The declared geometric and register interfaces

Let $C_{\mu }$ be a spinless spatial cone with a supplied deficit $\mu$, and use the regular-part ultrastatic metric

The cone and its metric are declared inputs.

A slicing family is a graph

on each regular branch. The incidence parameter $s$ is supplied by the controller, not solved from a scalar-field equation.

A finite implementation consists of a finite code set $\mathcal{J}$, an installed parameter table

and a declared update $U_{\mathcal{J}}:\mathcal{J}\to \mathcal{J}$. When a reversible realization is intended, the corresponding complete finite update is a permutation of its declared code space. These definitions do not acquire a matter expectation or define a Hamiltonian.

This separates the geometric parameter from its finite code, as required by the supplied VIII-A/B records CheungVIIIA,CheungVIIIB. The clock code is denoted by $j$; it is not the finite Hermitian source matrix also written $j[f]$ in that track.