vo2maxCert
plain-language theorem explainer
The definition supplies a concrete instance of the maximum oxygen uptake certificate by assigning the canonical certificate to its base field. Sports physiologists modeling aerobic capacity limits via J-cost would cite this when linking oxygen delivery ratios to training ceilings. It is realized as a direct one-line field assignment inside the structure.
Claim. The structure for the maximum oxygen uptake certificate, whose sole field is a base of type canonical certificate, is instantiated by setting that base equal to the given canonical certificate.
background
The module treats VO2max as the point where the oxygen delivery-to-demand ratio r equals 1, forcing J(r) to zero. Above the ceiling, r drops below 1/phi and demand exceeds delivery. The VO2maxCert structure packages a CanonicalCert as its base field, drawing on the imported CanonicalJBand for J-band conventions. Empirical elite-athlete VO2max values (65-90 mL/kg/min) are interpreted as phi-ladder genetic tiers whose adjacent bands differ by phi^{-1} per unit mass.
proof idea
The definition is a one-line wrapper that constructs the VO2maxCert instance by setting its base field to cert.
why it matters
It supplies the concrete certificate required to apply the J-cost model to physiological ceilings in the Sport domain. The module doc states that training-induced improvement satisfies J(r_after) ≤ J(phi) per block, and this definition closes the packaging step so the phi-ladder correspondence can be used downstream. It touches the T5 J-uniqueness landmark by providing the zero-cost point at r=1.
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