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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.

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Celestial z4 orbifold

v492_celestial_z4_orbifold.py · frontier

Read the original description and evidence links

CELEST.WP1.01: WP1 of the celestial-holographic research contract CELEST.SEAM.01 -- the E8 mu4-glue grading (v128) IS the flat Z4 monodromy of the glue-equivariant celestial chiral algebra on the A3 ALE space C^2/Z4 (Bittleston-Homans-Sharma, arXiv:2305.09451, the Z2/Eguchi-Hanson case; Kronheimer-Nakajima flat connection). [E] inner grading: h = (2,2,2,2,2;0^4) reads the glue class mod 4 on all 240 roots => glue = Ad(exp(2 pi i h/4)) = flat Z4 monodromy; A3-side h' = (0^5;1,1,1,-3) = the diagonal (1,1) glue of Z4 x Z4 (v92/v125); Z2 halfway 120 = SO(16) / 128 = spinor. [E] C^2/Z4 IS the A3 singularity XY = Z^4 (Molien + Hilbert (1+t^4)/((1-t^2)(1-t^4)) exact). [E] equivariant SDYM(E8) sector closes: D[d] = 60(d+1) even / 64(d+1) odd -- works ONLY because dim g_j = (60,64,60,64); zero modes = carrier D5+A3+Cartan = 60; density 1/4 = 1/|Z4|. [E] (E8)_1 character = sum of the 4 glue-coset sectors (1+248q+4124q^2+34752q^3, v377); sector weights = the v92/v125 discriminant form (5x^2+3y^2)/8; glue diagonal h = (0,1,1,1) integer = local extension. [E] correction: the A3 deck acts on the celestial sphere as z -> -z (order 2); the order-4 clock z -> iz is the U(2) phase diag(i,1) (normalises the deck, det = i rotates omega by the mu4 generator), spin bridge (spin clock)^2 = deck, Z8 with 8 = 2|mu4|. [E] clock-invariant A3 deformation = 1-parameter XY = Z^4 + a0, branch points = ONE mu4 orbit, cross-ratio 2 (v168/v214 pillowcase). [E] negative controls: diag(i,i) killed 3 ways; false glue breaks additivity 3112/6720; rigidity = Aut(Z4). [C] verdict B: match under the ONE named identification clock^2 = deck. [O] structural arithmetic only -- no celestial duality constructed; CELEST.SEAM.01 stays a research contract; SEAM.EQUIV.01 stays [O]. Exact (sympy).

Read the original Python source

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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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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