Definition: Certified interface rules

A finite run uses:

1. A geometric rule, or $(G)$-rule, which replaces supported geometric labels by a specified function of those labels and declared resources. It does not inspect matter state or matter-name cardinality. Its complete output is admissible and includes location transport.

   A transition rule specifies incoming and outgoing germs, their common event realization, and both one-sided continuations.

2. A matter rule, which applies a declared channel

   $${\Psi }_q:L({\mathcal{H}}_{{\Gamma }_0})⟶L({\mathcal{H}}_{{{\Gamma }^{\prime }}_0})$$

   on a named local interface, tensored with the identity on the remaining names. It may depend on $q$, but does not change $q$. Allocation and output locations are part of its certificate.

3. A coupling rule, which declares a unital observable algebra ${\mathcal{A}}_v$ and updates geometry by

   $$q^{\prime }=F_v(q,{\omega }_{\rho }{|}_{{\mathcal{A}}_v}).$$

   It returns a complete admissible configuration and a location transport map. It leaves the matter density operator unchanged.