About the work
A₄ is the companion matrix of λ⁴−√5λ³+√5λ−1, constructed from spec(A₂) via factor completion (Proof 17). spec = {φ, 1/φ, +1, −1}, preserves G₄ with sig(3,1), det = −1. Closes Proof 4 dependency on Theory #15c. No free numerical input — √5 forced by Δ(C₂) = 5.
AI Availability Declaration
The work is allowed to be accessed by AI systems.
Creativity declaration
No AI has been used in the creative process of this work
Print work information
Work information
Title CCFU Proof 19 — Explicit A₄: Companion Matrix from C₂
A₄ is the companion matrix of λ⁴−√5λ³+√5λ−1, constructed from spec(A₂) via factor completion (Proof 17). spec = {φ, 1/φ, +1, −1}, preserves G₄ with sig(3,1), det = −1. Closes Proof 4 dependency on Theory #15c. No free numerical input — √5 forced by Δ(C₂) = 5.
Work type Research papers, Thesis, Lecture notes
Tags ccfu, signature, invariant form, spectrum, explicit construction, companion matrix, mathematics, proof
-------------------------
Registry info in Safe Creative
Identifier 2605195700865
Entry date May 19, 2026, 3:37 AM UTC
License All rights reserved
-------------------------
Copyright registered declarations
Author 100.00 %. Holder Captain Cookie Face Universe. Date May 19, 2026.
Information available at https://www.safecreative.org/work/2605195700865-ccfu-proof-19-explicit-a4-companion-matrix-from-c2
/
Registration: 2605195700865
