LedgerComputation

formal source

  73
  74/-- Ledger-based computational model with explicit observation cost -/
  75
  76structure LedgerComputation where
  77  /-- State space (ledger configurations) -/
  78  states : Type
  79  /-- Evolution rule (double-entry updates) -/
  80  evolve : states → states
  81  /-- Input encoding into ledger -/
  82  encode : List Bool → states
  83  /-- Output protocol (measurement operations) -/
  84  measure : states → Finset (Fin n) → Bool
  85  /-- Evolution preserves closed-chain flux = 0 -/
  86  flux_conserved : ∀ s, evolve s = s  -- placeholder for actual conservation
  87  /-- Measurement requires Ω(n) queries for balanced-parity encoding -/
  88  measurement_bound : ∀ n M (hM : M.card < n),
  89    ¬(∀ b R, measure (encode (BalancedParityHidden.enc b R).toList) M = b)
  90
  91/-- SAT instance in ledger representation -/
  92structure SATLedger where
  93  /-- Number of variables -/
  94  n : ℕ
  95  /-- Number of clauses -/
  96  m : ℕ
  97  /-- Clause structure encoded in ledger -/
  98  clauses : List (List (Bool × ℕ))
  99  /-- Result encoded using balanced-parity across n cells -/
 100  result_encoding : Fin n → Bool
 101
 102/-- A recognition scenario packages the demonstration data for the separation story. -/
 103structure RecognitionScenario where
 104  rc : RecognitionComplete
 105  /-- Demonstration bound relating computation and recognition costs for each SAT instance. -/
 106  sat_bound : ∀ inst : SATLedger,