eegPredictions

formal source

  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 -/
  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 -/