fibonacci_interpretation
plain-language theorem explainer
The declaration supplies a string that interprets the Fibonacci factor as 5, identified as the fourth Fibonacci number and the smallest integer greater than 1 coprime to 8. Workers tracing the emergence of the 45-gap from the eight-tick structure and golden-ratio forcing would reference this when assembling the factorization 45 = 9 × 5. The definition is a direct string literal with no computation or lemmas.
Claim. The Fibonacci factor equals 5, which is the fourth Fibonacci number and the smallest Fibonacci number greater than 1 that is coprime to 8.
background
The Gap45.Derivation module derives the number 45 from the eight-tick period (T8) together with the Fibonacci sequence tied to φ. Key local definitions include closure_factor = 9 (one full eight-tick cycle plus return) and fibonacci_factor = 5. The upstream definition fibonacci_factor : ℕ := 5 states that 5 is the smallest Fibonacci number greater than 1 coprime with 8. MODULE_DOC notes that 45 = T(9), the ninth triangular number, which equals 9 × 5 and represents cumulative phase accumulation over a closed 8-tick cycle. Related upstream structures include SpectralEmergence (forcing D = 3 and gauge content) and PhiForcingDerived (J-cost structure).
proof idea
One-line definition that directly assigns the string literal encoding the interpretation of the Fibonacci factor.
why it matters
The definition supplies the interpretive text for the fibonacci_factor used in the 45 = (8 + 1) × 5 factorization inside the Gap45 module. It supports the claim that 45 emerges from T8 (eight-tick octave) and the closure principle rather than being arbitrary, and it connects to the later observation that lcm(8, 45) = 360 forces D = 3. No downstream theorems are listed; the entry closes the interpretive layer of the derivation without adding new theorems.
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