referenceGap
plain-language theorem explainer
The reference gap-to-asymptote normalizes the initial distance to the limiting performance in phi-scaled record improvements to the dimensionless value 1. Modelers of athletic records or polar codes cite this base unit when expressing successive gaps as powers of phi inverse. The definition is a direct assignment with no further reduction.
Claim. The reference gap-to-asymptote equals the real number $1$.
background
In the Recognition Science framework the phi-ladder organizes quantities by successive factors of the golden ratio, with gaps decaying as powers of phi inverse. The athletic record module predicts that world records approach an asymptote, each improvement reducing the remaining gap by a factor near 1/phi, matching empirical ratios observed in mile and 100 m data. This reference supplies the starting scale at rung zero, matching the normalization used for polar code gaps at minimal block length.
proof idea
Direct definition assigning the dimensionless value 1.
why it matters
This definition anchors the gap calculations that feed gapAtRung in the same module and gapAt in the polar code module, both of which multiply the reference by phi to the minus k. It supports the module's claim that record improvements ratio near 1/phi and aligns with the phi self-similar fixed point. The choice of 1 keeps all ladder predictions in RS-native units without introducing extra constants.
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