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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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Flataway a2 exact

v295_flataway_a2_exact.py · frontier

Read the original description and evidence links

FLATAWAY.A2.01 — the EXACT analytic a₂ coefficient, upgrading the v292 positive-definiteness from numerical to a proof. [E] first variation vanishes: d/dε Tr e^{−tΛ(ε)}|₀ = −t f̂(0) Σe^{−t|n|} = 0 (smooth off-mark curvature has zero mean, Gauss-Bonnet); [E] convexity ⇒ global minimum: φ(x)=e^{−tx} strictly convex ⇒ Λ↦Tr e^{−tΛ} convex (Klein/Peierls), so ε=0 is the GLOBAL minimum and ΔTr≥0 for ALL ε (verified even in ε over [−1,2]), =0 iff f=0; [E] exact a₂ kernel ΔTr⁽²⁾=(1/4)Σ_n[Φ(|n|,|n+4k|)+Φ(|n|,|n−4k|)]g² with the divided-difference kernel of e^{−tx} (Duhamel), matched to numerics to rel.err<1e−6; [E] degenerate-split closed form 2e^{−2kt}(cosh(tg/2)−1)≥0; [O] reduction now analytic: Flat-Away ⟸ 'the seam fixes a₂'. Lean-mirrored (FORM.FLATAWAY.01).

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Linked claims: FLATAWAY.A2.01 FORM.FLATAWAY.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

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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