We study exact recovery from deterministic partial views of a finite latent tuple. A family of admissible views induces a confusability graph on latent states, and this graph is the structural object governing zero-error recovery. In the exact coordinate-view model on the full labeled tuple space, we characterize the realizable confusability relations exactly: they are precisely those determined by upward-closed families of coordinate-agreement sets. We show that exact recovery with a $T$-ary auxiliary tag is equivalent to $T$-colorability of the induced graph, while exact recovery on a designated success set is equivalent to colorability of the corresponding induced subgraph. 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-$\vartheta$ upper theory. We also identify a structural equality route: when confusability is transitive, the induced graph collapses to a cluster graph, yielding capacity--$\vartheta$ equality, with meet-witnessing and fiber coherence as sufficient conditions. Finally, 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. A classification of representative channel families shows that the majority of widely deployed deterministic partial-view architectures operate above the zero-incoherence boundary, rendering the graph-capacity limits operationally unavoidable.

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