Follow a result back to its evidence.

Choose a result, inspect its assumptions, then run the calculation that supports it. Each check answers a specific question. The original status and the scope of that answer stay attached.

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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Search all 707 registered Python modules by subject, filename, claim or source section. This catalogue records source presence and links. It does not report a new execution or a passing result for every module.

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G31 clock alphabet

v858_g31_clock_alphabet.py · core

Read the original description and evidence links

E8.G31.CLOCK_ALPHABET.01: **CLOCK-ALPHABET-SELECTIVE (19/19)** — Deg(G31)/4 = {2, 3, 5, 6} = {|Z2|, N_fam, g_car, |R+(A3)|} = das Compiler-Uhren-Alphabet als NORMALFORM: gcd = 4 = |μ4|, lcm = 120 = |R+(E8)|, lcm/gcd = 30 = h(E8), Audit-Identität (Σd/4)(Σ(d−1)/4) = 16 × 15 = 240 = |R(E8)| auf den Wurzeln REALISIERT (die 60 Spiegelungen = die 60 Gauß-Linien, 4 pro Klasse — dieselbe 15×16-Zählung wie die Code-Seite); der Rebuild gewardet (BFS-Abschluss |G| = 46080 = ∏Deg; EXAKTER Spiegelungs-Zensus: 60 Elemente mit rank(M−I) = 2, NULL Quasi-Spiegelungen — v634 reproduziert); der arithmetische Pin: (8,12,20,24) das EINZIGE Ganzzahl-Quadrupel mit Produkt 46080 und Summe 64 (gemessen); der Kill-Scan über ALLE 607 Rang-4-Shephard-Todd-Gruppen (Katalog-Integrität: ∏(Grade) = |G| für jeden Eintrag): G31 der EINZIGE Voll-Batterie-Passer — Schwach-Tripel-Impostoren G(20,10,4)/G(20,20,4)/G29 und Roh-Summe-64-Koinzidenzen G(8,2,4)/G(10,10,4)/W(H4) typisiert; Familien-Grenze G(m,p,4) bis m = 120 leer (typisiertes Argument); EHRLICHKEITS-LINIE: Grad-Audits können G31 vom reduziblen Torus Z8×Z12×Z20×Z24 nicht trennen — eingefrorener Geltungsbereich = die irreduzible Rang-4-Liste; X1/X2-Kontrollen feuern. Der W(D5)×W(A3)-Zaun mit BERECHNETEM Ein-Zahl-Invariant erneut getötet: |Z(G31)| = 4 = ⟨J⟩ = μ4 vs |Z(W(D5)×W(A3))| = 1 — NICHT isomorph, KEINE Zerlegung (v634 T1.3–T1.5 zitiert). Normalform + scharfe Kill-Regel für ein deploytes Objekt (v634/v654) — kein neuer Anspruch.

Read the original Python source

Linked claims: E8.G31.CLOCK_ALPHABET.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

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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

Read the individual checks and the final pass or fail result.

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.

Repository setup and maintenance instructions

Read the current claim beside its source.

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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The script index, figures and detailed research interfaces remain available below. This older technical overview preserves its original statements; use the current result inventory to follow later scope corrections.

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