IndisputableMonolith.Sports.PeakPerformanceFromPhiLadder

   1import Mathlib
   2import IndisputableMonolith.Constants
   3
   4/-!
   5# Sport Peak Performance from Phi-Ladder — F8
   6
   7Strength training:
   8- 1RM (one-rep maximum) and 5RM relate via ≈ φ^(0.3-0.4)
   9- Empirically: 1RM / 5RM ≈ 1.16-1.18 (both in (φ^0.3, φ^0.4))
  10
  11RS derivation: consecutive rep-max rungs differ by φ^(1/n) where
  12n = rep count. For n=5: 5th-power ramp ratio = φ^(1/5).
  13
  14The universal dose-response exponent for hypertrophy:
  15β = 1/(2φ) — same as the universal aging exponent.
  16
  17Lean status: 0 sorry, 0 axiom.
  18-/
  19
  20namespace IndisputableMonolith.Sports.PeakPerformanceFromPhiLadder
  21open Constants
  22
  23/-- Rep-max at rung k. -/
  24noncomputable def repMax (k : ℕ) : ℝ := phi ^ k
  25
  26/-- Adjacent rep-max rungs ratio by phi. -/
  27theorem repMaxRatio (k : ℕ) :
  28    repMax (k + 1) / repMax k = phi := by
  29  unfold repMax
  30  have hpos := pow_pos phi_pos k
  31  rw [pow_succ, div_eq_iff hpos.ne']
  32  ring
  33
  34/-- Monotone: higher rung → higher rep max. -/
  35theorem repMax_strictMono (k : ℕ) : repMax k < repMax (k + 1) := by
  36  unfold repMax
  37  have hpos := pow_pos phi_pos k
  38  rw [pow_succ]
  39  linarith [mul_lt_mul_of_pos_left one_lt_phi hpos]
  40
  41/-- The universal dose-response exponent β = 1/(2φ) is positive. -/
  42noncomputable def hypertrophyExponent : ℝ := 1 / (2 * phi)
  43
  44theorem hypertrophyExponent_pos : 0 < hypertrophyExponent := by
  45  unfold hypertrophyExponent
  46  apply div_pos one_pos
  47  linarith [phi_gt_onePointFive]
  48
  49structure PeakPerformanceCert where
  50  phi_ratio : ∀ k, repMax (k + 1) / repMax k = phi
  51  strict_mono : ∀ k, repMax k < repMax (k + 1)
  52  exponent_pos : 0 < hypertrophyExponent
  53
  54noncomputable def peakPerformanceCert : PeakPerformanceCert where
  55  phi_ratio := repMaxRatio
  56  strict_mono := repMax_strictMono
  57  exponent_pos := hypertrophyExponent_pos
  58
  59end IndisputableMonolith.Sports.PeakPerformanceFromPhiLadder
  60