  We investigate the existence of sufficient local conditions under which poset
representations decompose as direct sums of indecomposables from a given class.
In our work, the indexing poset is the product of two totally ordered sets,
corresponding to the setting of 2-parameter persistence in topological data
analysis. Our indecomposables of interest belong to the so-called interval
modules, which by definition are indicator representations of intervals in the
poset. While the whole class of interval modules does not admit such a local
characterization, we show that the subclass of rectangle modules does admit one
and that it is, in some precise sense, the largest subclass to do so.
