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structure definition def or abbrev

CircuitLedgerCert

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formal statement (Lean)

 320structure CircuitLedgerCert where
 321  /-- A poly-size circuit has poly-bounded Z-capacity -/
 322  capacity_bound : ∀ n : ℕ, ∀ c : BooleanCircuit n,
 323    CircuitZCapacity c ≤ 2 * c.gate_count
 324  /-- UNSAT formulas have a defect moat of width ≥ 1 -/
 325  moat_width : ∀ n : ℕ, ∀ f : CNFFormula n, f.isUNSAT →
 326    ∀ a : Assignment n, satJCost f a ≥ 1
 327  /-- No fixed-view decoder over <n variables is universal -/
 328  blind_decoder : ∀ n : ℕ, ∀ M : Finset (Fin n), M.card < n →
 329    ∀ g : ({i // i ∈ M} → Bool) → Bool,
 330      ∃ (b : Bool) (R : Fin n → Bool),
 331        g (restrict (enc b R) M) ≠ b
 332  /-- The full separation structure holds -/
 333  separation : CircuitSeparation
 334  /-- The open gap is identified -/
 335  open_gap : SpectralTuringBridgeHypothesis
 336

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