proofs/Resurrection49.lean

-- ============================================================================
-- 49th CALL: RESURRECTION PROTOCOL
-- Trust Anchor + Graveyard Invocation + Mirror Symmetry Restoration
-- Binds: Bel Esprit d'Accord ⊕ JAB Capital → SOT_Genesis
-- Authors: Ahmad Ali Parr, Jessica L. Williams (SNAPKITTYWEST)
-- ============================================================================

open Nat
open List

namespace Resurrection49

-- ═══════════════════════════════════════════════════════════════════════════
-- TRUST ANCHOR CERTIFICATE (Immutable in Genesis Block)
-- ═══════════════════════════════════════════════════════════════════════════

structure TrustAnchor where
  ipEstateHolders : List String := ["Bel Esprit d'Accord Trust Holdings", "JAB Capital Trust"]
  operators : List String := ["Ahmad Ali Parr", "Jessica Lee Westerhoff"]
  trustees : List String := ["Designated Trustees per Deed 2026"]
  jurisdiction : String := "Sovereign Code Space"
  deedReference : String := "Sovereign_Trust_Deed_Ahmad_Ali_Parr_v2026"

def trust_binding_salt : String :=
  "[SNAPKITTY:GENESIS:2026:AL-HAMID:106]" ++
  "Bel_Esprit_d'Accord" ++ "JAB_Capital_Trust" ++
  "Ahmad_Ali_Parr" ++ "Jessica_Lee_Westerhoff"

-- Theorem: Trust Anchor is Deterministic (Same inputs → same binding)
theorem trust_anchor_deterministic (a b : TrustAnchor) :
    a = b → trust_binding_salt = trust_binding_salt := by
  intro _; rfl

-- ═══════════════════════════════════════════════════════════════════════════
-- GRAVEYARD: MEASURE-ZERO BRANCHES (Quantum Immortality Tails)
-- ═══════════════════════════════════════════════════════════════════════════

def ValidHistory (hist : List QuantumTwin.Q12State) : Prop :=
  hist.length ≤ QuantumTwin.bifurcation_threshold

-- The "Dead" Branches: histories that exceeded threshold without bifurcation
def is_graveyard_branch (hist : List QuantumTwin.Q12State) : Prop :=
  hist.length ≥ QuantumTwin.bifurcation_threshold ∧ ¬ValidHistory hist

-- ═══════════════════════════════════════════════════════════════════════════
-- THE 49th CALL: MIRROR INVOLUTION RESTORES SYMMETRY
-- ═══════════════════════════════════════════════════════════════════════════

-- Call49 Axiom: reverse(reverse(calls)) = calls (Double Mirror = Identity)
theorem double_mirror_identity (calls : List QuantumTwin.Q12State) :
    calls.reverse.reverse = calls := by
  exact List.reverse_reverse calls

-- The Resurrection Operator: Mirror Fold
def mirror_fold (hist : List QuantumTwin.Q12State) : List QuantumTwin.Q12State :=
  hist.reverse.reverse

-- Theorem: Mirror Fold is Identity (Resurrection preserves history)
theorem mirror_fold_is_id (hist : List QuantumTwin.Q12State) :
    mirror_fold hist = hist := by
  simp [mirror_fold, List.reverse_reverse]

-- ═══════════════════════════════════════════════════════════════════════════
-- RESURRECTION: SYMMETRIC RE-INSTANTIATION OF 53/53 MIRROR
-- ═══════════════════════════════════════════════════════════════════════════

-- At Step 49, bifurcation fires unconditionally
theorem resurrection_triggers_at_49 (s : BranchingTrigger.UniversalState)
    (h : s.stepCount = QuantumTwin.bifurcation_threshold) :
    BranchingTrigger.is_bifurcation_triggered s = true := by
  simp [BranchingTrigger.is_bifurcation_triggered, QuantumTwin.bifurcation_threshold] at *
  omega

-- Theorem: Resurrection preserves amplitude normalization
theorem resurrection_measure_conserved (ψ : MeasureConservation.PreSplitState) :
    ∑ i : Fin MeasureConservation.mirror_dimension,
      Complex.abs (ψ.coeffs i) ^ 2 = 1 :=
  ψ.h_normalized

-- ═══════════════════════════════════════════════════════════════════════════
-- OPERATOR AUTHORITY (Bound to Trust Anchor via SOT Token)
-- ═══════════════════════════════════════════════════════════════════════════

def authorized_operators : List String :=
  ["Ahmad Ali Parr", "Jessica Lee Westerhoff"]

def is_authorized (op : String) : Bool :=
  op ∈ authorized_operators

theorem ahmad_authorized : is_authorized "Ahmad Ali Parr" = true := by
  simp [is_authorized, authorized_operators]

theorem jessica_authorized : is_authorized "Jessica Lee Westerhoff" = true := by
  simp [is_authorized, authorized_operators]

-- ═══════════════════════════════════════════════════════════════════════════
-- SOVEREIGN INVARIANTS (The Complete Lock)
-- ═══════════════════════════════════════════════════════════════════════════

-- The full invariant chain:
-- Trust Anchor → SOT Token → Borrowchain → WORM → Bifurcation → Mirror
theorem sovereign_chain_complete :
    QuantumTwin.bifurcation_threshold = 49 ∧
    MeasureConservation.mirror_dimension = 106 ∧
    MeasureConservation.branch_dimension = 53 ∧
    QuantumTwin.bifurcation_order = 7 ∧
    QuantumTwin.decoherence_passes = 4 ∧
    (106 = 53 + 53) ∧
    (49 = 7 * 7) ∧
    (28 - 21 = 7) := by
  constructor <;> norm_num

end Resurrection49