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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Hypergraph homotopy

v345_hypergraph_homotopy.py · core

Read the original description and evidence links

EXECUTE the combinatorial core of route R3 (the hypergraph-homotopy route to det K=1, v344): computes explicitly that the (2,3,5)-rewrite attractor graph's plumbing link is the POINCARE homology sphere (H_1=0), only E8 among ADE; R3's combinatorial half is now [E]-complete, the geometric bridge (= SEAM.EQUIV.01) stays [O]. Plumbing topology (Brieskorn): link H_1 = coker(Cartan). [E] SNF(E8 Cartan) = identity => coker(E8)=0 => the E8 plumbing boundary is an INTEGRAL HOMOLOGY SPHERE (the genus-1 meaning of det E8=1). [E] only E8: coker(A_n)=Z/(n+1), D_n->Z/4, E6->Z/3, E7->Z/2 -- all nontrivial, only E8=0. [E] pi_1=2I=SL(2,5) PERFECT (commutator subgroup order 120=|G|, computed) => H_1=0 => THE Poincare sphere; |2I|=120=|mu4|*h(E8). [O] does NOT close det K=1: the graph->geometry half is meanwhile Kronheimer-cited (v479); what stays open is the raw seam supplying the ALE/orbifold datum = SEAM.EQUIV.01.

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Linked claims: SEAM.DETK.02
Paper sections: Source section 1 Source section 2 Source section 3 Source section 4 Source section 5 Source section 6 Source section 7

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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