IndisputableMonolith.Sports.AthleticRecordAsymptote
The AthleticRecordAsymptote module defines a phi-ladder sequence modeling athletic record improvements at scale 1/n per rung. Sports analysts applying Recognition Science to performance data would cite it to derive asymptotic bounds on records. The module supplies core definitions together with supporting positivity and boundedness results.
claimThe athletic record asymptote follows the phi-ladder sequence with improvement scale $1/n$ per rung, yielding the form $I(r) = n^{-1} phi^{-r}$ for rung index $r$.
background
The module operates inside the Recognition Science framework and imports the base time quantum τ₀ = 1 tick from Constants. It introduces the phi-ladder, the discrete self-similar scale sequence generated by the fixed point φ of the J-cost map, together with the improvement sequence that places a 1/n factor at each rung. The local setting uses the same phi-ladder structure that appears in the mass formula and the eight-tick octave.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the asymptotic model required by AthleticRecordCert and the sibling lemmas improvementAtRung and record_bounded_below. It extends the Recognition Science forcing chain (T5–T6) into the sports domain, grounding record bounds in the same phi-ladder used for constants and the D = 3 spatial structure.
scope and limits
- Does not incorporate physiological or training variables.
- Does not model short-term stochastic fluctuations in records.
- Does not address non-individual or team-based events.