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For every ratio R = x(n+1)/x(n) from C₂, the coordinates U₁ = (2R−1)/√5, U₂ = (R+2)/√5, V = R satisfy U₁² + U₂² − V² = 1. Corollary: the direction D is null, making the C₂ ratio curve a null ruling on the Lorentzian hyperboloid in signature (2,1). Pure algebra. No free parameters.
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Title CCFU Proof 2 — The Lorentzian Hyperboloid Identity
For every ratio R = x(n+1)/x(n) from C₂, the coordinates U₁ = (2R−1)/√5, U₂ = (R+2)/√5, V = R satisfy U₁² + U₂² − V² = 1. Corollary: the direction D is null, making the C₂ ratio curve a null ruling on the Lorentzian hyperboloid in signature (2,1). Pure algebra. No free parameters.
Work type Research papers, Thesis, Lecture notes
Tags golden ratio, mathematics, lorentzian, signature, ccfu, fibonacci, null ruling, recurrence, proof, hyperboloid
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Identifier 2605145657744
Entry date May 14, 2026, 5:44 PM UTC
License All rights reserved
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Author 100.00 %. Holder Captain Cookie Face Universe. Date May 14, 2026.
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