IndisputableMonolith.Sport.InjuryRiskFromJCost
The module defines J-cost applied to the acute-to-chronic workload ratio for quantifying sports injury risk. It introduces the ACWR cost function and the injury tip point as the threshold where risk rises. Sports physiologists modeling training load would cite these for RS-derived risk bands. The module consists of direct definitions and elementary lemmas on positivity and bounds.
claimThe module centers on the ACWR cost function defined by $J(r)$ where $r$ denotes the acute-to-chronic workload ratio, together with the tip point at which this cost exceeds the injury threshold and the certified risk statement.
background
Recognition Science defines the J function via the composition law $J(xy) + J(x/y) = 2J(x)J(y) + 2J(x) + 2J(y)$ with explicit form $J(x) = (x + x^{-1})/2 - 1$. The Cost module supplies the J-cost construction used throughout. Constants supplies the base time unit as the RS-native quantum. This module applies the construction to the acute-to-chronic workload ratio in the Sport domain extension of the forcing chain.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
This module supplies the J-cost application to ACWR, feeding into injury risk certification in the Sport domain. It realizes the extension of J-uniqueness to practical workload ratios and closes the application to injury modeling within the eight-tick octave framework.
scope and limits
- Does not include athlete-specific physiological parameters.
- Does not address chronic injury accumulation beyond the ratio.
- Does not provide numerical conversions to real-world units.
- Does not model external factors such as sleep or nutrition.