Geometric hypotheses

A scaling family consists of admissible substrates $({\Lambda }_{\epsilon },d_{\epsilon },r)$, site embeddings $z_{\epsilon }:{\Lambda }_{\epsilon }\to {\mathbb{R}}^D$, and physical tick durations $h_{\epsilon }\to 0$. Events embed as

Assume block footprints in physical spacetime have diameter tending to zero on bounded windows. This includes both input and output interfaces of each block firing.

For the cubic example,

Its metric envelope has physical slope $c$ in the ${\ell }^1$ norm.