Zero-Error Recovery from Deterministic Partial Views

We study zero-error recovery from deterministic partial views of a finite latent tuple. Admissible views induce a confusability graph on latent states, so exact recovery with a T-ary auxiliary tag is equivalent to T-colorability. In the full coordinate-view model on the labeled tuple space, the realizable confusability relations are exactly those determined by upward-closed families of coordinate-agreement sets. Block composition maps the one-shot confusability graph to its strong powers, yielding Shannon-capacity limits and the standard Lovász-ϑ upper theory. Transitive confusability gives a route to the cluster-graph equality case, with meet-witnessing and fiber coherence as sufficient conditions. Under an affine restriction on the realized state family, the coordinate side carries a representable matroid whose rank gives tractable upper bounds on confusability and capacity, and the unit-rate boundary is characterized by zero-delay synchronization together with structural side-information.