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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E8 char cm duality

v404_e8_char_cm_duality.py · frontier

Read the original description and evidence links

E8.CMDUAL.01: the (E8)_1 vacuum character chi_E8=E4/eta^8=j^{1/3} at the two CM points -- 12 at the seam (tau=i), 0 at the family (tau=omega), extending v282. [E] chi_E8^3=j (q-series). [E] SEAM tau=i (Q(i), order 4): cross-ratio 2 => j=1728 => chi_E8(i)=12 (E8 present, v214/v282). [E] FAMILY tau=omega (Q(sqrt-3), order 6): equianharmonic lambda (lambda^2-lambda+1=0) => j=0 => chi_E8(omega)=0 (E4 vanishes, v220/v267). [E] tau=i,tau=omega are the only elliptic points of PSL(2,Z) so the values are forced. [C] the seam/flavor rigidity duality: seam rigid where E8 present (chi=12), flavor the soft residual where E8 degenerates (chi=0); dual-keystone candidate. Core values j=1728/j=0 already mirrored (v214/v220/v267/v282).

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Linked claims: E8.CMDUAL.01
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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