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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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Python runs in your browser using Pyodide. The first run downloads the runtime. Its output appears in the existing verification viewer, including any failure and the local reproduction command.

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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Alpha quillen betafunction

v434_alpha_quillen_betafunction.py · em

Read the original description and evidence links

ALPHA.QUILLEN.PROGRESS.03: a THIRD honest step on ALPHA.QUILLEN.EXACT.01 (v382) -- it settles the three residuals named after v433 and shows they are NOT three independent problems; the target stays [O], alpha^-1 stays [E]. [E] b1 IS THE U(1) a_4 HEAT-KERNEL COEFFICIENT (beta=a_4 theorem): from the carrier hypercharge content with spin weights (2/3 Weyl, 1/3 complex scalar), sum (2/3)Y_f^2+(1/3)Y_s^2 = 41/6 (SM), (3/5)*that = 41/10 = b1 (GUT) -- the b1 in 8 b1 c3^6 is the a_4 content coefficient, not a fitted multiplicity (same number as the beta, v159/v246; same KIND as the alpha^2 Calderon a_4, v342). [E] 8 b1 c3^6 = b1*(rank E8)*c3^6 (rank 8 = chi=2 boundary, v216; c3^6 = six insertions, v342). [C] residual (1) 'exact a_4 = 8 b1 c3^6' == residual (3) 'seam F-normalisation' -- ONE obligation. [E] residual (2) located: a^3-2c3^3 a^2 = a^2(a-2c3^3), so a^3 = the first moment of the Chern density (a level, order c3^0); origin stays [O]. [E] net reduction: the EM-Ward residual is 1[C]+1[O], not three. [O] NOT CLOSED; alpha^-1 stays [E]. Python-only.

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Linked claims: ALPHA.QUILLEN.PROGRESS.03
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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