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Mathematical proof that the golden ratio φ = (1+√5)/2 is the unique positive globally attracting fixed point of the ratio dynamics R_{n+1} = 1 + 1/R_n derived from the recurrence C₂: x(n+1) = x(n) + x(n-1). Four steps: ratio dynamics, fixed point, local stability, global convergence. No parameters chosen. Pure algebra.
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Title CCFU Proof 1 — φ is the unique positive attracting fixed point of C₂
Mathematical proof that the golden ratio φ = (1+√5)/2 is the unique positive globally attracting fixed point of the ratio dynamics R_{n+1} = 1 + 1/R_n derived from the recurrence C₂: x(n+1) = x(n) + x(n-1). Four steps: ratio dynamics, fixed point, local stability, global convergence. No parameters chosen. Pure algebra.
Work type Research papers, Thesis, Lecture notes
Tags systems, theory, structure
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Identifier 2605135641760
Entry date May 13, 2026, 3:32 PM UTC
License All rights reserved
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Author 100.00 %. Holder Captain Cookie Face Universe. Date May 13, 2026.
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