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Among all four second-order recurrences with a,b ∈ {±1}, only (1,1) and (−1,1) give Δ=5 and real hyperbolic roots. These are isomorphic via x_n → (−1)ⁿx_n. The other two give Δ=−3 and complex roots on the unit circle. C₂ is unique up to isomorphism. Self-contained. No dependencies.
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Title CCFU Proof 18 — Uniqueness of C₂ Among ±1 Recurrences
Among all four second-order recurrences with a,b ∈ {±1}, only (1,1) and (−1,1) give Δ=5 and real hyperbolic roots. These are isomorphic via x_n → (−1)ⁿx_n. The other two give Δ=−3 and complex roots on the unit circle. C₂ is unique up to isomorphism. Self-contained. No dependencies.
Work type Research papers, Thesis, Lecture notes
Tags recurrence, ccfu, uniqueness, proof, mathematics, classification, discriminant, golden ratio
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Identifier 2605175681207
Entry date May 17, 2026, 9:07 AM UTC
License All rights reserved
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Author 100.00 %. Holder Captain Cookie Face Universe. Date May 17, 2026.
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