The exact degree-sampling identity

This identity transports a specified sampling law. It does not identify degree mass with quantum entropy. Different coding nodes can have the same map pole; a node-channel assignment does not descend to vertices unless its averaging or compatibility rule is supplied.

For the serial model of Section sec:serial, the right side of (eq:degreechannel) is itself depolarizing, with coefficient

Its half-diamond error converges to the random integral in (eq:serialintegral). This is an exact, declared finite degree-sampling operation, not an entropy–area prescription.