Manuscript En01-A@1 · En01-A.tex · remark · 558b972b
Remark: Resolved and unresolved combinatorics
Operator-valued Möbius hierarchy and three orders › Arbitrary channels can realize arbitrary support families · lines 1901–1908
Down-closure for arbitrary channel support is false, not an open question. Unrestricted support-family realizability is settled by Theorem thm:anysupport. Realizability with a prescribed subsystem, branch support, locality restriction, or implementability class is a different problem and is not settled by that theorem.