An explicit increasing-stencil substrate

Fix a length ${\ell }_0>0$. At target scale $n\ge 1$, put

The sites are $h_n{\mathbb{Z}}^D$. The allowed generators are

A two-site block is legal whenever its displacement is $h_{n}s$ with $s\in S_n$. Singleton blocks are legal.

At each integer tick, the active pairs must be a matching. Every remaining used site is a singleton. The partition may depend on the deterministic experiment skeleton, but not on the payload values, input state, outcomes, or external reference.

The distinction between a skeleton-dependent schedule and a fixed autonomous periodic schedule is part of the model.