CCFU Proof 23 — dim Stab(Ω_W) = 14

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CCFU Proof 23 — dim Stab(Ω_W) = 14

05/24/2026

Given.
Ω_W = e₀₁₄ + e₀₂₅ + e₀₃₆ + e₁₂₃ + e₄₅₆ [Proof 22].

Action of X ∈ gl(7) on Ω_W:
    (X·Ω_W)ᵢⱼₖ = Σₗ (XₗᵢΩₗⱼₖ + XₗⱼΩᵢₗₖ + XₗₖΩᵢⱼₗ)
35 × 49 matrix A.

Exact computation (Fraction over Q, no floating point):
    rank(A) = 35.
    dim ker(A) = 49 − 35 = 14.  ∎

Note: the matrix has only 5 nonzero triples (vs 7 in old Ω),
making hand verification feasible.

[Dependency: Proof 22.]