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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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P2 partition corollary

v491_p2_partition_corollary.py · core

Read the original description and evidence links

P2.PARTITION.01: g_car = 5 as a COROLLARY of the four marks -- the partition sharpening of v53 (sympy exact). The lemma: exactly 3 positive integers summing to 4 = uniquely {1,1,2} => e = (4,5,2) => g_car = e2 = 5, |Z2| = e3 = 2, N_fam = e2-e3 = 3 as corollaries; consistency fixed point (2^4-1)/5 = 3 = rank H^1. Negative controls (each assumption load-bearing): drop positivity -> 4 solutions, e2 in {0,3,4,5}; sum 3 -> e2 = 3; sum 5 -> not unique; 2/4 parts -> e2 {3,4}/{6}; Mehta-Seshadri rational weights -> 16/3 resp. 44/9 != 5 (integrality = Birkhoff-Grothendieck splitting-type typing). [E] v53 sharpening: v53 needs all three targets (4,5,2), the partition only e1 = 4. [E] sum rule 4 x (N-1)/2 = 4 iff N = 3; v115 route 4 tr(A0) = 4. Independence: #marks = 4 (v216, P1-side), rank H^1 = 3 (v137/v228), |a|_1 = 4 g_car-free (v115). [C] honest residual: P2 NOT axiom-free -- the weight-typing postulate remains; AX.P2.01 stays a declared axiom; N_fam direction reversal typed as over-determination. Exact (sympy); Wolfram-mirrored.

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Linked claims: P2.PARTITION.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 Source section 14 Source section 15 Source section 16 Source section 17 Source section 18 Source section 19 Source section 20

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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