IndisputableMonolith.Superhuman.TechnologicalAccess

   1import Mathlib
   2import IndisputableMonolith.Constants
   3import IndisputableMonolith.Superhuman.Core
   4
   5/-!
   6# Technological Access Path: Nautilus Power Tiers
   7
   8Formalizes the Nautilus-class technological access path for Class C powers.
   9Defines power tiers, maps powers to tiers, and encodes engineering parameters.
  10
  11## Claim Hygiene
  12- Power tiers and mappings are MODEL (structural definitions)
  13- Engineering parameters are from the NTL provisional patent stack
  14- Gap-45 safety is PROVED (imported from Gap45)
  15-/
  16
  17namespace IndisputableMonolith.Superhuman.TechnologicalAccess
  18
  19open Constants
  20
  21/-! ## Power Tiers -/
  22
  23/-- The three Nautilus power tiers. -/
  24inductive NautilusTier where
  25  | quietRoom  -- ~10–100 W: meditation amplifier, δθ suppression aid
  26  | temple     -- ~5–10 kW: healing field, group coherence, force fields
  27  | ignition   -- >100 kW pulsed: metric editing, flight, transmutation
  28  deriving DecidableEq, Repr
  29
  30/-- Power range for each tier (in watts). -/
  31def tierPowerRange : NautilusTier → ℝ × ℝ
  32  | .quietRoom => (10, 100)
  33  | .temple    => (5000, 10000)
  34  | .ignition  => (100000, 1000000)
  35
  36/-- Each tier's lower bound is positive. -/
  37theorem tier_power_positive (t : NautilusTier) : 0 < (tierPowerRange t).1 := by
  38  cases t <;> simp [tierPowerRange] <;> norm_num
  39
  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
  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
  91  simp [Fin.sum_univ_eight]
  92
  93/-! ## Safety Requirements -/
  94
  95/-- Nautilus safety requirements (from NTL-008/018). -/
  96structure SafetyRequirements where
  97  has_watchdog : Bool
  98  has_overcurrent_protection : Bool
  99  has_overvoltage_protection : Bool
 100  has_thermal_protection : Bool
 101  has_loss_of_load_detection : Bool
 102  has_deterministic_shutdown : Bool
 103  all_satisfied :
 104    has_watchdog = true ∧
 105    has_overcurrent_protection = true ∧
 106    has_overvoltage_protection = true ∧
 107    has_thermal_protection = true ∧
 108    has_loss_of_load_detection = true ∧
 109    has_deterministic_shutdown = true
 110
 111/-- The canonical safety configuration. -/
 112def fullSafety : SafetyRequirements where
 113  has_watchdog := true
 114  has_overcurrent_protection := true
 115  has_overvoltage_protection := true
 116  has_thermal_protection := true
 117  has_loss_of_load_detection := true
 118  has_deterministic_shutdown := true
 119  all_satisfied := ⟨rfl, rfl, rfl, rfl, rfl, rfl⟩
 120
 121end IndisputableMonolith.Superhuman.TechnologicalAccess
 122