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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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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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St31 degree8

v654_st31_degree8.py · core

Read the original description and evidence links

E8.ST31D8.01: die ST31-Grad-8-Runde + der vereinheitlichte d/4-SATZ — **JEDE Springer-reguläre d-Uhr von G31 erfüllt x^{d/4} = ±i·Id, einen ERZEUGER von μ₄ (nie ±1; eine Formel aus der Exponenten-Systematik: alle Exponenten ≡ 3 mod 4); DIE UMKEHRUNG IST EXAKT BEI d ∈ {8, 20, 24}, UND DIE EINZIGE AUSNAHME BEI d = 12 IST DIE COMPILER-UHR-KLASSE** (1280 Extra-Elemente = Klasse von c und Galois-Zwilling; χ_c = (x−i)²(x²+ix−1) = die HALBE reguläre 12er-Springer-Box, alle Eigenwerte λ³ = −i — exakt darum ist c³ = J³ zentral: die Compiler-Uhr-Klassen sind die EINZIGEN nicht-regulären Uhren in ganz G31, deren d/4-Potenz das Zentrum erzeugt); **Ordnung-8-Landschaft komplett (10560 Elemente, 480 regulär = 2 Galois-Klassen, χ = (x²+i)² exakt) und der ehrliche KILL: „frei ⇒ regulär“ ist FALSCH** (4320 freie 8er nichtzentral; schon bei Ordnung 4: 510, keins regulär); Grade = freie Ordnungen mit 4 | d, d > 4 (30 checks, ~10 s)

Read the original Python source

Linked claims: E8.ST31D8.01
Paper sections: Source section 1 Source section 2 Source section 3 Source section 4 Source section 5

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

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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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