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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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Arf vacuum ovoid

v852_arf_vacuum_ovoid.py · core

Read the original description and evidence links

ARF.VACUUM.SYNDROME.01 + OVOID.DECODER.01: **ARF-VACUUM-SYNDROME-EXACT (24/24) + OVOID-DECODER-EXACT (23/23)** — der Arf-Bit-Satz: a(t+U) = h̄(u,v) für ALLE 140 affinen Flats (positions-unabhängig; alle 4 Nebenklassen stimmen überein); die Zwei-Bit-Syndromtafel (s_vac, s_Arf) zerlegt die 140 Flats EXAKT in 15/20/45/60 (die v821- und v834-Zählungen als Zeilen EINER Tafel auf dem Hamming-Code); der LOKALE Hecke-Satz an ALLEN 15 Punkten (12+16 = 28 = σ₃(3), 12−16 = −4 = a₃, mit den isotropen Richtungen in Bijektion zu den Punkten von x^⊥/⟨x⟩); der Code-Bleistift H = [15,11,3] ⊃ {D = [15,10,4], C_iso, C_non = [15,10,3]} ⊃ K = [15,9,4] (Gewicht-3/4-Wörter = die 35 Geraden / 105 Off-Origin-Flats als MENGEN-Gleichheiten; das Kanonizitäts-Lemma: alle 16 Verfeinerungen differieren um Simplex-Wörter und induzieren EIN Arf-Funktional auf H); der Vakuum-Bit IST das Paritätsbit, das RM(2,4) restauriert (Punktierung → H, Verkürzung → D, Bijektion exakt). DER DECODER: NᵀV = 0 aus perfekten Matchings, Gram VᵀV = 36I−6J, SNF(N) = diag(1¹⁰,0⁵) TORSIONSFREI über ℤ (det-±1-Minor exhibiert), Moore-Penrose N⁺ = Nᵀ/4 − J/36 (alle vier Penrose-Axiome exakt in ℚ), der Träger-Projektor P₅ = I/2 − B/4 + J/12 mit tr = 5 = g_car, der geschlossene Decoder m̂ = (I−P₅)m EXAKT auf dem vordeklarierten Testsatz (Kernmoden unsichtbar, im(N) voll sichtbar), ker Nᵀ = die S₆-STANDARD-Darstellung (11/11 Klassen-Charaktere = fix−1), und der Mod-2-Schatten v_a mod 2 = q_a: DREI RINGE (ℝ-Ovoid-Spann / ℤ-torsionsfrei Rang 5 / F₂-Code A_q = [15,5,6]), EIN Kern — der Doily-Erholungskanal hat jetzt eine explizite integrale Inverse, nicht nur ein Spektrum. Exakte Algebra durchgehend; Kontrollen feuern; KEINE Marker-Bewegung. KEIN RH-Anspruch.

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Linked claims: ARF.VACUUM.SYNDROME.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

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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.

Repository setup and maintenance instructions

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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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