Zero-error recovery under deterministic partial views is graph recovery for the induced confusability relation. A finite family of coordinate-subset observations determines a graph on latent states; $T$-ary exact recovery is graph $T$-colorability, block composition is strong powering, and asymptotic recoverability is Shannon capacity. Coordinate structure gives tractable certificates inside the graph semantics. For affine realized state families with explicit linear presentations, restricted coordinate ranks form a representable matroid certificate giving polynomial-time upper bounds on one-shot confusability and asymptotic capacity, with rank additivity matching direct-sum block composition. In the full tuple-space coordinate model, the realizable confusability relations are exactly the upward-closed coordinate-agreement families. Transitive confusability is equivalent to intersection closure of the generated agreement family, yielding a cluster graph whose capacity is determined by connected components. Host-level realizability fixes when the latent state family is canonical. Verifiable rate-$1$ realizability for structural facts holds if and only if the host provides zero-delay synchronization and structural side-information; eleven representative host architectures instantiate the criterion. The inter-fact and intra-fact layers share the same clique-size bit-budget bound. All cited results are mechanized in Lean 4 against a shared kernel.

翻译：确定性部分视图下的零错误恢复是针对诱导混淆关系的图恢复问题。坐标子集观测的有限族确定潜在状态上的图；$T$元精确恢复对应图$T$可着色性，块组合对应强幂运算，渐近恢复能力对应香农容量。坐标结构在图语义内提供了可处理的确认凭证。对于具有显式线性表示的仿射实现状态族，受限坐标秩构成可表示的拟阵凭证，从而给出单次混淆性和渐近容量的多项式时间上界，其秩可加性与直和块组合相匹配。在全元组空间坐标模型下，可实现混淆关系恰为向上封闭的坐标一致族。传递性混淆等价于生成一致族的交封闭性，由此得到聚类图，其容量由连通分量决定。宿主级可实现性在潜在状态族为规范形式时确定。结构事实的可验证速率$1$可实现性成立当且仅当宿主提供零延迟同步与结构边信息；十一种代表性宿主体系结构实例化该准则。事实间层与事实内层共享相同的团规模比特预算界。所有引用结果均在Lean 4中基于共享内核机械化验证。