NautilusConfig

formal source

  57/-! ## Nautilus Architecture Parameters -/
  58
  59/-- Core architectural parameters for a Nautilus device. -/
  60structure NautilusConfig where
  61  kappa : ℤ
  62  n_coils : ℕ
  63  n_coils_pos : 0 < n_coils
  64  commutation_phases : ℕ := 8
  65
  66/-- The φ-log-spiral radius function: r(θ) = r₀ · φ^(κθ/2π). -/
  67noncomputable def spiralRadius (r₀ : ℝ) (kappa : ℤ) (theta : ℝ) : ℝ :=
  68  r₀ * phi ^ (kappa * theta / (2 * Real.pi))
  69
  70/-- The spiral radius is positive for positive r₀. -/
  71theorem spiralRadius_pos (r₀ : ℝ) (hr : 0 < r₀) (kappa : ℤ) (theta : ℝ) :
  72    0 < spiralRadius r₀ kappa theta := by
  73  unfold spiralRadius
  74  apply mul_pos hr
  75  apply Real.rpow_pos_of_pos phi_pos
  76
  77/-! ## 8-Tick Neutral Scheduling -/
  78
  79/-- An 8-tick schedule: a function from tick index to signed contribution. -/
  80abbrev Schedule := Fin 8 → ℤ
  81
  82/-- The neutrality constraint: sum over any aligned 8-tick window is zero. -/
  83def scheduleNeutral (s : Schedule) : Prop := (∑ i : Fin 8, s i) = 0
  84
  85/-- A neutral schedule with half positive and half negative is achievable. -/
  86def balancedSchedule : Schedule :=
  87  fun i => if i.val < 4 then 1 else -1
  88
  89theorem balancedSchedule_neutral : scheduleNeutral balancedSchedule := by
  90  unfold scheduleNeutral balancedSchedule