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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

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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.

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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Celestial wp4 character shadow

v496_celestial_wp4_character_shadow.py · frontier

Read the original description and evidence links

CELEST.WP4.01: WP4 of the celestial-holographic research contract CELEST.SEAM.01 -- the (E8)_1 character E4/eta^8 vs the glue-equivariant E8[C^2] S-algebra (the 'type mismatch, head-on'). [E] Base: v492 replication (52+64+60+64, dims (60,64,60,64)); equivariant tower D[d] = 60(d+1)/64(d+1); cumulative count QUADRATIC 31 s^2 + 92 s + 60, 31 = k + h_vee; [C] CP Table 1: spin 1 - d/2 UNBOUNDED BELOW => no rational VOA contains the towers. [E] Hilbert series chi_sp(t) = (60+128t+60t^2)/(1-t^2)^2 (palindrome, 248 at t = 1); all mu4 collapses + the SU(2)_+ slice fail to start (1, 248, ...). [E] Character: chi = E4/eta^8 = (1,248,4124,34752,213126,...) exact through q^6 (cross-check q j = E4^3/eta^24); theta split, sector currents (60,64,60,64), glue-diagonal h = (0,1,1,1) integer; Sugawara c = 248/31 = 8 = 2|mu4|. [E] Bridges: zero-mode slice = 60 currents exact; jet slice cycles (60,64,60,64); BOUNDARY/PERIOD LIMIT: one mu4 period sums EXACTLY to 248 (single-particle level); 248 is NOT a jet-tower dimension (d <= 100); loop Fock level 1 = 897266 >> 248 (rational truncation absent). [E] Mismatch localised THREE ways: (a) grading; (b) growth n^{2/3} vs n^{1/2} (Meinardus pole s = 2 vs 1; f_n/chi_n strictly increasing n = 1..12); (c) the level-2 null ideal deletes EXACTLY 27000 = 30^3 = h_vee^3 (Sym^2(248) = 1+3875+27000; character keeps 4124) -- no jet analogue. [E] K4 three-way: exact realisation NO; boundary-limit PARTIAL YES -- the SAME MMST scaling-limit structure as SEAM.EQUIV.01 (v336/v449); K4 does NOT degrade the contract to 'E8 admissible'. [C] verdict B(ii): the character is a BOUNDARY/LIMIT shadow, not a conformal block in the bulk grading. [O] the constructive limit -> WP5; SEAM.EQUIV.01 stays [O]. Exact (integer/Fraction/sympy).

Read the original Python source
Linked claims
CELEST.WP4.01

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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