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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.
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.

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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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Cfin normal form

v845_cfin_normal_form.py · core

Read the original description and evidence links

NORMALFORM.CFIN.01: der endliche Compiler als EIN Objekt C_fin = (V, ħ, q*, σ, ι), vom Gaußschen Quotienten ABGELESEN (nicht postuliert), mit dem Code-zu-Materie-Kill als eingebautem NEGATIV und der verbleibenden P2-Brücke typisiert — **NORMAL-FORM-ASSEMBLED (28/28, SPEC v2): V = L/(1+i)L (Zensus 240 = 15×16, Nullklasse LEER); ħ = die Bit-Form (GEFUNDENE Familien/Anker-Basis (F1,F2,F3,A) mit Gram J − I, auf allen 256 Paaren); σ = der abgestiegene Ordnung-3-Deck (σ³ = id, symplektisch, genau 3 Fixklassen {A, F_Σ, F_Σ+A}, 4 freie 3-Orbits — der Familienzyklus); q* = die EINDEUTIGE Verfeinerung (genau 16 per Brute-Force über 2^16, Arf-Zensus 6 + 10; Selektor σ-invariant: 4 → q(A)=1: 2 → q(F_Σ)=0: 1, Arf-Typ 1, σ-erhalten); ι = der Paritäts-Lift bijektiv auf C_even(5) (β == ħ in allen 256 Zellen, q_wt == q*, σ wirkt auf den FÜNF Träger-Slots als 3+2-Split — Nachrichten- und Trägerregister verschränkt). ABGELEITET aus dem EINEN Objekt: |Sp(4,2)| = 720 (voller 65536-Matrizen-Zensus), Stab(q*) = 120 TREU als S5 auf den Fünf, Orbits [1, 5, 10]; 16 = 1+5+10, 15 = 5+10; PASCAL-Lesart (1, 10, 5) = (C(5,0), C(5,2), C(5,4)); PROJEKTIVE Lesart: PG(3,2) mit 15 Punkten, 35 Geraden, 15 isotrop (das Doily), die 5̄ ist ein OVOID (trifft jede isotrope Gerade genau einmal); Budget gegen die echten Gitterobjekte: 240 = 16·15, 60 Linien = 4·15, 30 = 2·15 = h(E8), Rang 8, 248 = 16·15 + 8. EINGEBAUTES NEGATIV (v775 neu verankert): die exakte 128-Spinor-Zählschranke — höchstens 8 rein-spinorale Klassen, ≥ 7 der 15 Klassen tragen IMMER Adjoint-Seiten-Wurzeln (konkreter Zensus SATURIERT beide Schranken: 8 + 7, NULL Mischklassen — der J-Quotient respektiert die D8-Graduierung); Gewichts-Kill am kanonischen Split: jede Spinor-Klasse = 8 verschiedene Halbspinor-Gewichtspaare, NIE 1 — v775 ROOTCLASS-MIXED bestätigt, NICHT umgestoßen. P2 TYPISIERT (kein Upgrade): alle 30 Platzierungen sind Typ-II-[8,4]-Codes (v799-Echo); C_fin leitet A1–A3, die OPE-Linearitäts-Notiz und die v776-Auswahl NICHT her — P2 (g_car = 5 = ι-Slot-Zahl) auf v799s Residuum R1′ ([C]) VERENGT, nicht eliminiert. Kontrollen feuern (Dot-Form: 0 Verfeinerungen; trivialer Deck: q* nicht eindeutig; falscher Lift bricht β == ħ).

Read the original Python source
Linked claims
NORMALFORM.CFIN.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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