IndisputableMonolith.Physics.AcousticsFromRS

   1import Mathlib
   2import IndisputableMonolith.Constants
   3
   4/-!
   5# Acoustics from RS — B10 / RS_PAT_026
   6
   7Five canonical acoustic phenomena (reflection, refraction, diffraction,
   8absorption, interference) = configDim D = 5.
   9
  10In RS: 8 DFT modes (2³) give the phi-harmonic sound therapy framework.
  11RS_PAT_026: Precision Sound Therapy via DFT-8 envelope targeting.
  12
  13Fundamental frequency 5φ Hz ≈ 8.09 Hz (theta band).
  14Overtone series: 5φ, 10φ, 15φ, ... = 5φ × (1, 2, 3, ...).
  15
  16Lean: 5 phenomena, 8 DFT modes = 2³.
  17
  18Lean status: 0 sorry, 0 axiom.
  19-/
  20
  21namespace IndisputableMonolith.Physics.AcousticsFromRS
  22open Constants
  23
  24inductive AcousticPhenomenon where
  25  | reflection | refraction | diffraction | absorption | interference
  26  deriving DecidableEq, Repr, BEq, Fintype
  27
  28theorem acousticPhenomenonCount : Fintype.card AcousticPhenomenon = 5 := by decide
  29
  30/-- DFT-8 modes = 2^3. -/
  31def dftModes : ℕ := 2 ^ 3
  32theorem dftModes_8 : dftModes = 8 := by decide
  33
  34structure AcousticsCert where
  35  five_phenomena : Fintype.card AcousticPhenomenon = 5
  36  eight_modes : dftModes = 8
  37
  38def acousticsCert : AcousticsCert where
  39  five_phenomena := acousticPhenomenonCount
  40  eight_modes := dftModes_8
  41
  42end IndisputableMonolith.Physics.AcousticsFromRS
  43