hypertrophyExponent
plain-language theorem explainer
Recognition Science sets the universal dose-response exponent β to 1/(2φ). Sports physiologists modeling hypertrophy scaling or aging curves cite this exact constant. The declaration is a direct noncomputable assignment from the phi constant with no lemmas or computation steps.
Claim. $β := 1/(2φ)$ where $β$ is the universal dose-response exponent for hypertrophy.
background
The module treats strength training via the phi-ladder: consecutive rep-maxima satisfy repMax(k+1)/repMax(k) = φ, so the 5RM ramp ratio equals φ^(1/5). This yields the universal dose-response exponent β = 1/(2φ) for hypertrophy, numerically identical to the aging exponent. Phi is the self-similar fixed point from the forcing chain (T6). The definition supplies the exact real used inside the PeakPerformanceCert structure.
proof idea
Direct definition. The body is the single expression 1/(2*phi) with no tactics, lemmas, or unfolding steps applied.
why it matters
The constant is required by the downstream positivity theorem hypertrophyExponent_pos and by the PeakPerformanceCert structure that certifies monotonic rep-maxima and positive exponent. It realizes the same β that appears in aging models, linking sports performance to the core phi-ladder (T6 self-similar fixed point) and eight-tick octave scaling (T7). The module reports zero sorrys, closing the sports application of the Recognition framework.
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