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-$\vartheta$ 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.

翻译：我们研究有限潜在元组在确定性部分视图下的零错误恢复问题。可允许视图在潜在状态上诱导出混淆图，因此借助 $T$ 元辅助标签实现精确恢复等价于 $T$ 可着色性。在标记元组空间的全坐标视图模型中，可实现的混淆关系恰好由坐标一致集的上闭族决定。块组合将单次混淆图映射为其强幂，从而导出香农容量极限与标准 Lovász-$\vartheta$ 上界理论。传递性混淆提供了达到簇图等式情形的途径，其中交验证与纤维一致性是充分条件。在现实状态族满足仿射限制时，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，而单位速率边界由零延迟同步与结构化边信息共同刻画。