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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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Resonance uniqueness

v116_resonance_uniqueness.py · registry

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RESONANCE THEOREM (the v115 [N] findings promoted to [I] by a LINEAR computation — the anticipated Gröbner step was unnecessary): TWISTED-AVERAGE LEMMA [I] — at infinity the equivariant system reads dY/dw = −(1/w)(B₀ + B₁w + …)Y with B_m = Σₖ i^{km} Uᵏ A₀ U⁻ᵏ; the twisted μ₄ averages collapse to B₀ = 4 diag(A₀) and B₁ = 4a₁₂E₁₂ + 4ā₁₃E₃₁ (only the eigenvalue-ratio −i cells survive); RESONANCE THEOREM [I]: the anchor exponents diag(2,1,1) have resonance gap 1, the level-1 gauge equation is singular exactly on cells {(2,1),(3,1)} where B₁ = (0, 4ā₁₃), higher levels non-resonant, formal monodromy = 1 ⇒ M∞ = 1 ⟺ a₁₃ = 0 — the transcendental Riemann–Hilbert condition collapses to ONE linear equation; UNIQUENESS COROLLARY [I]: a₁₃ = 0 + the (8,0,5)/144 moduli + diagonal gauge ⇒ THE FLAT ANCHOR LOCUS IS EXACTLY ONE GAUGE ORBIT = the exact A₀* — within the μ₄-equivariant anchor class the U_wall bundle datum is ALGEBRAICALLY unique; FALSIFICATION CONTROL [N]: ‖M∞ − 1‖ ≈ 8.5|a₁₃| (sharp), 1.6e−10 at A₀*; honest scope: residue side [I], holonomy values (harmonic diagonal) remain [N]

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Linked claims: GATE.UWALL.08
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

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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