CCFU Proof 22 — Explicit Ω_W

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CCFU Proof 22 — Explicit Ω_W

05/24/2026

Given.
V_W = R·τ ⊕ W ⊕ W* [Proof 21].
Basis: e₀ = τ, (e₁,e₂,e₃) = W, (e₄,e₅,e₆) = W*.

The canonical 3-form:

    Ω_W = e₀₁₄ + e₀₂₅ + e₀₃₆ + e₁₂₃ + e₄₅₆

Five terms. Constructed from W after choosing a volume form.
The GL(7)-orbit is independent of the volume choice [Proof 21].  ∎

Note: the Ω of the earlier construction:
    Ω_old = e₀₁₂ − e₀₃₄ − e₀₅₆ − e₁₃₅ + e₂₄₅ + e₁₄₆ + e₂₃₆
is GL(7)-equivalent to Ω_W. Both give the same stabilizer.

[Dependency: Proof 21.]