Theorem: Response and admission release

For the source and completion specified in this manuscript, $u_{\mathrm{D}}$ and its completed root exist, ${\mathcal{C}}_{3,\mathrm{D}}(f,g)\in {\mathcal{F}}_{\mathrm{mc},\mathrm{pol}}$, and $Q_H{\mathcal{C}}_{3,\mathrm{D}}(f,g)\in {\mathcal{E}}_H$. The enlarged named sector is stable under admissible ordering transport. Its classical finite plateau variation is (eq:plateau-identity), with the additional cancellation hypotheses stated in Proposition prop:causal-plateau.

Proof. The response is Theorem thm:response, the compact root is Theorem thm:root, and the cone verdict is Theorem thm:admission. Section sec:descent applies the inherited carrier and ordering maps. The finite variation is Theorem thm:response-law and Corollary cor:plateau.