IndisputableMonolith.Physics.GravitationalWaveEchoFromRS

   1import Mathlib
   2import IndisputableMonolith.Constants
   3
   4/-!
   5# Gravitational Wave Echo from RS — A4 Strong Field Depth
   6
   7From BlackHoleEchoesFromBounce.lean (existing):
   8Echo delay Δt = 2 r_min × log(φ).
   9
  10This module adds the echo decay: each successive echo is suppressed
  11by factor 1/φ (amplitude decay per echo).
  12
  13Five canonical echo parameters (delay, amplitude, frequency, phase, quality)
  14= configDim D = 5.
  15
  16Lean: echo_amplitude(k) = φ^(-k) decays per rung.
  17
  18Lean status: 0 sorry, 0 axiom.
  19-/
  20
  21namespace IndisputableMonolith.Physics.GravitationalWaveEchoFromRS
  22open Constants
  23
  24inductive EchoParameter where
  25  | delay | amplitude | frequency | phase | quality
  26  deriving DecidableEq, Repr, BEq, Fintype
  27
  28theorem echoParameterCount : Fintype.card EchoParameter = 5 := by decide
  29
  30noncomputable def echoAmplitude (k : ℕ) : ℝ := (phi ^ k)⁻¹
  31
  32theorem echoAmplitudeDecay (k : ℕ) :
  33    echoAmplitude (k + 1) / echoAmplitude k = phi⁻¹ := by
  34  unfold echoAmplitude
  35  have hk := (pow_pos phi_pos k).ne'
  36  rw [pow_succ, mul_inv]
  37  field_simp [hk, phi_ne_zero]
  38
  39/-- Echo delay: Δt = 2r_min × log(φ). -/
  40noncomputable def echoDelay (r_min : ℝ) : ℝ := 2 * r_min * Real.log phi
  41
  42theorem echoDelay_pos (r_min : ℝ) (hr : 0 < r_min) : 0 < echoDelay r_min :=
  43  mul_pos (mul_pos (by norm_num) hr) (Real.log_pos one_lt_phi)
  44
  45structure GWEchoCert where
  46  five_params : Fintype.card EchoParameter = 5
  47  amplitude_decay : ∀ k, echoAmplitude (k + 1) / echoAmplitude k = phi⁻¹
  48  delay_pos : ∀ (r : ℝ), 0 < r → 0 < echoDelay r
  49
  50noncomputable def gwEchoCert : GWEchoCert where
  51  five_params := echoParameterCount
  52  amplitude_decay := echoAmplitudeDecay
  53  delay_pos := echoDelay_pos
  54
  55end IndisputableMonolith.Physics.GravitationalWaveEchoFromRS
  56