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From W = S₁ ∩ S₂ dim 3 constructs V_W = R ⊕ W ⊕ W* dim 7 and the natural 3-form Ω_W = τ∧ev + vol_W + vol_{W*}. Six steps: (1) higher closure construction, (2) exactly 3 SL(W)-invariant 3-forms, (3) generic form Ω_{a,b,c} with 5 terms, (4) stability criterion det(b_Ω) = 4374·a⁹b⁶c⁶, (5) all stable forms in one GL(7)-orbit via explicit rescaling, (6) minimality of dim 7. Volume choice absorbed by GL(W). Algebraic, no computation. Verified by verify_higher_closure.py (CCFU Script 1). Dependencies: Proof 20.
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Title CCFU Proof 21 — Higher Alternating Closure
From W = S₁ ∩ S₂ dim 3 constructs V_W = R ⊕ W ⊕ W* dim 7 and the natural 3-form Ω_W = τ∧ev + vol_W + vol_{W*}. Six steps: (1) higher closure construction, (2) exactly 3 SL(W)-invariant 3-forms, (3) generic form Ω_{a,b,c} with 5 terms, (4) stability criterion det(b_Ω) = 4374·a⁹b⁶c⁶, (5) all stable forms in one GL(7)-orbit via explicit rescaling, (6) minimality of dim 7. Volume choice absorbed by GL(W). Algebraic, no computation. Verified by verify_higher_closure.py (CCFU Script 1). Dependencies: Proof 20.
Work type Research papers, Thesis, Lecture notes
Tags explicit construction, signature, mathematics, proof, invariant form, companion matrix, spectrum, ccfu
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Identifier 2605245766544
Entry date May 24, 2026, 3:47 PM UTC
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Author 100.00 %. Holder Captain Cookie Face Universe. Date May 24, 2026.
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