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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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Atom trichotomy

v416_atom_trichotomy.py · core

Read the original description and evidence links

The atom trichotomy: {2,3,5} are ramified/inert/split in the two exceptional CM rings, and each atom is the unique ramified prime of one quadratic facet of K=Q(i,sqrt-3,sqrt5) (v403). Z[i] (square/seam, tau=i): 2=|Z2| ramifies (2=-i(1+i)^2), 3=N_fam inert (norm 9=N_fam^2), 5=g_car splits ((2+i)(2-i)) -- the carrier rank factors on the seam; Z[omega] (hex/flavor, tau=omega): 3=N_fam ramifies (N(1-omega)=3), 2 inert (norm 4), 5 inert (norm 25=g_car^2); the ramified prime of each ring IS its atom (Z[i] at 2 = sheet/seam, Z[omega] at 3 = family/flavor); the three facets Q(i)/Q(sqrt-3)/Q(sqrt5) (disc -4,-3,5) ramify over one atom each, product 2*3*5=30=h(E8); 2 imaginary (CM/dynamic) + 1 real (RM/static).

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Linked claims: ARITH.TRICHOTOMY.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

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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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