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：我们研究了有限潜在元组在确定性局部视图下的零错误恢复问题。可容许视图诱导了潜在状态间的混淆图，因此使用 $T$ 元辅助标签进行精确恢复等价于 $T$-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向上封闭族所确定。块组合将单次混淆图映射至其强幂，由此导出香农容量极限及标准Lovász-$\vartheta$上界理论。传递性混淆提供了簇图相等情形的路径，其中交见证与纤维协调性是充分条件。在可实现状态族的仿射限制下，坐标侧承载了一个可表示的拟阵，其秩为混淆度与容量提供了可处理的上界，而单位速率边界则通过零延迟同步与结构边信息共同刻画。