Definition: Full-tail limit objects and modifications

A limit object is $\xi =(K,R,\mu )$, where $K$ is compact, $R$ is a finite tuple of labelled acquisition events in $K$, and $\mu$ is a law on fixed finite alphabets.

It belongs to $\mathcal{X}$ if experiments exist at every sufficiently large scale with

Two objects differ by a modification in compact $K^{\prime }$ when matched full-tail families have the same skeletons and report designations, and payloads differ only on block footprints in $(K^{\prime }{)}_{{\rho }_n}$, with ${\rho }_n\to 0$. The initial default state is common.

The theory $\mathcal{T}$ consists of these objects, this witnessed modification relation, admitted disjoint composites, and conditioning of laws at positive-probability events.