repMax
plain-language theorem explainer
repMax assigns the rep-maximum strength at rung k to phi raised to the power k. Strength training researchers applying Recognition Science to dose-response curves cite it when deriving empirical ratios such as 1RM to 5RM. The declaration is a direct noncomputable definition with no proof obligations or computational content.
Claim. The rep-maximum strength at rung $k$ is defined as $phi^k$.
background
The Sports.PeakPerformanceFromPhiLadder module models strength training via the phi-ladder, where consecutive rep-max rungs differ by factors of phi. Module documentation states that 1RM / 5RM ratios lie in (phi^0.3, phi^0.4) and introduces the universal hypertrophy exponent beta = 1/(2 phi), matching the aging exponent. This definition supplies the base rung values used to derive those ratios.
proof idea
The declaration is a direct definition. Downstream results such as repMaxRatio unfold it and apply pow_succ together with ring to obtain the adjacent ratio equal to phi; repMax_strictMono uses the same unfold followed by linarith on the positive power and one_lt_phi.
why it matters
This definition supplies the rung values that feed the PeakPerformanceCert structure, which asserts the phi ratio for adjacent rungs together with strict monotonicity and positive hypertrophyExponent. It realizes the F8 derivation for rep-max ratios, linking to the self-similar fixed point phi from the forcing chain and the universal dose-response exponent beta = 1/(2 phi).
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.