l_rec

formal source

  63
  64/-- Recognition length l_rec = √(ℏG/(πc³)) (Planck scale) -/
  65-- In natural units where c = ℏ = G = 1:
  66noncomputable def l_rec : ℝ := Real.sqrt (1 / Real.pi) -- Check if rewrite failed here
  67
  68/-! ## Observability Constraints -/
  69
  70/-- Observability threshold: minimum flux for recognition -/
  71noncomputable def F_threshold : ℝ := E_coh / τ_0
  72
  73/-- Coherence volume: maximum assembly volume -/
  74noncomputable def V_coherence : ℝ := l_rec ^ 3
  75
  76/-- Maximum mass from coherent assembly in N cycles -/
  77noncomputable def M_max (N : ℕ) (ρ : ℝ) : ℝ := ρ * V_coherence * N
  78
  79/-! ## J-Cost Optimization -/
  80
  81/-- The J-cost for mass configuration at scale ratio r -/
  82noncomputable def J_mass (r : ℝ) : ℝ := Cost.Jcost r
  83
  84/-- The J-cost for luminosity configuration at scale ratio r -/
  85noncomputable def J_light (r : ℝ) : ℝ := Cost.Jcost r
  86
  87/-- Total J-cost for stellar configuration -/
  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 -/