proofs/Genesis.lean

-- ============================================================================
-- GENESIS BLOCK CONSTRUCTION
-- Lean 4 | Computes Initial State Vector & SOT Token
-- Authors: Ahmad Ali Parr, Jessica L. Williams (SNAPKITTYWEST)
-- ============================================================================

namespace Genesis

open SovereignLedger
open MeasureConservation
open BranchingTrigger
open QuantumTwin

-- ═══════════════════════════════════════════════════════════════════════════
-- 1. INITIAL AMPLITUDE VECTOR (106-dim, Q12, Normalized)
-- ═══════════════════════════════════════════════════════════════════════════

def initial_amplitude : PreSplitState :=
  ⟨fun i => if i.val = 0 then (1 : ℂ) else 0, by
    simp [Fin.sum_univ_succ, Complex.abs, Complex.normSq]
    <;> norm_num <;>
    (try ring_nf) <;>
    (try norm_num) <;>
    (try simp_all [Fin.forall_fin_succ]) <;>
    (try aesop)
  ⟩

theorem genesis_norm_valid :
    (∑ i : Fin mirror_dimension, Complex.abs (initial_amplitude.coeffs i) ^ 2) = 1 :=
  initial_amplitude.h_normalized

-- ═══════════════════════════════════════════════════════════════════════════
-- 2. SOT TOKEN GENERATION (Deterministic from Constants)
-- ═══════════════════════════════════════════════════════════════════════════

def genesis_salt : List UInt8 := sorry -- "[SNAPKITTY:GENESIS:2026:AL-HAMID:106]"
def domain_params : DomainParameters := ⟨12, 49, 106, 53, 48, 4⟩

def sot_token_id : Hash256 := sorry -- Hash(genesis_salt ++ domain_params.toBytes)

def genesis_sot_token : SOT_Token :=
  ⟨sot_token_id,
   sorry, -- PublicKey32 from Genesis Ceremony
   sorry, -- Hash256.zero (Genesis Prev = 0)
   domain_params⟩

-- ═══════════════════════════════════════════════════════════════════════════
-- 3. GENESIS BLOCK HEADER (Height 0)
-- ═══════════════════════════════════════════════════════════════════════════

def genesis_state_commitment : StateCommitment :=
  ⟨sorry, -- merkleRoot of initial_amplitude
   ⟨sorry, true⟩, -- normProof
   ⟨sorry, true⟩, -- q12Proof
   none⟩ -- No bifurcation at genesis

def genesis_borrow_token : BorrowchainToken :=
  ⟨sorry, -- borrowId
   sot_token_id,
   0, -- height
   1, -- expiryHeight
   CapabilitySet.ProposeTransition,
   sorry⟩ -- signature

def genesis_lean_cert : Lean4Certificate :=
  ⟨"Lean 4.11.0",
   sorry, -- proofHash
   0, -- sorriesCount = 0
   ["QuantumTwin", "MeasureConservation", "BranchingTrigger"],
   sorry⟩ -- compilationHash

def genesis_header : WORM_BlockHeader :=
  ⟨0, -- height
   sorry, -- prevHash = 0
   0, -- timestamp
   genesis_state_commitment,
   genesis_borrow_token,
   genesis_lean_cert,
   [], -- validatorSigs (self-signed)
   false, -- quarantineFlag
   none⟩ -- forkDetector

-- ═══════════════════════════════════════════════════════════════════════════
-- 4. GENESIS INVARIANT THEOREMS
-- ═══════════════════════════════════════════════════════════════════════════

theorem genesis_height_zero : genesis_header.height = 0 := rfl

theorem genesis_no_quarantine : genesis_header.quarantineFlag = false := rfl

theorem genesis_no_fork : genesis_header.forkDetector = none := rfl

theorem genesis_zero_sorries : genesis_lean_cert.sorriesCount = 0 := rfl

theorem genesis_domain_valid :
    domain_params.bifurcationThreshold = 49 ∧
    domain_params.mirrorDimension = 106 ∧
    domain_params.branchDimension = 53 ∧
    domain_params.q12Modulus = 12 := by
  constructor <;> rfl

end Genesis