fibonacci_factor
plain-language theorem explainer
The Fibonacci factor is introduced as the natural number 5, the smallest Fibonacci number greater than 1 that is coprime to 8. Researchers closing the dimension-forcing argument in Recognition Science cite this constant to produce the 45-tick gap from the eight-tick cycle. The declaration is a direct assignment justified by the surrounding closure and triangular-phase construction.
Claim. The Fibonacci factor is the natural number 5, equal to the fourth Fibonacci number in the framework indexing and the smallest such number exceeding 1 while remaining coprime to 8.
background
In the Recognition Science setting the eight-tick period arises directly as 2^3 once spatial dimension is fixed at 3. Closing this cycle requires one additional step, producing a 9-step loop whose cumulative phase equals the ninth triangular number 45. The gap is therefore expressed as the product of this closure factor 9 and the Fibonacci factor 5.
proof idea
The declaration is a one-line definition that directly assigns the value 5. No lemmas or tactics are invoked; the assignment is taken as the numerical factor that satisfies 9 times 5 equals the required gap of 45.
why it matters
This definition supplies the numerical factor required by the parent theorem D_3_forced_from_structure, which asserts that the eight-tick period equals 8, the gap equals 9 times the Fibonacci factor, and the full period is the least common multiple of 8 and 45. It addresses the paper's noted gap in physical motivation for the 45-tick synchronization by tying the closure principle to the golden-ratio sequence, thereby keeping the T7 eight-tick octave and T8 dimension-forcing steps internally consistent.
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