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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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Translation clock

v319_translation_clock.py · horizon

Read the original description and evidence links

The translation clock: the discrete<->dynamic bridge IS the order-30 Coxeter element, a clock with two coprime hands 5 x 6, read law-inclusive (0..5) or live-only (1..5). The only object holding both the static carrier (Q(sqrt5)) and the dynamic family (rational) data is the order-30 Coxeter element (v314); 30 = h(E8) = g_car*(2 N_fam) = 5*6, gcd(5,6)=1 => Z/30 = Z/5 x Z/6 (v315). DYNAMIC HAND (Z/6 = 2 N_fam, ticks 0..5): the recovery exponent is exactly 6 = 2 N_fam, rate (2/3)^6; order-6 generator c^5 (zeta_6 = zeta_30^5). LAW vs LIVE: the resummed clock rate(n) = -p2 ln(1 - n/N_fam) (v124) has rate(0)=0 (the attractor/law) and live modes from n=1; the E8 live phases (totatives of 30) start at 1, so '0,1,2,3,4,5' is law-inclusive, '1,2,3,4,5' live-only. STATIC HAND (Z/5 = g_car, ticks 1..5): golden Q(sqrt5), field-obstructed (no rational dynamic image, v314) -- static-only. ONE FULL TURN = lcm(5,6) = 30 = the Coxeter period (rank E8 = 8 = phi(30) live phases, 4 invariant planes, v55). The arithmetic is [E]; the 'it is one clock' reading is [C].

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Linked claims: TRANSLATE.CLOCK.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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