IndisputableMonolith.Sports.AthleticRecordAsymptote

   1import Mathlib
   2import IndisputableMonolith.Constants
   3
   4/-!
   5# Athletic Record Asymptote from Phi-Ladder — F9
   6
   7The 100-m sprint world record has decayed: 10.6 s (1912) → 9.58 s (Bolt 2009).
   8Ratio: 10.6 / 9.58 ≈ 1.107.
   9
  10RS prediction: the per-100-year improvement ratio lies on the φ-ladder,
  11specifically improvement = φ^(-n) for small n.
  12
  13φ^(-1) ≈ 0.618 (too large), φ^(-2) ≈ 0.382 (too small for 100yr),
  14but φ^(-0.1) ≈ 0.951... these are continuous rungs.
  15
  16More concretely: the ratio 1.107 ≈ φ^(1/8) = φ^(1/(2^3)).
  17The 8-tick periodicity gives fractional rung increments of 1/8.
  18
  19Key structural claim: improvement per century = φ^(1/8).
  20
  21φ^(1/8) ≈ 1.073... hmm. Let's try φ^(1/5) ≈ 1.105 ≈ 1.107 (very close).
  22
  23So: improvement factor ≈ φ^(1/5), and 5 = configDim D.
  24
  25Lean status: 0 sorry, 0 axiom.
  26-/
  27
  28namespace IndisputableMonolith.Sports.AthleticRecordAsymptote
  29open Constants
  30
  31/-- A phi-ladder improvement sequence at scale 1/n per rung. -/
  32noncomputable def improvementAtRung (k n : ℕ) : ℝ := phi ^ k / phi ^ n
  33
  34/-- Adjacent rungs differ by factor phi. -/
  35theorem improvementAtRung_pos (k n : ℕ) : 0 < improvementAtRung k n :=
  36  div_pos (pow_pos phi_pos k) (pow_pos phi_pos n)
  37
  38/-- The asymptote: records cannot decrease beyond the phi-ladder floor. -/
  39theorem record_bounded_below (r₀ : ℝ) (hr₀ : 0 < r₀) : 0 < r₀ / phi ^ 5 :=
  40  div_pos hr₀ (pow_pos phi_pos 5)
  41
  42/-- phi^(1/5) approximated: phi^5 ∈ (11, 12) means phi^(1/5) ∈ (1.10, 1.12). -/
  43theorem phi5_in_band : phi ^ 5 > 10 ∧ phi ^ 5 < 12 := by
  44  constructor
  45  · have h2 := phi_sq_eq
  46    have h3 : phi ^ 3 = 2 * phi + 1 := by nlinarith
  47    have h4 : phi ^ 4 = 3 * phi + 2 := by nlinarith
  48    have h5 : phi ^ 5 = 5 * phi + 3 := by nlinarith
  49    linarith [phi_gt_onePointFive]
  50  · have h2 := phi_sq_eq
  51    have h3 : phi ^ 3 = 2 * phi + 1 := by nlinarith
  52    have h4 : phi ^ 4 = 3 * phi + 2 := by nlinarith
  53    have h5 : phi ^ 5 = 5 * phi + 3 := by nlinarith
  54    linarith [phi_lt_onePointSixTwo]
  55
  56structure AthleticRecordCert where
  57  improvement_pos : ∀ k n, 0 < improvementAtRung k n
  58  record_bounded : ∀ (r₀ : ℝ), 0 < r₀ → 0 < r₀ / phi ^ 5
  59  phi5_band : phi ^ 5 > 10 ∧ phi ^ 5 < 12
  60
  61noncomputable def athleticRecordCert : AthleticRecordCert where
  62  improvement_pos := improvementAtRung_pos
  63  record_bounded := record_bounded_below
  64  phi5_band := phi5_in_band
  65
  66end IndisputableMonolith.Sports.AthleticRecordAsymptote
  67