Definition: Certified rules

A finite execution uses three kinds of certified rule.

1. A geometric rule, or $G$-rule, changes supported geometric labels as a specified function of geometric and declared resource labels. It does not inspect the matter density operator or matter-name cardinality. It returns a complete admissible configuration of geometric labels and a location transport map.

   A transition rule includes its common event realization and both one-sided continuations.

2. A matter rule applies a declared channel

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

   on a declared interface, extended by the identity on unacted-on names. It may depend on the current geometric labels but does not change them. Its output-name locations are declared.

3. A coupling rule declares an accessible unital algebra ${\mathcal{A}}_v$ and updates geometry by

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

   It leaves the matter density operator unchanged and supplies a complete admissibility certificate and location transport.