Contract G: finite completely positive hybrid evolution

Let $\mathsf{G}$ be a finite classical label set. Each label contains every variable used by the controller: geometric marking, permission, relevant records, and control memory. Matter occupies a fixed $d$-dimensional space $H$. Set

States have $X_g\ge 0$ and ${\sum }_g\mathrm{Tr}{X}_g=1$. The blocks are subnormalized; their normalization is not part of the unconditional evolution.

A certified edge $g\to h$ includes all changed classical data, exact guards, geometric matching, and location maps. No edge certificate is inferred from its probability alone.