coherence_exponent_is_fib_5
plain-language theorem explainer
The coherence exponent, defined as the difference between the octave and spatial dimension D, equals the fifth Fibonacci number. Researchers deriving mass scales from the phi-ladder in Recognition Science cite this to fix the coherence energy at phi to the minus five. The proof is a direct rewrite using the prior equality of the exponent to five together with the computation that the fifth Fibonacci number is five.
Claim. The coherence exponent defined by the difference between the octave and the spatial dimension equals the fifth Fibonacci number $F_5$.
background
This module derives the coherence exponent from the Fibonacci constraint that both D and 2^D must be Fibonacci numbers, which selects D=3. The coherence exponent is defined as octave minus D, where the octave is the eight-tick period 2^D. The Fibonacci sequence is defined recursively with fib 0 = 1, fib 1 = 1, and fib (n+2) = fib n + fib (n+1). Upstream results establish that the coherence exponent equals 5 and that fib 5 equals 5.
proof idea
The proof is a one-line wrapper that applies the rewrite tactic to the theorems establishing the coherence exponent equals 5 and fib 5 equals 5.
why it matters
This supplies the identification coherence exponent equals fib 5 that feeds the parent theorems coherence_exponent_from_fibonacci and coherence_exponent_unique. It completes the step showing that the coherence exponent 5 arises uniquely from the Fibonacci identity F6 minus F4 equals F5, fixing E_coh at phi to the minus five. The result connects to the eight-tick octave and D=3 in the forcing chain, confirming that the mass formula yardstick times phi to the power (rung minus 8 plus gap(Z)) has its coherence term structurally fixed.
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