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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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Simplex fourier winding

v857_simplex_fourier_winding.py · core

Read the original description and evidence links

E8.SIMPLEX.FOURIER.01 + FLAVOR.WINDING.QUADRATIC.01: **SIMPLEX-FOURIER-EXACT + INTERTWINER-IDENTIFIED (26/26) + WINDING-QUADRATIC-EXACT (20/20)** — die E8-Audits I: der Gauß-Zensus IST ein Fourier-Gesetz — r̂ = (240, −16¹⁵), Kanal P = (J−I)/15 mit Spektrum {1, (−1/15)¹⁵} und Zwei-Schritt-Kontraktion 1/225 (exakt in Brüchen); Ramifikation Θ₀(ungerade) = 0 mit Ein-Zeilen-Beweis; Äquidistribution auf JEDEM Level ≤ 16; der Paket-Zähler (Th0−Th1+Th2−Th3)(n) == die Code-Walsh-Transformierte auf JEDEM Level ≤ 16 (beide Leitern [−16, 112, −448, 1136, …]; Eisenstein-Normalform 15Θ_D8 = 7Θ_L + 8Θ₀); der WERT-SATZ: mh₂(n) = −1/15 für JEDES ungerade n ≤ 16500 (Ganzzahl-Identität, alle 1911 ungeraden Primzahlen abgedeckt) — v817s Pro-Primzahl-Messung ist die Primzahl-Restriktion eines CHARAKTER-SATZES des Codes; ehrlich typisiert: SPEKTRAL (die Paket-Gradierung (52,60,128) und die Code-Gradierung 15×16 verfeinern einander NICHT); 3 Kontrollen feuern, 2 Invarianzen halten (24 explizite Isometrien; die andere invariante Platzierung C**). Die Windungs-Quadratik (tfpt_2 I.5): χ_{R_s} − χ_R = −s·q_wind mit q_wind = e₁ᵀ adj(tI−R) 1 = t² − g_car·t + |Z2| EXAKT (Adjugat-Lemma; irreduzibel über Q, disc 17); die Keybox-Koeffizienten (9+s, 10+5s, 8+2s), das det-Inkrement 2 = |Z2| und das Minor-Gesetz (5, 3(s+1), 2(s+1)) sind Auslesungen der EINEN Quadratik; Dreifach-Lock s = 6 (Spur/Determinante/Coxeter-Lift, Schnitt {6} = {|R+(A3)|}); Δ(6) = 39200 = 2·140² > 0 (KEIN Kollisionspunkt; der EINZIGE 2×Quadrat-Treffer im Fenster −2…12); Realitäts-Schwelle s* ≈ 2.8250 = die einzige Δ-Wurzel in (2,3) (deployt ≈ 2.83); 4 Kontrollen feuern (Geschwister-Richtungen brechen Lock UND Quadratik). Exakte Korpus-Kompressionen deployter Ansprüche (v817/v833/v844, v4/v94) — kein neuer physikalischer Anspruch, keine Marker-Bewegung.

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Linked claims: E8.SIMPLEX.FOURIER.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

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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.

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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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