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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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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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Celestial dterm nonderivation

v513_celestial_dterm_nonderivation.py · frontier

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CELEST.DTERM.NONDERIV.01: the c_d negative certificate -- can geometry derive c_d = 1920? An anti-numerology certificate in the v508 style (honest rigid NEGATIVE result): the v511 [C] fence '1920 = |W(D5)|' stress-tested via four candidate routes with a PRE-DECLARED look-elsewhere ledger. Exact sympy/Fraction, no floats (24 checks, ~2 s). [E] CONVENTION TABLE: c_d in {1920, 120, 256, 32, 69120} across five normalisations (probe tr-fund/e8-Killing; Gell-Mann; su(4)-Killing; plain trace; ch3-normalised d/6) -- only 1 of 5 hits |W(D5)|; the convention-STABLE content is the factorisation c_d = Phi_T3(A_fix) x 2 h_vee(E8) = 32 x 60, both factors [E] (Killing propagator 60 from sum_alpha <alpha,e>^2 = 120 over the actual roots; T3-slot fixing via det(P-block) = -64 != 0). [E] K1 DEAD: the charge-legal flux pairings (1,3)/(2,2) give 2048/1800 -- they BRACKET 1920 and both miss; the only flux hit 64*60/2 is the FORBIDDEN (1,2) pairing (charge 3 mod 4, killed by the v511 innerness theorem). LOOK-ELSEWHERE LEDGER: 924 expressions from 21 [E] numbers x grammar {a*b, a*b/2, a*b/4, a+b}, 11 hits on 1920; control targets 1800 -> 8, 2048 -> 5, 2016 -> 0. [E] K2: quantisation delivers only lattices (60 Z: 1920 = 32nd multiple, no minimality; strict ch3-unit couplings 2160 Z EXCLUDE 1920); the cubic quantum is lattice-dependent (6 on coroots, 3/8 on weights); the residual integer 32 has 12 signed factorisations, nothing forces it. [E] K3 PROVENANCE CLASH (the death blow): cubic indices A_m = (0, 16, 0, -16), twisted sum i^m A_m = 32i NUMERICALLY = Phi_T3(A_fix) -- BUT the quartic class decomposition (10, -4, 30, -4) is dominated by classes 0/2 while the cubic 32 is built 16 + 16 from classes 1/3: same number, disjoint mechanism = coincidence exposed; the Weyl side is WRONG (the d-channel is an A3-side object, |W(A3)| = 24; D5 has no cubic invariant, Inv(S^3 45) = 0; |W(E8)|/|W(A8)| = 1920 a second accidental 1920). [E] K4 NEGATIVE CONTROLS: SO(16)/D8 fails every candidate formula consistently; k = 2 flux doubling scales the flux formula x4 (7680); false g0 = d5+a2+u(1) has SIX symmetric cubics; so(10) sanity (Tr X^3 = 0). VERDICT: NUMEROLOGY as a derivation claim -- the v511 [C] fence stays a fence, now typed look-elsewhere-loaded; the honest [E] core is c_d = 32 x 60; the physical generation of the 32 stays [O]. Exact (sympy/Fraction); no marker moves.

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Linked claims: CELEST.DTERM.NONDERIV.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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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.

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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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