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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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Galois net bridge

v422_galois_net_bridge.py · core

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The Galois<->Net bridge: the seam mu4 = Gal(Q(zeta5)) is the SAME cyclic Z/4 as the (E8)_1 simple-current glue -- not a mere order-4 coincidence -- connecting the Galois gearbox of v419 to G_net/SEAM.EQUIV.01. disc(A3)=disc(D5)=Z/4 (one SNF invariant factor 4 = cyclic, det 4); D_n disc is Z/4 for n ODD, Z2xZ2 for n EVEN, so the carrier D5 (rank 5=g_car, odd) is cyclic while the control D8 (rank 8, even) is Klein; Gal(Q(zeta5))=(Z/5)^x=<2> is cyclic order 4 (only the carrier prime 5 among the atoms gives order 4); in disc(D5(+)A3)=Z4xZ4 (16=dim S+) the simple current (1,1) is order 4 (cyclic) with Lagrangian quotient 16/4^2=1 => (E8)_1 (1 primary, holomorphic). NEG control: the Klein Z2xZ2 / order-2 halfway <(2,2)> gives 16/2^2=4=|disc(D8)|=SO(16) (det 4), NOT E8 (det 1) -- cyclic Z/4 -> E8, Klein -> D8, so the carrier-Galois matches E8 not D8. The bridge: one cyclic Z/4 threads the seam deck mu4 (v419), Gal(Q(zeta5)) (v419) and the (E8)_1 glue (v1/v89/v154); cyclicity forced by 5, Klein excluded. This is the four-fold mu4 identity (deck/divisor=Galois=discriminant=simple-current); per v428 a COMPRESSION (one object read four ways, a unification that makes the carrier less axiomatic), NOT four independent witnesses that multiply.

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Linked claims: SEAM.GALOIS.NET.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

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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.

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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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