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.

Read the Python source

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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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Review validation

v106_review_validation.py · registry

Read the original description and evidence links

External-review validation (v79-style identities + disciplined typing): SEED NORMAL FORM — φ₀ = (|μ₄|/N_fam)·c₃ + Ω_adm·c₃^|μ₄| exactly (linear seam term + topological 4th-order correction; 4/3 = |μ₄|/N_fam, 48 = Ω_adm, exponent = |μ₄|); hypercharge second moment computed from the explicit charge table: Tr X = 0, Tr X² = 120 = 5! (X = 6Y, 16 states); FACTORIAL SPINE: 5! = 120 = |R⁺(E₈)| = Σ E₈ exponents = Tr X², 240 = 2·120, 1920 = 2⁴·5! = |W(D₅)| — one moment, four projections; DEGREE-2 INVENTORY: Pascal K=2 closure UNIQUE at g=5 (scan 1..40), glue norms 5/4+3/4 = 2 = root norm, c₃ = ½·1/(4π), pair sector C(5,2) = 10; NAMED HYPOTHESIS [P]: Quadratic Boundary Locality (seam supports only bilinear data ⇒ K=2 forced — would upgrade the Pascal selection [A]/[P] → [L]: locality ⇒ K=2 ⇒ g=5 ⇒ 16 ⇒ D₅ ⇒ E₈); audit: 240 = 16×15 reading exact but non-unique, not promoted

Read the original Python source

Linked claims: ARCH.QUAD.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 Source section 9 Source section 10 Source section 11

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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The script index, figures and detailed research interfaces remain available below. This older technical overview preserves its original statements; use the current result inventory to follow later scope corrections.

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