SpiralArray

formal source

  33  phase_offset : ℕ -- 0..7 (8-tick phase)
  34
  35/-- The geometry of a Virtual Rotor is a discrete sampling of the φ-spiral. -/
  36def SpiralArray (n_coils : ℕ) (r0 : ℝ) (kappa : ℤ) : List Coil :=
  37  List.range n_coils |>.map fun i =>
  38    let theta := (i : ℝ) * 2 * Real.pi / n_coils
  39    let r := Geometry.SpiralLemmas.logSpiral r0 theta { kappa := kappa }
  40    let phase := i % 8
  41    { id := i, angle := theta, radius := r, phase_offset := phase }
  42
  43/-- The Tip Speed of the virtual field.
  44    v = distance / time = (2π r) / (period).
  45    Period = n_coils * pulse_width. -/
  46def FieldVelocity (r : ℝ) (n_coils : ℕ) (pulse_width : ℝ) : ℝ :=
  47  (2 * Real.pi * r) / (n_coils * pulse_width)
  48
  49/-- RS Hypothesis: Relativistic Field Effect.
  50    If the virtual field velocity approaches c, the ILG kernel treats it
  51    as a relativistic mass current, even if no matter is moving. -/
  52def RelativisticFieldEffect (v_field c : ℝ) : Prop :=
  53  v_field > 0.1 * c -- Significant fraction of c
  54
  55/-- RS Falsifier: 8-Tick Coherence.
  56    The pulse sequence must strictly obey the 8-tick neutrality constraint.
  57    Any jitter or phase slip destroys the "solid" nature of the virtual object. -/
  58def PulseCoherence (schedule : ℕ → Bool) : Prop :=
  59  Schedule.eightGateNeutral (fun t => if schedule t then 1 else -1) 0
  60
  61end VirtualRotor
  62end SolidState
  63end Flight
  64end IndisputableMonolith