Definition: Certified transition graph

A certified finite interface consists of:

1. the finite labels $\mathsf{G}$, each with a declared admissible geometric realization and controller interpretation;

2. a directed edge relation $\mathcal{E}\subseteq \mathsf{G}\times \mathsf{G}$;

3. a fixed certificate for each edge $(g,h)\in \mathcal{E}$, specifying all affected output data, matching requirements, controller updates, and any location transport;

4. a declared reserve for implementation history and spectators, not inspected by geometric control.

The certificates are classical data. The definition does not prove a gravitational constraint equation.