octave_is_fib_6
plain-language theorem explainer
The octave period equals the sixth Fibonacci number. Physicists deriving the coherence energy exponent in Recognition Science cite this to confirm that five arises uniquely from the dimension choice. The proof is a direct rewrite substituting the octave definition of eight with the precomputed Fibonacci value at index six.
Claim. $2^D = F_6$, where $D=3$ is the spatial dimension and $F_n$ is the Fibonacci sequence with $F_0=1$, $F_1=1$, $F_{n+2}=F_{n+1}+F_n$.
background
Recognition Science fixes the spatial dimension at three via the T8 step of the forcing chain. The octave is the fundamental evolution period $2^D$, which evaluates to eight. The Fibonacci sequence is generated by the recurrence fib 0 = 1, fib 1 = 1, fib (n+2) = fib n + fib (n+1). Upstream results from MusicalScale and Constants define the octave as the ratio two or as eight ticks, while the Gap45 derivation supplies the Fibonacci generator used here.
proof idea
The term proof rewrites the left side via octave_eq_8 and the right side via fib_6_eq.
why it matters
This supplies one conjunct of the uniqueness theorem coherence_exponent_unique, which concludes that the coherence exponent equals five. It closes the link from T8 dimension forcing through the eight-tick octave to the Fibonacci identity $F_6 - F_4 = F_5$, showing that the coherence energy $E_{coh} = phi^{-5}$ is required by the framework rather than chosen freely.
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