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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Orbit60 quotient

v633_orbit60_quotient.py · core

Read the original description and evidence links

E8.ZIQUOTIENT.01: die μ₄-Quotienten-Runde — **DER QUOTIENT DER 240 E8-WURZELN NACH DER FREIEN μ₄-CLOCK IST DAS HERMITESCH-UNIMODULARE ℤ[i]-E8 MIT DEM 60-HYPEREBENEN-SYSTEM VON ST31; DIE 60→6-KASKADEN-ROUTE AUF DEM QUOTIENTEN IST GEKILLT**. [E] H(v,v) = 2 auf allen 60 Repräsentanten; ℤ[i]-Spann = volles E8 (Covolumen 256), hermitesch-unimodulare Basis unter den Reps (det Gram = 1); σ auf den 60 Linien: 19×3 + 3 fix (= die J-Orbits der 12 σ-fixen Wurzeln); alle 60 Ordnung-2-Reflexionen erhalten die Wurzeln, Linien-Gruppe der Ordnung 11520 = 46080/4 (ST31-Fingerprint; ST32 durch 40 Hyperebenen gekillt). [E, KILL] Kaskaden-Harttest: Gram-Rang 4, beide Quotienten-Graphen regulär, keine kanonische Paar-Regel — getyptes Negativ (17 checks, ~3 s)

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Linked claims: E8.ZIQUOTIENT.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

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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