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

Python runs in your browser using Pyodide. The first run downloads the runtime. Its output appears in the existing verification viewer, including any failure and the local reproduction command.

This is a mathematical lattice check. Identifying that lattice with a physical system requires additional arguments and retains its own status.

Find the source behind a check.

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.

1 matching module · showing 1–1

Clear filters

Hexagon family dictionary

v118_hexagon_family_dictionary.py · registry

Read the original description and evidence links

THE HEXAGON IS THE SIGN-TWISTED FAMILY SPECTRUM (first exact piece of the H2 dictionary; the v20 lepton coefficients are resolvent determinants of the exact W(A₃) monodromy): SIGN-TWIST LEMMA [I] — −M̃₀ has order 6 ((−M̃₀)³ = −1) and spec(M̃₀) ∪ spec(−M̃₀) = μ₆: the 6-site hypercharge hexagon spectrum IS the family monodromy spectrum plus its sheet twist (ℤ₆ = ℤ₂×ℤ₃ = (−1)×⟨M̃₀⟩); the v20 denominators 5/4 − cos(rπ/3) = |1 − ζ₆ʳ/2|² are the eigen-denominators of the two family resolvents (1 ∓ M̃₀/2)⁻¹; CYCLOTOMIC DETERMINANT [I]: det(1 − tM̃₀) = 1 − t³ = (1−t)Φ₃(t) ⇒ det(1 ∓ M̃₀/2) = (7/8, 9/8); LEPTON COEFFICIENTS = RESOLVENT DETERMINANTS [I]: c_e = |μ₄|/(2det₋) = 16/7, c_μ = N_fam/(2det₊) = 4/3, c_τ = |μ₄|det₋/N_fam = 7/6, product rule = |μ₄|/det₊ = 32/9 — the lepton 7 and 9 ARE the family-resolvent determinants (×8), and δ = ½ = |(M̃₀)₂₂| is supplied by the matrix itself; the e/μ/τ leg assignment stays v20's established input (nothing re-fished); SHEET-EXTENDED GROUP [I]: ⟨U, M̃₀, −1⟩ has order 48 = Ω_adm = N_fam·dim S⁺ (the seed quartic coefficient); residue [P]: the dictionary's VALUES are exact, its ADDRESS TABLE (site per fermion, quark composition) remains open

Read the original Python source

Linked claims: FLAV.H2.02
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 Source section 12 Source section 13 Source section 14 Source section 15 Source section 16 Source section 17 Source section 18 Source section 19 Source section 20 Source section 21

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.

Find a result and its premises Download the ledger Inspect snapshot coverage

Trace the dependencies.

Select a node to inspect its inputs, outputs, scope and verification scripts. Browser compatible checks open the same verification viewer; native certificates provide their local command.

Explore the complete dependency graph

Keep the detailed research in reach.

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.

Open the script index, figures and research details