Corollary: Thermal replacement versus endpoint recovery budget

If, in addition to the endpoint package,

then

Thus a nearly featureless complete accessible channel and a small outgoing-recovery endpoint budget cannot be independently asserted in the same interface when these allowances violate (eq:endpoint-compatibility).

Proof. Proposition prop:featureless gives ${\epsilon }_{\mathrm{rec}}({\hat{\mathcal{N}}}_t)\ge q_d-{\eta }_t$. Theorem thm:endpoint gives the upper bound ${\nu }_t+\sqrt{2\zeta }$. Combine them.