  40/-! ## Power-to-Tier Mapping -/
  41
  42/-- Maps each Class C power to its minimum required Nautilus tier. -/
  43def requiredTier : Power → Option NautilusTier
  44  | .flight          => some .ignition
  45  | .invulnerability => some .temple
  46  | .superStrength   => some .temple
  47  | .forceFields     => some .temple
  48  | .energyProjection => some .ignition
  49  | .transmutation   => some .ignition
  50  | _                => none
  51
  52/-- All Class C powers have a required tier. -/
  53theorem classC_has_tier (p : Power) (h : powerClass p = .NautilusClass) :
  54    (requiredTier p).isSome = true := by
  55  cases p <;> simp_all [powerClass, requiredTier]
  56
  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

papers checked against this theorem

No papers in the current corpus map onto this theorem yet.