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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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Message doily rank

v844_message_doily_rank.py · core

Read the original description and evidence links

MESSAGE.LADDER.01 + DOILY.PASCAL.RANK.01: die E8-Adressformel und das Doily-Pascal-Rangtheorem — zwei exakte Korpus-Kompressionen, EIN Modul aus zwei Probes — **MESSAGE-LADDER-EXACT + DOILY-PASCAL-RANK-EXACT (23/23 + 16/16): TEIL A: M_n = 15·Δp_n = 15·2^n gegen die TATSÄCHLICH neu aufgebauten Objekte zertifiziert, eine BENANNTE Struktur pro Sprosse: M_0 = 15 = Adressraum (Klassen von V = L/(1+i)L); M_1 = 30 = h(E8), HIER aus dem neu aufgebauten Wurzelsystem hergeleitet, nicht zitiert (8 einfache Wurzeln, zusammenhängende einfach geschnürte Cartan-Matrix mit det 1 und E8-Gradfolge, höchste Wurzel EINDEUTIG bei Höhe 29 mit Marken {2,2,3,3,4,4,5,6}, h = 1 + 29 = 30 = |R|/Rang); M_2 = 60 Gaußsche Wurzellinien (μ4-Orbits, alle Größe 4, genau 4 pro Klasse); M_3 = 120 = |R+| = Vorzeichenpaare; M_4 = 240 = |R(E8)| mit Zensus 240 = 15×16 (Nullklasse LEER); Coda 248 = 15·16 + 8 gegen Zensus und HNF-Rang; die strukturelle Verdopplung 60 → 120 → 240 typisiert. Kontrollen feuern (falscher Anker (1,2,2) → (45,105,225,465); falsche Multiplikatoren 14/16 verfehlen alle Ziele und brechen die Coda). TEIL B: die Duaden-Synthemen-Inzidenz N des Cremona-Richmond-Doilys (15×15, 3-regulär beidseitig) und die symplektische Punkt-Inzidenz B auf PG(3,2) (B·B^T = 4I + 3J zellweise, charpoly (x−7)(x−2)^9(x+2)^5 exakt) sind EIN Objekt: über das K6-Duaden-Modell trägt die Bijektion N·N^T auf B + 2I ZELLWEISE (alle 225 Zellen) — Duaden-Kollinearität = symplektische Orthogonalität. DAS RANGTHEOREM (exakt): charpoly(N·N^T) = (x−9)(x−4)^9·x^5 — Rang N = 10 = A_Λ (Dekupel-Sektor), Kern = 5 = g_car (Fünf-Slot-Träger), Multiplizität 9 = N_fam², Top-Singulärwert 3 = N_fam; die SECHS Ovoid-Indikatoren SPANNEN den Kern — die P2-Ganzzahlen sind die Singulärwert-Daten der Doily-Inzidenz. Recovery-Wert sing(N/3) = {1, 2/3 ×9, 0 ×5} exakt, 2/3 = (N_fam−1)/N_fam (v327); Exponentiationsidentität: der Sechs-Schritt hat exakt (2/3)^6 = 64/729 als λ_2 (v330/v486); TYPISIERTE Lücke erneut bestätigt, KEIN Upgrade: 1/729 ist KEINE Wurzel — der deployte (1/3)^6-Modus bleibt auf der Uhr-Seite (v814). Kontrollen feuern (zirkulante und LCG-3-reguläre Paarungen: Rang 13 ≠ 10, falsches charpoly). Exakte Integer/Fraction/sympy-Arithmetik.

Read the original Python source
Linked claims
MESSAGE.LADDER.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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