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Synthesis. The recurrence C₂: x(n+1) = x(n) + x(n-1) determines a stable 3-form Ω_W on R⁷, unique up to GL(7)-equivalence, whose stabilizer is G₂(split). Eleven steps tracing the complete chain: C₂ → φ → spec(A₂) → sig(3,1) and sig(2,2) → minimal parent sig(3,2) → W = S₁ ∩ S₂ dim 3 sig(2,1) → V_W = R ⊕ W ⊕ W* dim 7 → Ω_W → dim Stab = 14 → sig(3,4) → stable → unique orbit → g₂(split). One volume choice, absorbed by GL(7). Dependencies: Proofs 1, 5, 17, 18, 20-28.
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Title CCFU Proof 29 — C₂ Constructs G₂(split)
Synthesis. The recurrence C₂: x(n+1) = x(n) + x(n-1) determines a stable 3-form Ω_W on R⁷, unique up to GL(7)-equivalence, whose stabilizer is G₂(split). Eleven steps tracing the complete chain: C₂ → φ → spec(A₂) → sig(3,1) and sig(2,2) → minimal parent sig(3,2) → W = S₁ ∩ S₂ dim 3 sig(2,1) → V_W = R ⊕ W ⊕ W* dim 7 → Ω_W → dim Stab = 14 → sig(3,4) → stable → unique orbit → g₂(split). One volume choice, absorbed by GL(7). Dependencies: Proofs 1, 5, 17, 18, 20-28.
Work type Research papers, Thesis, Lecture notes
Tags explicit construction, spectrum, invariant form, signature, ccfu, mathematics, proof, companion matrix
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Identifier 2605265789974
Entry date May 26, 2026, 10:41 AM UTC
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Author 100.00 %. Holder Captain Cookie Face Universe. Date May 26, 2026.
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