peakPerformanceCert
plain-language theorem explainer
The peak performance certificate is constructed by assigning its base field to the canonical certificate. Exercise physiologists modeling strength-training dose-response would cite it to map classical 5x5 and 1RM schemes onto the J-cost band at one phi-step from baseline. The definition is a direct one-line construction from the imported canonical cert.
Claim. Let $r$ be the load ratio (observed load over 1RM baseline). The peak performance certificate is the structure whose base field is the canonical certificate, with peak performance at $r=1$ and per-rep J-cost staying below the canonical band at one phi-step from baseline.
background
The module develops F8 on sport peak performance dose-response from J-cost. Per-rep J-cost is taken on the ratio $r :=$ observed load / 1RM baseline, with peak at $r=1$ (no skew). Classical 5x5, 3x3 and 1RM-progression schemes are treated as J-cost-managed approaches to the canonical band at one phi-step from baseline. The structure PeakPerformanceCert consists of a single base field of type CanonicalCert, drawn from the CanonicalJBand import. The upstream phi-ladder certificate in the sibling module requires a phi ratio, strict monotonicity of repMax, and positive hypertrophy exponent.
proof idea
The definition constructs PeakPerformanceCert by assigning the base field directly to the canonical certificate cert. It is a one-line wrapper that applies the structure constructor to the imported cert.
why it matters
This definition supplies the J-cost foundation referenced by the peak performance certificate in the phi-ladder module. It realizes the F8 structural prediction that training programmes whose per-set J-cost stays below the canonical band yield steady progression. It connects the Recognition Science J-cost trajectory to the phi-ladder fixed point and the eight-tick octave framework.
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