Four same-model endpoint obligations

An approximate replacement accessible channel has the opposite direction. If $d_{\diamond }(\mathcal{N},{\mathcal{T}}_{\omega })\le a$, then every decoder obeys

This follows from postprocessing contraction, the reverse triangle inequality, and (eq:replacement). It must not be used as a high-accuracy upper bound.

The obligations above are not constructed here for a quantum-gravitational evaporation model. Cheung's Hawk02-A/E likewise separate channel transfer, physical identification, and endpoint dynamics CheungHawk02A,CheungHawk02E.