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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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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.

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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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Celestial wp3 gs alignment

v495_celestial_wp3_gs_alignment.py · frontier

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CELEST.WP3.01: WP3 of the celestial-holographic research contract CELEST.SEAM.01 -- the Green-Schwarz axion coefficient lambda_g of celestial SDYM (Costello, arXiv:2111.08879) vs the TFPT seam constant c3 = 1/(8 pi); the pre-registered 'alignment test only'. [E] Okubo identity DERIVED, not quoted: Sum <alpha,x>^4 = [5/(2(dim+2))] (Sum <alpha,x>^2)^2 exact for all 8 algebras on Costello's list (e6/e7 carved out of the v492 E8 root set); sl4 negative control fails (5/32 vs 3/32). [E] Killing = 2 h_vee <.,.>; closed form lambda~^2 = 10 h_vee^2/(dim+2) = h_vee + 6 over the Deligne series; Dynkin indices (1,1,2,2,6,6,12,60); E8: lambda~ = 6, lambda_fund = 1/10 EXACT; Costello cross-checks sl2 = 8 / sl3 = 9; so8 slip flagged (exact 3, printed 3/2). [E] Alignment: (kappa/c3)^2 = lambda^2/3 = 12 = |mu4| N_fam resp. 1/300 exact; kappa/c3 itself irrational (2 sqrt3); anchors h_vee = 30 = |Z2| N_fam g_car, phi(30) = 8 = rank, lambda~ = |Z2| N_fam, lambda_fund = 1/(|Z2| g_car). [E] LOOK-ELSEWHERE (hard fence, alignment != selection): alignment 8/8 (zero selectivity), smoothness 8/8, lambda-integrality 2/8 (with sl3), phi(h_vee) = rank 4/8; only g_car | h_vee is e8-selective (1/8); the isolating conjunction is post hoc. [E] K3 does NOT fire but is scope-demoted: compatibility + lambda-arithmetic, NOT e8-selective evidence. [C] the 8 pi is the anomaly 2 pi convention, the sqrt3 the box diagram's sqrt48 -- WP3 can never derive c3. [O] WP5 + SEAM.EQUIV.01 stay [O]. Verdict B. Exact (Fraction/sympy).

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Linked claims: CELEST.WP3.01
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 Source section 12 Source section 13

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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

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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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