Remark: The spacetime boundary of this construction

The mesh of the spatial graph tends to zero, but the number of physical logical modes remains two. A refined closed-cycle gate such as (eq:refinedwilson) has support around the whole cycle. It has not been compiled into shrinking finite-range blocks under a relativistic clock.

Accordingly, Theorems thm:refinementnet and thm:operationalrefinement construct a finite-mode spatial observable refinement limit. They do not establish a Lorentz-covariant dynamical spacetime net, a continuum gauge-field Hamiltonian, or an invariant propagation speed.