e_over_phi
plain-language theorem explainer
The definition sets the real ratio of Euler's number to the golden ratio as exp(1) divided by phi. Researchers checking numerical links between constants in Recognition Science cite it during exploration of phi-summation routes to e. It is supplied as a direct one-line assignment with no lemmas or reductions applied.
Claim. The real number $e / phi$, where $e = exp(1)$ and $phi$ is the golden ratio fixed point.
background
Module Mathematics.Euler targets derivation of Euler's number from phi-related summations. Euler's number is the base of the natural logarithm, the limit of (1 + 1/n)^n as n tends to infinity, and the sum of 1/n!. Recognition Science links e to J-cost exponential decay, phi-continued fractions, and 8-tick probability normalization.
proof idea
One-line definition that directly assigns exp(1) / phi.
why it matters
This definition supplies a concrete ratio for the numerical checks listed in MATH-003. It supports exploration of connections between e and phi where no simple algebraic relation is known. The entry touches the phi fixed point from the forcing chain and the 8-tick normalization step.
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