A label-tagged finite interface

Fix a record $\mathcal{R}$ with $K=|\mathcal{L}|$. For each tested label $\lambda$, independently supply a complete finite channel

It may already include an encoding, noise process, and chosen deterministic decoder. Every failure branch is completed by a specified output.

A physical or mathematical net specialization requires further data. For example, suppose a named sector is represented on $H_{\lambda }$, with local range

Supply an isometry $J_{\lambda }:{\mathbb{C}}^2\to H_{\lambda }$ and a normal CPTP process and extraction

where $\mathcal{T}(H_{\lambda })$ is the trace-class space. Then

is a finite logical channel.

These maps are assumptions or independently constructed interfaces. Finite statistical dimension does not supply $J_{\lambda }$, ${\Theta }_{\lambda }$, a calibration, or an implementation.