Coherent local reception remains a separate gate

The hypothesis is not supplied by the local sine-effect theorem. It must include the actual receiver's unselected modes, noise, initial preparations, and quantum outputs. In particular, a protocol that first converts all message-bearing field influence into classical records remains entanglement breaking.

No unrestricted bosonic diamond convergence follows merely from coefficient convergence. The channel stability established here is on the specified finite-dimensional source input and fixed background.