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.

翻译：我们研究有限隐元组在确定性部分视角下的精确恢复问题。一族可容许视角在潜在状态上诱导一个混淆图，该图是支配零误恢复的结构对象。在完整标号元组空间的精确坐标视角模型中，我们精确刻画了可实现混淆关系：它们恰是由坐标一致集的上闭族决定的。研究表明，使用$T$元辅助标签的精确恢复等价于诱导图的$T$-可着色性，而指定成功集上的精确恢复则等价于对应诱导子图的可着色性。在重复组合下，分块混淆图是单次图的强幂，因此归一化零误率收敛至诱导图的香农容量，并继承标准Lovász-$\vartheta$上界理论。我们还发现一条结构性等式路径：当混淆性具有传递性时，诱导图退化为团图，产生容量-$\vartheta$等式，其中相遇见证性与纤维相干性构成充分条件。最后，在可实现状态族的仿射限制下，坐标侧承载一个可表示拟阵，其秩给出混淆性与容量的可处理上界。对代表性信道族的分类表明，广泛部署的确定性部分视角架构大多运行在零不连贯边界之上，这使得图容量极限在操作层面不可避免。