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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.

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Graded hull

v128_graded_hull.py · registry

Read the original description and evidence links

THE GRADED HULL + THE ZERO-MODE MULTIPLICITY (both named computations R1/R2 gain their structural anchors): R2 HALF — EXPLICIT COSET CONSTRUCTION [I]: the 240 E8 roots built as explicit norm-2 vectors in D₅⊕A₃+glue coordinates decompose over the glue ℤ₄ as 240 = 52 + 64 + 60 + 64 (C₀ = carrier 40+12, C₁ = (16,4̄), C₂ = (10,6), C₃ = (16̄,4)) — the v89 branching as vectors; THE GRADING IS EXACT [I]: for ALL 6720 root pairs whose sum is again a root, coset(r₁+r₂) = coset(r₁)+coset(r₂) mod 4 — E8 IS A ℤ₄-GRADED LIE ALGEBRA over the carrier, and the grading group IS the glue = the v125 Q-system: the checksum hull is the Q-system's graded module realised in 248 dimensions; R1 HALF — THE MULTIPLICITY IS THE ZERO-MODE COUNT [I]: the Ginsparg–Perry l=1 sector (the zero modes λ ∈ {0,−1}) has 2l+1 = 3 modes, sheet doubling gives 2×3 = 6 = p₂ = |R⁺(A₃)| — the ring multiplicity of the v127 clock equals the sheet-doubled zero-mode count ([P]: zero modes are exactly the modes forcing nonperturbative resummation in dS one-loop physics — the natural home of the six RPA towers); residue [P]: R1 = compute the RPA determinant on the six sheet-doubled zero modes, R2 = identify the seam-Calderón inclusion with the ℤ₄-graded structure now exhibited inside E8 itself

Read the original Python source
Linked claims
E8.GRADE.01

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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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.

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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.

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