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module module moderate

IndisputableMonolith.Sport.VO2maxCeilingFromJCost

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The module derives the VO2max ceiling directly from the J-cost function applied to metabolic activity ratios in the sport domain. Exercise physiologists and Recognition Science modelers cite it when placing upper bounds on aerobic capacity. It instantiates the reusable six-clause J-cost template imported from CanonicalJBand to enforce the matched-zero and nonnegativity conditions.

claimThe VO2max ceiling is the value of the J-cost function $J(r)$ evaluated at the ratio $r$ of maximal to basal oxygen uptake rates, satisfying $J(1)=0$ and $J(r)≥0$ for $r>0$.

background

Recognition Science obtains all physical limits from the J-function obeying the Recognition Composition Law. The imported CanonicalJBand module supplies the six-clause template that every domain cert must satisfy: matched-zero requires $J(1)=0$ while nonneg requires $J(x)≥0$ for all $x>0$, with $J(x)=(x+x^{-1})/2-1$. This sport module specializes that template to the VO2max domain by defining the ceiling as the J-cost on the relevant uptake ratio.

proof idea

This is a definition module that applies the CanonicalJBand template to the sport domain. It defines the sibling objects VO2maxCert and vo2maxCert by direct instantiation of the six-clause structure, with no independent proofs or tactics.

why it matters in Recognition Science

The module supplies the sport-domain instance required by the master cert chain for B-tier whole-science openings. It completes the J-cost band application for physiological limits and is referenced by any downstream result that needs the VO2max ceiling expressed in RS-native units.

scope and limits

depends on (1)

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