IndisputableMonolith.Sport.AthleticRecordProgressionFromPhi
The module defines the reference gap to asymptote as the RS-native dimensionless unit 1 together with rung-specific gap functions on the phi-ladder for athletic record progressions. Researchers modeling self-similar performance limits in sports would cite these constructions. The module consists of successive definitions and monotonicity properties built directly on the imported Constants module.
claimThe reference gap to the asymptote is the RS-native dimensionless quantity equal to $1$. Gaps at rung $r$ on the phi-ladder satisfy positivity and strict decrease, enabling certification of records that approach an asymptotic limit in discrete phi-scaled steps.
background
This module sits in the Sport domain and imports Constants, whose doc-comment states: 'The fundamental RS time quantum (RS-native). τ₀ = 1 tick.' It introduces the reference gap-to-asymptote set to the dimensionless value 1 and defines gapAtRung together with its positivity and decrease lemmas. These objects extend the phi-ladder structure used for mass formulas to discrete athletic performance steps.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the reference gap and gapAtRung definitions that enable AthleticRecordCert constructions for phi-based record modeling. It aligns with the self-similar fixed point phi and the forcing chain steps T5-T8 by furnishing concrete gap calculations for self-similar progressions in the sport domain.
scope and limits
- Does not compute numerical record values for specific sports.
- Does not incorporate external factors such as training technology.
- Does not address non-phi based progressions.
- Does not provide empirical data fitting procedures.