EEGPrediction

formal source

  46  electrodes : List String := ["Fz", "Cz", "Pz", "O1", "O2"]
  47
  48/-- Predicted EEG peaks with confidence intervals -/
  49structure EEGPrediction where
  50  /-- The mode index n in φ^n -/
  51  mode_index : ℤ
  52  /-- Central frequency (φ^n Hz) -/
  53  center_freq : ℝ
  54  /-- Expected peak width (Hz) -/
  55  bandwidth : ℝ := 0.2
  56  /-- Minimum peak amplitude (μV²/Hz) -/
  57  min_amplitude : ℝ
  58  /-- Confidence level for detection -/
  59  confidence : ℝ := 0.95
  60
  61/-- The set of predicted EEG frequencies -/
  62noncomputable def eegPredictions : List EEGPrediction :=
  63  [⟨-2, φ^(-2 : ℤ), 0.2, 0.5, 0.95⟩,   -- ~0.38 Hz (infra-slow)
  64   ⟨-1, φ^(-1 : ℤ), 0.2, 0.5, 0.95⟩,   -- ~0.62 Hz (delta-low)
  65   ⟨0, 1, 0.2, 1.0, 0.95⟩,              -- 1.00 Hz (delta-high)
  66   ⟨1, φ, 0.2, 1.0, 0.95⟩,              -- ~1.62 Hz (delta-theta)
  67   ⟨2, φ^(2 : ℤ), 0.2, 0.8, 0.95⟩,     -- ~2.62 Hz (theta-low)
  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 -/