable stack (v297)
Flat-Away hard-pinned from the (E₈)₁ Steklov data (v300); Route A invertible via free fermions (v301); the gap = derived 6 ln(3/2) > 0 (v302)
QGEO.SYM.01 = a corollary of SEAM.EQUIV.01 (v335); the gapped lattice model (v367/v368) + the S3 stack (v376–v379, ground-state witnesses v489/v490), Lean-pinned MMST
the 128-spinor extension leg certified by the peer-reviewed crossed-product package, realisation at invariant level (v469); the R3 graph→geometry bridge discharged to Kronheimer 1989 (v479); the four-interval μ₄ mechanism exhibited, ω∘ρ = ω manifest (v480)
the SEAM.EQUIV.01 residual = the cited continuum scaling-limit existence (v336) over established facts; stays [O] (not machine-proved end-to-end)
Everything above the bedrock is a theorem, a Lean proof or an established citation; the bedrock, once a definition (QGEO.SYM.01), is now one falsifiable physical question — and the emergent-QFT layer (v258–v261, the Modular Spectral Closure) collapses onto this same bedrock, so the boundary QFT adds no new open item. The full step-by-step reduction lives on the /changelog page.
The actual bridge from compiler to physics: a global real structure Θ plus interacting reflection positivity plus OS reconstruction on the twistorial algebra. Three of its preregistered stages are executed; the contract itself stays open.
Θ exists at the free level; free RP selects the same family
the μ₄ clock is the euclidean rotation; gaugeable datum = the GSO ℤ₂; gauge-fixed RP holds
OS quotient explicit: H_phys positive definite, the clock a positive transfer operator with spectral calculus
next — under the straddle-law constraint
The bedrock is closed modulo cited theorems via the Seam Equivalence Theorem (SEAM.EQUIV.01) — the raw RP seam IS the holomorphic (E₈)₁ net at τ=i (its conformal-deck face QGEO.SYM.01 is a corollary): the target is pinned at every computable level by an explicit lattice model (v367/v368) and the S3 closure stack (v376–v379, ground-state witnesses v489/v490), Lean-pinned (FORM.SEAM.MMST.01) to the published MMST/Adamo theorems, leaving [O] = the cited continuum scaling-limit existence only (v336; extension leg on the peer-reviewed crossed-product package, realisation at invariant level, v469; stays [O]). The emergent-QFT layer (v258–v261, the Modular Spectral Closure) collapses onto this same bedrock — the boundary QFT is one relative object that adds no new open item — and v_geo stays the one no-unit primitive.
The entanglement first law (Jacobson; Faulkner et al.), run with TFPT’s atoms, gives the full covariant Einstein equation (fixed-volume stationarity → the Einstein tensor, v359) with both coefficients fixed — no free dimensionless dial. The seam constant c₃ = 1/(8π) arrives by three independent routes that all agree.
The Hawking normalisation is no longer only postulated into the horizon sector: the reconstructed free seam OS quotient admits exactly one detailed-balance thermal representation, and its temperature comes out T_seam = 4c₃ — the same Bisognano–Wichmann/Hawking normalisation the geometry and anomaly legs carry. Temperature is the third leg of c₃ = 1/(8π).
After the compiler closure the live residual is just three named items — Rest = v_geo ⊕ G_net ⊕ F_transfer. Sharper still: the structural part (the metric inclusion and the carrier P2) is one condition that forces E₈ three equivalent ways — and the entire boundary-QFT layer (Dirac, cutoff, gauging, glue) now collapses onto that same condition via the Modular Spectral Closure. Nothing is hidden, nothing is overclaimed.
The metric inclusion (G_net), the carrier P2 and red-team Target A are not three gates but three faces of a single condition — and all three force E₈:
In words: The seam has exactly one one-dimensional representation (a trivial abelianisation, a homology-sphere link) if and only if it is E₈ — equivalently, the K-matrix has determinant one.
In short. The whole boundary QFT collapses onto this one premise (the Modular Spectral Closure, v258–v261), so SEAM.EQUIV.01 is closed modulo cited theorems: the explicit lattice model (v367/v368) and the S3 stack (v376–v379, ground-state witnesses v489/v490) pin the target at every computable level, Lean-pinned (FORM.SEAM.MMST.01) to the published MMST/Adamo theorems — the only residual [O] is their abstract continuum-existence (v336; its 128-spinor extension leg is certified at net level by the peer-reviewed crossed-product package v469, LR/Böckenhauer/KLM, with AGT/AMT an independent second witness; stays [O]). The ambient measure QG.AMB.01 is a [C] redundancy (v369/v379) — a certification object, not missing dynamics — and perturbative spin-2 graviton unitarity is established (the Stelle ghost is a truncation artefact, v304/v370/v380).
Modular Spectral Closure (v258–v261). The finite Dirac is a covariance induction of the seam KMS state, the spectral-action cutoff is that KMS weight (f₂/f₀ = 1), and seam, carrier-16 and E₈ live on one Kummer/K3 surface — so Dirac, cutoff, gauging, glue and orientability are readouts of one seam state. QGEO.SYM.01 is then a corollary (a conformal net's vacuum is rotation-invariant by axiom, v335).
Seam keystone.The keystone's residual is a composition of standard cited theorems (OS/clustering, the Kitaev free-fermion classification, the AQFT stack) over established TFPT facts — Lean-pinned to those named steps plus the derived gap Δ = 6·ln(3/2) ≈ 2.43 > 0, no undischarged TFPT-internal assumption. Its two heavy legs are literature-anchored (v336): the MMST continuum scaling limit and the Adamo–Moriwaki–Tanimoto OS reconstruction, with (E₈)₁ inside their range (c=8, rank 8, 16 Majoranas) — and the 128-spinor extension leg is now certified at net level by the peer-reviewed crossed-product package (v469, LR/Böckenhauer/KLM), with the AGT/AMT route demoted to an independent second witness; stays [O].
QG decoupling is a theorem (v337).Every readout factors through the gapped admissible spectrum (χ = 729/665, margin 1.648 > 0), so TFPT provably does not need the ambient measure.
4D-QFT fork (v265). Boundary QFT — closed modulo cited theorems; ambient QG — discharged as redundancy [C]; 4D GUT — not claimed (E₈ is the audit hull, not a 4D gauge group); optional UV branch — carrier-native Pati–Salam, falsifiable by thresholds and proton decay. The sprint-by-sprint reduction (v234 → v302) is on the changelog.
One dimensionful scale — irreducible by the No-Unit theorem and over-determined (gravity = dark energy = M̄_Pl to 0.11%, v274); the same primitive as gravity's 1/G.
Metric inclusion: the (E₈)₁ target is closed and pinned at every computable level (lattice v367/v368 + S3 stack v376–v379, ground-state witnesses v489/v490); the seam coupling SEAM.EQUIV.01 now carries two named routes (route split 2026-07-22, no status change in substance): the MMST route SEAM.EQUIV.MMST.01 is closed modulo cited theorems (Lean FORM.SEAM.MMST.01), residual [O] = the cited MMST continuum existence only (v336; extension leg crossed-product certified, v469); the twistor route SEAM.EQUIV.TWISTOR.01 (Costello–Li construction, prepared by CELEST.SEAM.01) is [O]; the parent closes if either route closes and stays [O] as an unconditional claim.
One typed runnable solver suite (v371–v374) + a prediction-observatory CI (v375), each with a kill test — bridges, never primitive outputs.
Quark ratios are closed (Readout Rigidity, c_u/c_d = 55/117); only the absolute scale v_geo remains. The No-Unit theorem (v153) makes it an irreducible metrology primitive — the same unit as gravity's 1/G, over-determined to 0.11% by gravity vs dark energy (v274). A unit, not a gap.
The (E₈)₁ target is closed [E] (v154/v175). The seam coupling SEAM.EQUIV.01 is closed modulo cited theorems: the lattice model (v367/v368) + the S3 stack pin it at every computable level (c = 8, the (E₈)₁ character, torus GSD = 1, RP; v376–v379, ground-state witnesses v489/v490), Lean-pinned (FORM.SEAM.MMST.01). Residual [O] = the cited MMST continuum-existence only (v336; extension leg on the peer-reviewed crossed-product package, realisation at invariant level, v469; stays [O]).
One typed, runnable solver suite — Koide (v371), η_B (v372), axion relic (v373), m_p/m_e (v374) — each with a kill test, folded into a prediction-observatory CI (v375). A guard (v187) keeps them [C] bridges, never compiler outputs.
F_transfer: one shape, four rates
Every transfer instance is a gapped relaxation to a unique attractor — the same shape as the main-branch update to the E₈ marks.
Only F_pole (Koide) runs at the seam rate — its Möbius multiplier is (2/3)⁶ = λ₂, the seam-clock eigenvalue. The other three share the shape with external rates (thermal washout, cosmological freeze, RG flow). So F_transfer is the readout end of the one discrete→dynamic principle, not a bolt-on (v303).
Two axioms at the source, the E₈ compiler in the middle, the observables as sinks. Click any node to see what it is, its status marker, its inputs and outputs, how it can fail, and the scripts that machine-check it — then click a script to run it live in your browser. The dashed rose edges are the bootstrap: the E₈ closure feeds back and fixes the inputs.
D₅ and A₃ share the discriminant group ℤ₄; their glue norms add to the root norm, q(D₅) + q(A₃) = 5/4 + 3/4 = 2. So E₈ = (D₅ ⊕ A₃) + μ₄ closes as a lattice theorem — the unimodular audit hull, not a gauge group; 240 = 16·5·3 roots, 248 = 240 + 8. It is the forced choice, not a guess: no nontrivial abelian sector ⇔ holomorphy ⇔ det K = 1 selects (E₈)₁ uniquely (v234/v235/v237), and the whole (2,3,5) skeleton drops out of the Brieskorn capstone (v236). The golden ratio φ is not a fitted number but the icosahedral (2,3,5) signature — an output of the bootstrap-forced geometry, not an input (v349/v354) — and a reverse numerology audit of the unmapped E₈ region finds no missed primary readout under a strict discriminator (v355). The sheet/deck complement (v430) closes the adversarial follow-up: the seam's “other side” (the double-cover deck |ℤ₂| = 2 and the conjugate half-spinor S⁻ = part of the 128-spinor, ∑deg) is matched structure, forced-disjoint from the five unmapped Casimir degrees {12,14,18,20,24}. Those five are not diffuse overhead either: they are the forced two-family decomposition deg(E₈) = 6·spine{2,3,4,5} ⊔ ({2}∪det-ladder{8,14,20}), the residue classes {0,2} mod 6 forced by h = 30 = 2·3·5 (v431) — exact arithmetic, with the functorial flavour identification honestly kept [P].
Dependencies: a LaTeX distribution, Python 3 with sympy / mpmath / numpy / matplotlib; optionally the Wolfram Engine and Lean 4. Every script cited in run_all.py is also cited inline in the documents, and the status heatmap is generated directly from the ledger.
# 1. Compile the active document set -> "10 ok, 0 failed"
bash build.sh notes
# 2. Run the Python verification suite -> "ALL CHECKS PASSED"
cd verification && python run_all.py
# 3. Independent Wolfram path (optional) -> "ALL WOLFRAM CHECKS PASSED"
wolframscript -file verification/wolfram/tfpt_readouts.wl
# 4. Lean carrier-rigidity proof (optional) -> "AUDIT: PASS"
cd experiments/lean4-carrier-rigidity && lake exe cache get && bash scripts/audit.sh
# 5. The sync audit (papers <-> suite <-> ledger <-> website) -> "AUDIT OK"
bash build.sh audit
# 6. Regenerate the reproducibility manifests (run last)
python verification/make_manifest.pyThe full verification suite, grouped by what it proves. Every script links to its source in the public repository.
The suite is organised by what it proves. Each script is one claim cluster, cited inline in the documents via \veri{vN} and registered in run_all.py, which ends ALL CHECKS PASSED. Click any script to run it live in your browser.
523 scriptsWhy the two axioms build E₈, why the carrier rank is forced, and the integer skeleton that follows.
The fine-structure constant as the unique root of the boundary U(1) Ward identity.
The integer operator ladder (R, K, Q, L) and its spectral invariants — the flavor signature.
The φ₀-ladder mass formula, the exact lepton coefficients, and the integer-Plücker quark ratios.
The Majorana texture, the dual anchor, and the previously open solar angle from the seam.
The R + R² spectral-action shadow, the seam-fixed scalaron, and the cosmological readouts.
The seam as the universal horizon code, the order-30 Coxeter cycle, and the gapped unique attractor that makes parameter-freeness a theorem.
The parabolic wall-selection contract: the quark ratios are closed; only the absolute amplitude scale stays open.
The quantum-gravity measure contract, the audit ledger, the data scorecard, and the honestly-typed frontier items.
The frozen prediction registry and the follow-up rounds: Target A merged to one residual, the CP residual quantified, N★ from reheating, the F_transfer gauge inputs cross-checked with an external RGE tool, and the AQFT closure round — net existence and full-cone reflection positivity discharged to [E], leaving the seam realisation as the single open premise. Every freeze machine-enforced.
These checks are reproducible by anyone — that is what “independent” means here: the same result falls out on your machine, on an independent Wolfram path, and (for the carrier) in Lean. We do not claim external endorsements; we invite review. Open questions and known limitations are tracked openly in the research contracts and the status ledger — disagreements go in the issue tracker.