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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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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Necessity of H

v331_necessity_of_H.py · frontier

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The NECESSITY of H reduced: rotation-invariance of the seam DtN is EQUIVALENT to the four marks at the square (tau=i), so the one open lemma is exactly the order-4 CM selection (the necessity companion to v329's sufficiency). [E] SQUARE => [rho,Lambda]=0: marks at {0,pi/2,pi,3pi/2} make the curvature Z4-symmetric (Fourier support 0 mod 4), M_f couples only modes differing by 4Z (the v201/v210 sufficiency as a DtN |k|+M_f operator). [E] NECESSITY: a mark off the square breaks Z4 and gives [rho,Lambda]!=0 -- equivalence, not just implication. [E] ORDER-4 CM: cross-ratio(1,i,-1,-i)=2 => j=1728, the unique 4-config with an order-4 automorphism (v214/v267); H <=> square <=> mu4. [E] NEG: a Z2 mark set commutes with rho^2 but not rho. [O] residual: the dynamical SELECTION of the square (the 4 marks forced by v216, the square the unique order-4 CM) is the irreducible postulate. Does NOT close the bedrock.

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Linked claims: QGEO.NECESS.01 FORM.MU4COMM.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

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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The script index, figures and detailed research interfaces remain available below. This older technical overview preserves its original statements; use the current result inventory to follow later scope corrections.

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