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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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Eisenstein cp operator

v417_eisenstein_cp_operator.py · flavor

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The Eisenstein/CP operator (hex dual of v415): the family rotation P=(1 2 3) and the CP clock W=-P^2 put the tau=omega flavor side on operators, unified with the seam into ONE order-30 clock. P^3=I, P^2+P+I=ONES (Eisenstein omega^2+omega+1=0 on the plane perp to (1,1,1)); (3I+2P)(3I+2P^2)=7I+6 ONES with Spec {7,7,25} -- 7=N_omega(3+2omega)=scalaron on the omega-plane, 25=g_car^2 on (1,1,1) -- the dual of v415's {13,13,9} (NEG: (5I+4P)(5I+4P^2)->{21,21,81}, N_omega(5,4)=21!=41); the CP clock W=-P^2 (order 6, =rho v233) has W^2=P, W^3=-I, Spec {-1,zeta6,zeta6^-1}, so delta_CKM=arg(zeta6)=pi/3 and delta_PMNS=arg(zeta6^4)=4pi/3 (W^4=P^2); all flavor clocks are powers of zeta30 (zeta30^15=-1, ^10=omega, ^6=zeta5, ^5=zeta6 = orders 2,3,5,6) while the seam mu4=i is the Galois side (Z/30)^x of order phi(30)=8=rank E8; the carrier mu5 has no clean 3x3 operator (golden phi an output-side trace, v313/v349).

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Linked claims: DIAMOND.EISEN.01
Paper sections: Source section 1 Source section 2 Source section 3 Source section 4 Source section 5

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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.

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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