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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

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Marks gauss bonnet

v216_marks_gauss_bonnet.py · registry

Read the original description and evidence links

the FOUR seam marks EMERGE from Gauss-Bonnet (QGEO.MARKS.03), executing the K1 lever of the v215 kill-test. [E] mark count = 2χ: Z2 branch points (deficit π) on a flat sphere (χ=2) give n·π = 2π·χ = 4π ⟹ n = 2χ = 4 = |μ4| = e1(a) = N_fam+1 (the same χ=2 as the 8 in c3=1/(8π)). [E] the Euclidean sphere 2-orbifolds (χ_orb=0) are exactly (2,3,6),(2,4,4),(3,3,3),(2,2,2,2). [E] all-order-2 (the |Z2| sheet branch) ⟹ uniquely (2,2,2,2); [E] N_fam=3 (rank H¹=#marks−1) ⟹ uniquely (2,2,2,2), picking the 4-mark square over the 3-mark hexagonal (3,3,3); [E] a free order-4 deck ⟹ uniquely (2,2,2,2) — three independent selectors converge. [O] residual: the square modulus (cross-ratio 2 ⟹ j=1728, v214) needs the one order-4 carrier input. The mark COUNT + EQUALITY are now derived; does NOT close QGEO.REALIZE.01.

Read the original Python source
Linked claims
QGEO.MARKS.03
Paper sections
Source section 1Source section 2Source section 3Source section 4Source section 5Source section 6Source section 7Source section 8Source section 9Source section 10Source section 11Source section 12Source section 13Source section 14Source section 15Source section 16Source section 17Source section 18Source section 19Source section 20Source section 21Source section 22Source section 23Source section 24Source section 25Source section 26Source section 27Source section 28Source section 29Source section 30Source section 31Source section 32Source section 33Source section 34Source section 35Source section 36Source section 37Source section 38Source section 39Source section 40Source section 41Source section 42Source section 43Source section 44Source section 45Source section 46Source section 47Source section 48Source section 49Source section 50Source section 51Source section 52Source section 53Source section 54Source section 55Source section 56Source section 57Source section 58Source section 59Source section 60Source section 61Source section 62Source section 63Source section 64Source section 65Source section 66Source section 67Source section 68

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 ledgerInspect 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