IndisputableMonolith.Superhuman.Core

   1import Mathlib
   2import IndisputableMonolith.Cost
   3import IndisputableMonolith.Constants
   4
   5/-!
   6# Superhuman Core: Power Taxonomy and Capability Classification
   7
   8Formalizes the σ-Resolution Superhero Thesis power taxonomy.
   927 powers classified into five epistemic classes (A–E) by RS mechanism type.
  10
  11## Claim Hygiene
  12- THEOREM: structural results proved from RS axioms
  13- HYPOTHESIS: empirical claims with explicit falsifiers (Prop definitions)
  14- MODEL: structural definitions grounding the classification
  15
  16## Key Results
  17- `PowerClass`: five epistemic tiers (DirectMechanism, Derivable, NautilusClass, Speculative, Constrained)
  18- `Power`: enumeration of 27 canonical powers
  19- `powerClass`: classification function assigning each power to its class
  20- `powerCount_eq_27`: the taxonomy is complete at 27 powers
  21- `accessible_count_eq_23`: 23 powers have an RS path; 4 are constrained/forbidden
  22-/
  23
  24namespace IndisputableMonolith.Superhuman
  25
  26open Constants
  27
  28/-! ## Power Classification -/
  29
  30/-- The five epistemic classes for superhuman powers.
  31    Each class has a different relationship to proved RS structure. -/
  32inductive PowerClass where
  33  | DirectMechanism   -- Class A: Lean module with formalization exists
  34  | Derivable         -- Class B: follows from existing RS results
  35  | NautilusClass     -- Class C: requires localized J-cost minimization technology
  36  | Speculative       -- Class D: consistent with RS but needs theoretical extension
  37  | Constrained       -- Class E: forbidden or constrained by conservation laws
  38  deriving DecidableEq, Repr
  39
  40/-- Whether a power class represents an accessible (not forbidden) capability. -/
  41def PowerClass.accessible : PowerClass → Bool
  42  | .DirectMechanism => true
  43  | .Derivable       => true
  44  | .NautilusClass   => true
  45  | .Speculative     => true
  46  | .Constrained     => false
  47
  48/-! ## Power Enumeration -/
  49
  50/-- The 27 canonical superhuman powers from cross-cultural mythology, comics, and folklore. -/
  51inductive Power where
  52  -- Class A: Direct RS Mechanism
  53  | telepathy
  54  | precognition
  55  | empathy
  56  | healing
  57  | immortality
  58  | astralProjection
  59  -- Class B: Derivable from RS
  60  | superIntelligence
  61  | enhancedSenses
  62  | soundControl
  63  | animalCommunication
  64  | mindInfluence
  65  | collectivePower
  66  -- Class C: Nautilus-Class Technology
  67  | flight
  68  | invulnerability
  69  | superStrength
  70  | forceFields
  71  | energyProjection
  72  | transmutation
  73  -- Class D: Speculative but Consistent
  74  | timePerception
  75  | superSpeed
  76  | invisibility
  77  | elementalControl
  78  | sizeManipulation
  79  -- Class E: Constrained or Forbidden
  80  | duplication
  81  | realityWarping
  82  | creationExNihilo
  83  | absoluteInvulnerability
  84  deriving DecidableEq, Repr
  85
  86/-- Classification function: assigns each power to its epistemic class. -/
  87def powerClass : Power → PowerClass
  88  | .telepathy             => .DirectMechanism
  89  | .precognition          => .DirectMechanism
  90  | .empathy               => .DirectMechanism
  91  | .healing               => .DirectMechanism
  92  | .immortality           => .DirectMechanism
  93  | .astralProjection      => .DirectMechanism
  94  | .superIntelligence     => .Derivable
  95  | .enhancedSenses        => .Derivable
  96  | .soundControl          => .Derivable
  97  | .animalCommunication   => .Derivable
  98  | .mindInfluence         => .Derivable
  99  | .collectivePower       => .Derivable
 100  | .flight                => .NautilusClass
 101  | .invulnerability       => .NautilusClass
 102  | .superStrength         => .NautilusClass
 103  | .forceFields           => .NautilusClass
 104  | .energyProjection      => .NautilusClass
 105  | .transmutation         => .NautilusClass
 106  | .timePerception        => .Speculative
 107  | .superSpeed            => .Speculative
 108  | .invisibility          => .Speculative
 109  | .elementalControl      => .Speculative
 110  | .sizeManipulation      => .Speculative
 111  | .duplication           => .Constrained
 112  | .realityWarping        => .Constrained
 113  | .creationExNihilo      => .Constrained
 114  | .absoluteInvulnerability => .Constrained
 115
 116/-- A power is accessible if its class is not Constrained. -/
 117def Power.accessible (p : Power) : Bool := (powerClass p).accessible
 118
 119/-- List of all 27 powers. -/
 120def allPowers : List Power :=
 121  [.telepathy, .precognition, .empathy, .healing, .immortality, .astralProjection,
 122   .superIntelligence, .enhancedSenses, .soundControl, .animalCommunication,
 123   .mindInfluence, .collectivePower,
 124   .flight, .invulnerability, .superStrength, .forceFields, .energyProjection,
 125   .transmutation,
 126   .timePerception, .superSpeed, .invisibility, .elementalControl, .sizeManipulation,
 127   .duplication, .realityWarping, .creationExNihilo, .absoluteInvulnerability]
 128
 129theorem powerCount_eq_27 : allPowers.length = 27 := by native_decide
 130
 131theorem accessible_count_eq_23 :
 132    (allPowers.filter Power.accessible).length = 23 := by native_decide
 133
 134theorem constrained_count_eq_4 :
 135    (allPowers.filter (fun p => !(Power.accessible p))).length = 4 := by native_decide
 136
 137/-- Class A has exactly 6 powers. -/
 138theorem classA_count :
 139    (allPowers.filter (fun p => powerClass p == .DirectMechanism)).length = 6 := by native_decide
 140
 141/-- Class B has exactly 6 powers. -/
 142theorem classB_count :
 143    (allPowers.filter (fun p => powerClass p == .Derivable)).length = 6 := by native_decide
 144
 145/-- Class C has exactly 6 powers. -/
 146theorem classC_count :
 147    (allPowers.filter (fun p => powerClass p == .NautilusClass)).length = 6 := by native_decide
 148
 149/-- Class D has exactly 5 powers. -/
 150theorem classD_count :
 151    (allPowers.filter (fun p => powerClass p == .Speculative)).length = 5 := by native_decide
 152
 153/-- Class E has exactly 4 powers. -/
 154theorem classE_count :
 155    (allPowers.filter (fun p => powerClass p == .Constrained)).length = 4 := by native_decide
 156
 157/-! ## Constraint Type -/
 158
 159/-- Why a power is constrained or forbidden. -/
 160inductive ConstraintReason where
 161  | zConservation       -- Z is conserved; cannot duplicate patterns
 162  | jUniqueness         -- J is uniquely forced; cannot override cost structure
 163  | costOfNothing       -- J(0⁺) → ∞; cannot create from nothing
 164  | boundaryDissolution -- Dissolution always thermodynamically available
 165  deriving DecidableEq, Repr
 166
 167/-- Each constrained power has a specific conservation-law reason. -/
 168def constraintReason : Power → Option ConstraintReason
 169  | .duplication             => some .zConservation
 170  | .realityWarping          => some .jUniqueness
 171  | .creationExNihilo        => some .costOfNothing
 172  | .absoluteInvulnerability => some .boundaryDissolution
 173  | _                        => none
 174
 175theorem constrained_has_reason (p : Power) (h : powerClass p = .Constrained) :
 176    (constraintReason p).isSome = true := by
 177  cases p <;> simp_all [powerClass, constraintReason]
 178
 179end IndisputableMonolith.Superhuman
 180