EEGFalsification

formal source

  68   ⟨3, φ^(3 : ℤ), 0.2, 0.5, 0.95⟩]     -- ~4.24 Hz (theta)
  69
  70/-- FALSIFICATION: The EEG prediction is falsified if no φ-peaks found -/
  71structure EEGFalsification where
  72  /-- Measured peak frequencies -/
  73  measured_peaks : List ℝ
  74  /-- Tolerance for matching (Hz) -/
  75  tolerance : ℝ := 0.2
  76  /-- Minimum number of φ-matches required -/
  77  min_matches : ℕ := 3
  78
  79/-- Check if a measured frequency matches any φ^n prediction -/
  80noncomputable def matchesPhiPeak (f : ℝ) (tolerance : ℝ) : Bool :=
  81  (|f - φ^(-2 : ℤ)| < tolerance) ||
  82  (|f - φ^(-1 : ℤ)| < tolerance) ||
  83  (|f - 1| < tolerance) ||
  84  (|f - φ| < tolerance) ||
  85  (|f - φ^(2 : ℤ)| < tolerance) ||
  86  (|f - φ^(3 : ℤ)| < tolerance)
  87
  88/-- The EEG prediction is falsified if too few peaks match -/
  89def isEEGFalsified (data : EEGFalsification) : Prop :=
  90  (data.measured_peaks.filter (matchesPhiPeak · data.tolerance)).length < data.min_matches
  91
  92/-! ## Mode Ratio Predictions -/
  93
  94/-- Consciousness state classification -/
  95inductive ConsciousnessState
  96  | baseline
  97  | flow
  98  | analytical
  99  | meditation
 100  | sleep
 101  deriving DecidableEq, Repr