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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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Quartic half

v690_quartic_half.py · core

Read the original description and evidence links

E8.QUARTICHALF.01: die quartische Invarianten-Restriktion (Review-Vertrag E8.QUARTIC.HALF.01) — ist G31 der holomorphe μ4-Schatten des E8-Compilers? AM LEBEN, mit dem ehrlichen Split: **die Verschwinde-Hälfte {2,14,18,30} ist WAHR aber TRIVIAL (μ4-Orbitfaktor, symbolisch bewiesen: W(Jα) = −i·W(α) ⇒ jeder J-Orbit trägt t^d(1+(−i)^d+(−1)^d+i^d) = 0 für d ≢ 0 mod 4 — gilt auch für 6,10,22,26); DIE SUBSTANZ: F8|, F12|, F20|, F24| sind G31-invariant (60/60 Spiegel exakt), ALGEBRAISCH UNABHÄNGIG (exakte Jacobi-Determinante ≠ 0), Grade Molien-eindeutig mit Produkt 46080 = |G31| ⇒ per Chevalley [zitiert] BASISINVARIANTEN: die holomorphe Restriktion des W(E8)-Rings erzeugt den VOLLEN G31-Ring**; die Jacobi-Determinante trägt die 60 Spiegellinien (Grad 60 = Σ(d_i−1), punktverifiziert 60/60; volle Faktorisierung = zitierter Satz, benanntes Residual); Kontrollen: J′ = RJRᵀ bricht die informative Hälfte, das wurzelerhaltende J″ erhält alles (der Satz gilt der W(E8)-Konjugationsklasse); keine Floats; kein Marker-Move (22 Checks, ~1 s)

Read the original Python source

Linked claims: E8.QUARTICHALF.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

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

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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