IndisputableMonolith.Sport.AthleticRecordProgressionFromPhi
This module defines the reference gap-to-asymptote and supporting gap functions on the phi-ladder to model athletic record progression under Recognition Science. Researchers applying RS to performance limits and record asymptotes would cite it. The module consists entirely of definitions and basic properties with no proofs.
claimThe reference gap-to-asymptote is the constant $1$ (RS-native dimensionless). Related objects include gapAtRung$(r)$ giving the gap at rung $r$ on the phi-ladder, gapAtRung_pos, gapAtRung_succ_ratio, gapAtRung_strictly_decreasing, AthleticRecordCert, and athleticRecordCert.
background
The module imports the fundamental RS time quantum from IndisputableMonolith.Constants, where τ₀ = 1 tick. It introduces referenceGap as the reference gap-to-asymptote (RS-native dimensionless 1) together with gapAtRung and its monotonicity properties. These sit inside the broader Recognition Science setting that uses the phi-ladder and J-cost for self-similar scaling.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the gap definitions that support AthleticRecordCert and athleticRecordCert inside the same module. It extends the phi-ladder structure (T6 fixed point, T7 eight-tick octave) into the sport domain.
scope and limits
- Does not compute numerical predictions for specific athletic events.
- Does not incorporate measured performance data or external records.
- Does not address non-phi scaling mechanisms for record progression.