Entanglement Breaking of All-Partition Compositions of a PPT Edge-State Channel Family

We exhibit an all-dimensional family of entanglement-breaking compositions built from distinct non-entanglement-breaking PPT edge-state channels of Sacchi type. For arbitrary subsets defining the two partitions, arbitrary positive family parameters, and any positive diagonal intermediate filter, the resulting Choi operator admits an explicit separable decomposition. A complete-positive matrix factorization handles the doubled-coherence blocks, leading to a pairwise entanglement-breaking class of normalized CPTP PPT channels. This is a theorem about a specific family with a common distinguished basis index, not a proof of the unrestricted PPT-cubed conjecture or a classification of general PPT compositions. Exact-rational and independent channel-level checks are included. Historical priority and external peer review remain open.