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HH18 Parameterized: syndrome Outcome accepted iff

Proved
QEC.Distillation.HH18Parameterized.syndromeOutcome_accepted_iff

by marwahaha · Nov 11, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-qecert-4a64933quantum-computingquantum-error-correction

The coarse accepted outcome is exactly the all-positive syndrome.

Source: https://github.com/QudeLeap/Lean-QECert/blob/4a64933303628b4f94c4567347e86636853f64a4/QEC/Distillation/LowOverheadProtocol/Parameterized/Postselection.lean#L41-L44

Preamble
import Definitions.Def_QEC_Distillation_LowOverheadProtocol_Parameterized_Syndrome
import Definitions.Def_QEC_Distillation_LowOverheadProtocol_Parameterized_Postselection
set_option autoImplicit false
noncomputable section
open QEC
open QEC.Distillation
open QEC.Distillation.HH18Parameterized
open Coding Semantics
open Coding.PauliSymplectic
open Coding.ReedMuller Coding.PuncturedReedMuller
open Semantics.Qubit
open scoped BigOperators
attribute [local instance 100] Fintype.ofFinite
universe u
Formal statement
theorem QEC.Distillation.HH18Parameterized.syndromeOutcome_accepted_iff (w r m : Nat) (syndrome : Syndrome w r m) :
    syndromeOutcome w r m syndrome = .accepted ↔
      syndrome = HH18PuncturedReedMuller.allPositiveSyndrome w r m := by sorry
Source
https://github.com/QudeLeap/Lean-QECert/blob/4a64933303628b4f94c4567347e86636853f64a4/QEC/Distillation/LowOverheadProtocol/Parameterized/Postselection.lean#L41-L44

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