Correctability is not omitted from complementary recovery

The logical-factor statement used here is the exact channel condition

equivalently

It is actually proved for the named patch regions, not inferred from closure of a compressed operator space.

Jones and Pollack identify a missing correctability assumption in an earlier complementary-recovery uniqueness claim JonesPollack. Their correction is external context, not a premise of any local theorem here. Any application of such a uniqueness theorem must include correctability for the stated erasure channel, for example the algebraic Knill–Laflamme commutator condition on its compressed error products. No uniqueness theorem for all patch algebras or all boundary regions is claimed in this paper.