phiContinuedFraction
plain-language theorem explainer
This definition supplies the finite list of ten 1's as a continued fraction approximant to phi inside the Euler module. Researchers deriving e from phi-summations in Recognition Science cite it when building phi-related limits or normalizations. The declaration is a direct constant assignment with no reduction steps.
Claim. The finite continued fraction $[1;1,1,1,1,1,1,1,1,1]$ of length ten.
background
Module MATH-003 targets derivation of Euler's number e from phi-related summations and continued fractions. In Recognition Science, e appears in J-cost exponential decay P ∝ exp(-J/J₀) and 8-tick probability normalization. Upstream cost definitions supply the J-cost: MultiplicativeRecognizerL4.cost is the derivedCost of a comparator on positive ratios; ObserverForcing.cost is Jcost of a recognition event state. PhiForcing supplies the self-similar fixed point used for such fractions.
proof idea
Direct constant definition that assigns the list of ten 1's. No lemmas or tactics are invoked; the body is a literal List ℕ value.
why it matters
Supports MATH-003 exploration of e-phi links via continued fractions alongside e series and fixed-point properties. It touches the T6 phi self-similar fixed point and the J-cost connection to probability. With zero downstream uses, it serves as a placeholder for phi approximations in later summation or normalization steps.
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