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, reducing exact recovery with a T-ary auxiliary tag to T-colorability. In the full coordinate-view model on the labeled tuple space, we characterize the realizable confusability relations exactly as those determined by upward-closed families of coordinate-agreement sets. Under repeated composition, the block confusability graph is the strong power of the one-shot graph, so the normalized zero-error rates converge to the Shannon capacity of the induced graph and inherit the standard Lovász-ϑ upper theory. Transitive confusability yields a cluster-graph equality route, 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 composes by direct sum under block composition. Applied to representative channel families, the realizability criterion classifies eleven deterministic partial-view architectures and finds nine operating outside the verifiable zero-error regime.