IndisputableMonolith.Flight.SolidState.VirtualRotor

   1import Mathlib
   2import IndisputableMonolith.Flight.Geometry
   3import IndisputableMonolith.Flight.Schedule
   4
   5/-!
   6# RS Hypothesis: Virtual Rotor (Phased Array Physics)
   7
   8This module formalizes the "Solid State" metric engine:
   9A ring of stationary coils pulsed in sequence to create a rotating
  10magnetic field that mimics a physical φ-spiral rotor.
  11
  12## The Mechanism
  13Instead of spinning mass (limited by material strength), we spin
  14Information Density (magnetic flux) at relativistic speeds.
  15
  16v_field = (2π r) / (8 τ_pulse)
  17
  18If τ_pulse is small enough (MHz/GHz), v_field can approach c.
  19-/
  20
  21namespace IndisputableMonolith
  22namespace Flight
  23namespace SolidState
  24namespace VirtualRotor
  25
  26open IndisputableMonolith.Flight
  27
  28/-- A coil in the phased array. -/
  29structure Coil where
  30  id : ℕ
  31  angle : ℝ
  32  radius : ℝ
  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
  65