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Proves the GL(7)-orbit of Ω_W is unique and split. Algebraic proof: (1) all Ω_{a,b,c} with abc≠0 are GL(7)-equivalent (Proof 21 Step 5), (2) sig(b_Ω) = (3,4) rules out compact (Proof 24). Exhaustive computational confirmation: 1523/1524 C₂-compatible patterns are g₂(split), 1 compact (CCFU Script 3, exact). Additional numerical check: 4 patterns via GL(7) optimizer with scalar absorption (CCFU Script 4). Dependencies: Proofs 21, 22, 24.
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Title CCFU Proof 27 — Unique GL(7)-Orbit
Proves the GL(7)-orbit of Ω_W is unique and split. Algebraic proof: (1) all Ω_{a,b,c} with abc≠0 are GL(7)-equivalent (Proof 21 Step 5), (2) sig(b_Ω) = (3,4) rules out compact (Proof 24). Exhaustive computational confirmation: 1523/1524 C₂-compatible patterns are g₂(split), 1 compact (CCFU Script 3, exact). Additional numerical check: 4 patterns via GL(7) optimizer with scalar absorption (CCFU Script 4). Dependencies: Proofs 21, 22, 24.
Work type Research papers, Thesis, Lecture notes
Tags signature, invariant form, companion matrix, explicit construction, mathematics, proof, ccfu, spectrum
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Identifier 2605255780899
Entry date May 25, 2026, 4:07 PM UTC
License All rights reserved
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Author 100.00 %. Holder Captain Cookie Face Universe. Date May 25, 2026.
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