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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.

Read the Python source

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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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E8 torsor fourier

v800_e8_torsor_fourier.py · core

Read the original description and evidence links

E8.TORSOR.FOURIER.01: die projektiven Fourier-Moden der 15 Gauß-Torsoren — Träger-Reinheit auf CHARAKTER-Niveau mit der wechselseitig-unverzerrten Kappe — **TORSOR-FOURIER-PARTIAL (30/30): 120 kanonische projektive Strahlen (Phasengesetz exakt auf 960 Ursprungs-Shifts), orthogonale Basis (Gram = 16 I); Deck J und alle 16 Paulis diagonal nach Charakteren, G31 monomial durch Sp(4,2) (Kern 64 = μ₄ × Pauli16; Orbits 15 + 45 + 60). DER TRÄGERBLOCK: die 64 Strahlen der 8 R-Fasern = (1 + 5 + 10) ⊠ (1 + 3) unter W(D5) × W(A3) (Clebsch-Charakterpolynom (x−5)(x−1)¹⁰(x+3)⁵ exakt; S4-natürliche Tetrade mit σ = Familien-3-Zyklus + Anker) — das Träger-Pascal auf CHARAKTER-Niveau, auf Punkt-Niveau unmöglich (v775); P3 fällt wie vordeklariert: Gewichts- und Charakter-Basis WECHSELSEITIG UNVERZERRT (|⟨Paar|Mode⟩|² = 1/8 exakt) — ROOTCLASS-MIXED intakt; die 45 deck-geraden Moden SIND die 45 (Kontext, Pauli)-Inzidenzen unter der zertifizierten Karte (Operator-Wörterbuch für die v791-Intertwiner-Forderung notiert); Kontrollen feuern

Read the original Python source

Linked claims: E8.TORSOR.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

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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

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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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