Exact relevance certification asks which coordinates are necessary to determine the optimal action in a coordinate-structured decision problem. The tractable families treated here admit a finite primitive basis, but optimizer-quotient realizability is maximal, so quotient shape alone cannot characterize the frontier. We prove a meta-impossibility theorem for efficiently checkable structural predicates invariant under the theorem-forced closure laws of exact certification. Structural convergence with zero-distortion summaries, quotient entropy bounds, and support-counting arguments explains why those closure laws are canonical. We establish the theorem by constructing same-orbit disagreements for four obstruction families, namely dominant-pair concentration, margin masking, ghost-action concentration, and additive/statewise offset concentration, using action-independent, pair-targeted affine witnesses. Consequently no correct tractability classifier on a closure-closed domain yields an exact characterization over these families. Here closure-orbit agreement is forced by correctness rather than assumed as an invariance axiom. The result therefore applies to correct classifiers on closure-closed domains, not only to classifiers presented through a designated admissibility package.

翻译：精确相关性验证旨在确定坐标结构决策问题中哪些坐标对最优行动是必要的。本文所处理的可处理族具有有限原始基，但优化子-商可实现性已达到最大，因此仅凭商形状无法刻画上述前沿。针对精确验证的定理强制闭包律所不变的有效可检查结构谓词，我们证明了元不可能性定理。基于零失真摘要的结构收敛性、商熵界限以及支持计数论证，解释了这些闭包律为何是典范的。我们通过构造四种障碍族（即主导对集中性、边界掩蔽、幽灵行动集中性以及加性/状态偏移集中性）的相同轨道分歧来建立该定理，其中使用了行动无关的对靶仿射见证。因此，在闭包封闭域上，任何正确的可处理性分类器都无法在这些族上给出精确刻画。此处闭包轨道一致性是由正确性强制而非当作不变性公理假设的。因此该结果适用于闭包封闭域上的正确分类器，而不仅限于通过指定可容许性包呈现的分类器。