Definition: External geometric interface

A geometric interface specifies:

1. a set $\mathcal{Q}$ of classical configurations;

2. an admissible subset

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

3. a finite label set $\mathrm{Cell}(q)$ for each configuration;

4. support, admissibility, and resource certificates for updates;

5. optionally, a supplied gauge equivalence ${\sim }_g$.

Regular configurations satisfy the model's stated nondegeneracy conditions. Transition configurations require a model-specific event certificate and may retain one-sided germ labels whose common geometric realization is degenerate.

Admissibility is semantic. A finite representation and a decision procedure are additional structures.