peakPerformanceCert
plain-language theorem explainer
The definition constructs a certificate asserting that consecutive rep-max loads scale by the golden ratio, with strict increase and positive hypertrophy exponent. Strength training modelers applying the phi-ladder to dose-response would cite it. The construction is a direct field assignment from the rep-max ratio theorem, monotonicity lemma, and exponent positivity result.
Claim. Let repMax denote the maximum load for a given repetition count. The peak performance certificate is the structure with fields satisfying $forall k in mathbb{N}, frac{repMax(k+1)}{repMax(k)} = phi$, $forall k in mathbb{N}, repMax(k) < repMax(k+1)$, and $0 < beta$ where $beta$ is the hypertrophy exponent, with the ratio field supplied by the adjacent-rung ratio theorem.
background
The module develops strength training metrics from the phi-ladder, where repMax(k) is the maximum weight for k repetitions. Consecutive values satisfy repMax(k+1)/repMax(k) = phi, derived from the self-similar properties of the golden ratio. The hypertrophy exponent is defined as 1/(2 phi), proven positive using the fact that phi exceeds 1.5. This setting draws on the phi ratio definition from the quasicrystal module, which sets the inverse golden ratio as a convex energy proxy. The repMaxRatio theorem unfolds the repMax definition and applies ring simplification to establish the ratio equality.
proof idea
The definition is a direct construction that populates the PeakPerformanceCert structure by referencing three local results: repMaxRatio for the phi_ratio field, repMax_strictMono for strict_mono, and hypertrophyExponent_pos for exponent_pos. No additional tactics are applied beyond field assignment.
why it matters
It supplies the concrete certificate used by the peak performance construction in the J-cost sports module. This realizes the phi-ladder derivation for training as described in the module header, linking to the self-similar fixed point in the forcing chain. No open questions remain in this local definition.
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