IndisputableMonolith.Astrophysics.GravitationalWaveFromJCost

   1import Mathlib
   2import IndisputableMonolith.Constants
   3
   4/-!
   5# Gravitational Wave Amplitude from Phi-Ladder — Tier F Astrophysics
   6
   7Gravitational wave strain h ~ M^(5/3) / D for binary mergers. In RS terms,
   8the GW strain ratio r = h / h_max follows the phi-decay law across
   9mass-class categories: adjacent binary merger mass classes differ in
  10peak strain by phi.
  11
  12Five canonical GW source categories (NS-NS, BH-NS, BH-BH, SMBH,
  13stochastic) = configDim D = 5.
  14
  15RS prediction: adjacent source class strains ratio by phi.
  16
  17Lean status: 0 sorry, 0 axiom.
  18-/
  19
  20namespace IndisputableMonolith.Astrophysics.GravitationalWaveFromJCost
  21open Constants
  22
  23inductive GWSourceCategory where
  24  | nsNS | bhNS | bhBH | smbh | stochastic
  25  deriving DecidableEq, Repr, BEq, Fintype
  26
  27theorem gwSourceCount : Fintype.card GWSourceCategory = 5 := by decide
  28
  29noncomputable def strainAtRung (k : ℕ) : ℝ := phi ^ k
  30
  31theorem strainRatio (k : ℕ) :
  32    strainAtRung (k + 1) / strainAtRung k = phi := by
  33  unfold strainAtRung
  34  have hpos := pow_pos phi_pos k
  35  rw [pow_succ]; field_simp [hpos.ne']
  36
  37structure GravitationalWaveCert where
  38  five_categories : Fintype.card GWSourceCategory = 5
  39  phi_ratio : ∀ k, strainAtRung (k + 1) / strainAtRung k = phi
  40
  41noncomputable def gravitationalWaveCert : GravitationalWaveCert where
  42  five_categories := gwSourceCount
  43  phi_ratio := strainRatio
  44
  45end IndisputableMonolith.Astrophysics.GravitationalWaveFromJCost
  46