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Start with the E₈ construction.

The first module builds the lattice explicitly. It checks the glue, constructs its 240 roots and tests the lattice basis. You can read the source before running it.

Question: Does the explicit construction give the even, unimodular E₈ lattice?
What is tested: Shared ℤ₄ discriminant data; glue norms 5/4 + 3/4 = 2; 240 roots of squared length 2; an integral, even basis with determinant 1.

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This is a mathematical lattice check. Identifying that lattice with a physical system requires additional arguments and retains its own status.

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Alpha faces computed

v974_alpha_faces_computed.py · core

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ALPHA.QUILLEN.EXACT.01 [O-Update] + SEAM.CONTACT.UNIT.01/.02 + EM.WARD.01 / ALPHA.QUILLEN.INFLOW.01 + ALPHA.QUILLEN.FACES.01 [E, NEU] (Seam/Alpha-Promotionswelle 2026-08-27): **beide benannten Faces des Alpha-Targets tragen jetzt GERECHNETE Zeugen** — drei Probes byte-exakt eingebettet, sha256-gepinnt und wörtlich ausgeführt (21/21 MATCH_MODULO_LOCAL_FACTOR + 20/20 PUMP_QUANTIZED_MATCHES_CHERN + 18/18 CHAIN_SHADOW_OK) plus die modul-eigene Exaktsektion S0 (sympy/Fraction/mpmath, keine Probe-Importe). (1) Das BFK-Face AUSGEFÜHRT: die Burghelea–Friedlander–Kappeler-Klebekonstante ist EXAKT 2^−N (symbolisch hergeleitet N = 1..4, allgemeine Intervalllängen, Laurent-Polynom-Identität); masselose Reassemblierung det′_ζ(Δ_S¹) = l² = 2^−N·∏(2a_j)·(l/N)·det′(R₀) mit det′(R₀) = N·l/∏a_j; an der KMS-Skala l = 2π = 1/(4c₃): R₀ = 16c₃·circ(2,−1,0,−1) (16c₃ = |μ₄|·4c₃ pro Intervall), det′R₀ = 2¹⁶c₃³, Produkt (2π)²; Sprungmatrix R(m) = (G_m|_marks)⁻¹ exakt; gegen die v484-Markenmatrix G_marks = −4c₃ln2·circ(0,1,2,1) KEINE globale Proportionalität (Kerne in VERTAUSCHTEN μ₄-Kanälen: Eich-Nullmode vs. Vorzeichendarstellung), aber kanalweise EXAKT (gleiche μ₄-Fourier-Eigenbasis, |spec|-Multimengen {0,2,2,4}, Dublett-Verhältnis 4/ln2 mit KÜRZENDEM c₃, Tr B^k = 4^k + 2·2^k spiegelt Tr C^k = 4^k + 2(−2)^k — der Vorzeichen-Flip IST der Kern-Tausch); der v485-Skalenkanal EXAKT reproduziert über die KMS-Einheit (log det′-Differenz = (1/(4c₃))·G_reg(0;l)). (2) EM1 GERECHNET: gepumpte Ladung == Rand-Spektralfluss == Streda == Chern == 1 pro Flussquant auf dem v367-Kragenmodell (Wannier-Winding-Residuum 0.0; Streda ΔN = C·n_φ exakte Ganzzahlen; der Konjugations-Mutant kippt ALLE VIER Lesarten simultan, der Falschband-Projektor bricht die Quantisierung gitterinstabil); Buchhaltung exakt: 16 Majoranas = 8 komplexe Kopien, c₋ = 8 = g_car + N_fam, k_Y = 5/3, (1/k_Y)·41/6 = 41/10 = b₁. (3) Die endliche Quillen-Identität ZWEISEITIG: Berry-Integral == Poincaré–Lelong-Divisor-Integral == +1 über dem Twist-Torus (beide Referenzen, beide Größen), Differenz eine EXAKTE Form (3.3e−16), Übergangs-Winding == Chern (Dai–Freed); typisiert konditional auf die Quasi-frei-Rigiditäts-Prämisse (gemessen, nicht bewiesen — SEAM.STATE.RPMIXING.01). S0 leitet alles unabhängig her: die BFK-Geschlossenformen aus den ζ_R-Werten, den Alpha-Anker bei 50 Stellen (8b₁ = 164/5 exakt, EINDEUTIGE Wurzel im Scanfenster, α⁻¹ = 137.03599921684071, Split-Residuum 6.4e−58), die Inflow-Buchhaltung als exakte Brüche und ein probe-freies FHS-Chern-Zertifikat. Mutanten: Hash-Mutation vom sha256-Pin gefangen; die falsche KMS-Einheit (2π → 4π) bricht die Skalenidentität um EXAKT −2ln2; der b₁-Mutant gefangen. KEINE Marker-Bewegung: das Target bleibt [O] — Restinhalt typisiert als {Rigiditäts-Prämisse} + {Kanal-Tausch-Frage (das geschärfte Diagonal-Zeta-Face)} + {Kontinuums-Bismut–Freed-Identifikation}; α⁻¹ bleibt [E] unabhängig davon.

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Linked claims: ALPHA.QUILLEN.FACES.01
Paper sections: Source section 1 Source section 2 Source section 3 Source section 4 Source section 5 Source section 6 Source section 7 Source section 8 Source section 9 Source section 10 Source section 11 Source section 12 Source section 13 Source section 14 Source section 15 Source section 16 Source section 17 Source section 18 Source section 19 Source section 20 Source section 21 Source section 22 Source section 23 Source section 24 Source section 25 Source section 26

Different evidence answers different questions.

A numerical calculation, a formal theorem and an experimental comparison carry different kinds of information. Follow the source appropriate to the claim.

Python calculations: Inspect the algorithm, its inputs and its negative controls. Run a browser compatible module here, or use the repository for the complete environment.Browse Python sources
Formal mathematics: Read the actual Lean statement and its assumptions. The carrier formalization has a defined mathematical scope.Inspect the Lean formalization
Independent implementation: The Wolfram implementation checks algebraic results through a separate computational path. The recorded runs report 116/116 base checks and 603/603 extension checks. This is distinct from external experimental replication.Read the Wolfram implementation
Physical comparison: Read each prediction with its freeze, conditions and failure criterion. A passing mathematical check does not decide the experimental comparison.Open the prediction register

Run the same check on your machine.

From a checkout of the repository, install its Python requirements and run the first lattice module. The complete suite is a separate step.

Set up the repository

git clone https://github.com/sthamann/tfpt.git
cd tfpt
python3 -m venv .venv
.venv/bin/pip install -r requirements.txt

Check the E₈ lattice

.venv/bin/python verification/v1_e8_glue.py

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Run the registered suite

cd verification
../.venv/bin/python run_all.py

The full suite uses the dependencies and source context documented in the repository.

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The research snapshot dated 2026-11-02 includes the active ledger, reviewed findings and registered scripts. It records source coverage and stated scope; it is not a new execution of every proof or calculation.

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