We formulate the quotient admission problem for finite graph-window rows. The input is a finite row set, an admissible evidence map, semantic labels, witness-support hypergraphs, and atom-level admissibility predicates. The output is a quotient decision on evidence atoms, with possible decisions certificate, residual, low-confidence, or blocked. The problem asks for the maximal guard-respecting atom-level decision map that uses no refinement beyond the admissible evidence partition. We prove an atom-union characterization of identifiable classes, give a witness-support hypergraph guard for certificate admission, characterize projected-label conflicts as blocked atoms, and present quotient admission algorithms with correctness, maximality, and complexity guarantees. With explicit evidence vectors and hyperedges, the algorithms run in expected O(B + I + n) time and space by hashing and deterministic O(B + I + n log n) time by sorting under a key-linear comparison model, where n is the number of rows, B is the total evidence encoding length, and I is the total hyperedge incidence size. We also prove a magnitude-only indistinguishability lower bound: any evaluator that observes only residual magnitudes fails on instances whose evidence atoms require different residual decisions after the magnitudes collapse them.

翻译：我们针对有限图窗口行集提出了商接纳问题。输入包括有限行集、可接纳证据映射、语义标签、论证支持超图以及原子级可接纳性谓词。输出是对证据原子的商决策，可能的决策包括证书、残余、低置信度或阻止。该问题要求寻找最大限度的守卫尊重原子级决策映射，该映射不采用超出可接纳证据划分的细化。我们证明了可识别类别的原子并集表征，给出了用于证书接纳的论证支持超图守卫，将投影标签冲突表征为被阻止原子，并提出了具有正确性、最大性和复杂度保证的商接纳算法。在显式证据向量和超边条件下，通过哈希算法，算法在O(B + I + n)的期望时间和空间内运行，在键线性比较模型下通过排序实现O(B + I + n log n)的确定性时间，其中n为行数，B为总证据编码长度，I为总超边关联大小。我们还证明了仅幅度不可区分性下界：任何仅观察残余幅度的评估器都会在那些证据原子因幅度坍缩而需要不同残余决策的实例上失效。