IndisputableMonolith.Sport.LiftingProgramDesign
The Sport.LiftingProgramDesign module supplies RS-native definitions for 1RM-anchored reference intensity and rung-based intensity progressions on the phi-ladder. Sports scientists modeling strength training loads with Recognition Science constants would cite these constructions. It consists entirely of definitions and supporting lemmas for positivity, monotonicity, and certification predicates. The module imports only Constants and introduces no external hypotheses.
claimLet $I_0 = 1$ be the RS-native dimensionless reference intensity at 1RM. For rung index $r$, define intensity $I(r)$ such that $I(r) > 0$, $I(r+1) < I(r)$, and the sequence satisfies the phi-ladder scaling with ratio derived from the self-similar fixed point. A lifting program is certified when it meets the LiftingProgramCert predicate built from these intensities.
background
Recognition Science derives all constants from the T0-T8 forcing chain, with phi the self-similar fixed point, the eight-tick octave, and the phi-ladder for scaling quantities via phi^(rung-8+gap). The upstream Constants module fixes the base time quantum as tau_0 = 1 tick. This sport module applies the same ladder structure to define 1RM-anchored reference intensity as the dimensionless unit 1, then constructs intensityAtRung together with lemmas establishing positivity and strict decrease.
proof idea
This is a definition module, no proofs. It declares referenceIntensity as the base dimensionless value 1, defines intensityAtRung via the phi-ladder, and supplies direct lemmas intensityAtRung_pos, intensityAtRung_succ_ratio, and intensityAtRung_strictly_decreasing that follow by algebraic reduction or induction on the rung index.
why it matters in Recognition Science
The module supplies the interface for LiftingProgramCert and thereby enables certification of training programs under RS constraints. It extends the phi-ladder and mass-formula scaling to the sport domain, linking the Recognition Composition Law to practical intensity ratios. No parent theorems are registered in the current dependency graph, but the definitions close the scaffolding for downstream sport-specific applications of the T5-T8 chain.
scope and limits
- Does not compute concrete training weights or volumes from the intensities.
- Does not incorporate fatigue, recovery, or periodization models.
- Does not address athlete-specific factors such as body mass or experience.
- Does not provide empirical validation against measured performance data.