IndisputableMonolith.Sports.PeakPerformanceFromPhiLadder
This module defines rep-max at rung k on the phi-ladder together with ratio, exponent, and certification objects for sports performance. Athletic modeling that imports Recognition Science scaling would cite these definitions. The module is a collection of definitions and basic monotonicity statements built directly on the imported Constants.
claimThe module supplies the functions $repMax(k)$, $repMaxRatio$, $hypertrophyExponent$, and the certificate $PeakPerformanceCert$ for performance at phi-ladder rung $k$.
background
Recognition Science places all scaling on the phi-ladder whose rungs are integer powers of the golden ratio fixed point. The module imports the base time quantum from Constants, where tau_0 equals one tick. Its sibling definitions therefore express repetition maxima and hypertrophy exponents as direct functions of rung index k, inheriting the self-similar structure already fixed by the upstream forcing chain.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the sports-domain layer that applies the phi-ladder and mass-formula scaling to athletic metrics. It stands as a terminal application object with no listed downstream theorems.
scope and limits
- Does not incorporate measured training data or statistical fits.
- Does not derive the phi-ladder applicability to biology from first principles.
- Does not address performance factors outside the rung-k scaling.
- Does not produce numerical predictions for specific athletes or lifts.