Definition: External geometric interface

An external geometric interface supplies:

1. a set $\mathcal{Q}$ of classical geometric and declared resource labels;

2. an admissible subset

   $${\mathcal{Q}}_{\mathrm{adm}}={\mathcal{Q}}_{\mathrm{reg}}\cup {\mathcal{Q}}_{\mathrm{tr}};$$

3. a finite cell-label set $\mathrm{Cell}(g)$ for each admissible $g$;

4. support, boundary, and resource certificates for permitted updates;

5. an explicitly supplied gauge equivalence, when one is used.

Regular configurations satisfy the model's nondegeneracy conditions. A transition configuration is admitted only with an event certificate specifying its realization and its permitted one-sided continuations.