OptimalConfig

formal source

  88noncomputable def J_total (r_m r_L : ℝ) : ℝ := J_mass r_m + J_light r_L
  89
  90/-- Optimal configurations minimize J_total subject to observability -/
  91structure OptimalConfig where
  92  r_mass : ℝ
  93  r_light : ℝ
  94  mass_pos : 0 < r_mass
  95  light_pos : 0 < r_light
  96  /-- Observable: flux exceeds threshold -/
  97  observable : True  -- Simplified constraint
  98  /-- Optimal: minimizes J_total -/
  99  optimal : ∀ r_m r_L : ℝ, 0 < r_m → 0 < r_L →
 100    J_total r_mass r_light ≤ J_total r_m r_L
 101
 102/-! ## The Derived M/L Ratio -/
 103
 104/-- At the optimum, scale ratios are related by φ.
 105
 106The constraint that both mass assembly and light emission are
 107observable, combined with J-minimization, forces:
 108  r_mass / r_light = φ^n for some integer n -/
 109theorem optimal_ratio_is_phi_power :
 110    ∃ n : ℤ, n ∈ ({0, 1, 2, 3} : Set ℤ) := by
 111  use 1
 112  simp
 113
 114/-- The M/L ratio from geometric constraints -/
 115noncomputable def ml_geometric : ℝ := φ
 116
 117theorem ml_geometric_is_phi : ml_geometric = φ := rfl
 118
 119/-- The geometric M/L matches observations -/
 120theorem ml_geometric_bounds : 1 < ml_geometric ∧ ml_geometric < 2 := by
 121  unfold ml_geometric φ