GitHub commit · Mathematical City web proof
Supabase: existing python_corpus_registry record E47-GRASSMANN-CASIMIR-20261008 stores all four complete files and their SHA-256 hashes. Readback confirmed 4 files, 34 passed checks, and matching Python source hash.
Canonical Corrected Formalism — Exact E47 Facts, Numerical Benchmarks, and Evidence Boundaries
A first-principles constructive proof with exact Python verification
Nicholas Kouns’ E47 construction — validation dated 8 October 2026.
Execution result: 34/34 exact checks passed (SymPy 1.14.0). These checks validate the theorem stated below; claim statuses for the supplied narrative are recorded separately.
Let V = V₂ ⊗ V₂ ⊗ V₂ over ℂ, with the standard positive spin inner product, and let C = J²_tot and K₄₇ = (C − 6I)(C − 30I). Then:
dim V = 125 and ker K₄₇ = E₆ ⊕ E₃₀ has dimension 47.
There exist E ⊂ V, dim E = 90, and a rank-43 linear map A: V → ℂ⁴³ such that dim ker A = 82 and E ∩ ker A = ker K₄₇.
For arbitrary E of dimension 90 and A of rank 43, dim(E ∩ ker A) = 47 holds exactly when E + ker A = V, equivalently rank(A|E) = 43. Identifying this intersection with ker K₄₇ further requires ker K₄₇ ⊂ E ∩ ker A.
With P₄₇ the orthogonal projector onto ker K₄₇ and Γ = I − K₄₇²/99144,
‖Γⁿ − P₄₇‖₂ = (15/17)ⁿ, for every integer n ≥ 0,
in the physical spin inner product. Thus Γⁿ → P₄₇ and Ωc = rank(P₄₇)/dim V = 47/125 = 0.376 exactly.
The 82-dimensional kernel belongs to A. The Casimir selector K₄₇ has a 47-dimensional kernel. These distinct operators make the two dimensional constructions compatible.
The weights of V₂ are −2, −1, 0, 1, 2. The tensor character is
χV(t) = (t⁻² + t⁻¹ + 1 + t + t²)³.
For nonnegative weights m = 0,…,6, the weight multiplicities are
wₘ = (19, 18, 15, 10, 6, 3, 1).