研究有前提约束的序列干预，建立精确的顺序敏感性理论。
Order-Sensitive Sequential Interventions on Ideal Lattices
- 用理想格中的路径表示合法干预序列，基于钻石交换构造路径等价类。
- 路径独立性等价于钻石曲率为零，可导出具有莫比乌斯参数化的终点势能。
- 揭示局部钻石场与边基路径模型的对应关系，适合因果推断与规划研究者。
我们研究在前提约束下的序列干预问题。合法干预序列是有限前提偏序集的理想格中的路径，而非无约束的动作串。本文建立了该状态空间上的精确局部-全局顺序敏感性理论：首先证明任意两条同端点的合法路径可通过有限次基本钻石交换相互转化；其次，对于边加性路径赋值，路径独立性等价于钻石曲率为零，从而在理想格上导出具有标准莫比乌斯参数化的终点势能；第三，证明一个局部钻石场由边基路径模型诱导当且仅当满足立方一致性，且在固定参考树规范后具有唯一性。在简化状态纵向假设下，支持的参考路径可确定参考路径得分；而局部顺序效应需每个钻石两侧均有双向支持。这些结果带来精确的规划推论，包括顺序不敏感性界和截断理想格上的动态规划。
原文摘要 · Abstract (English)
We study sequential interventions under prerequisite constraints. In this setting, admissible intervention sequences are paths in the ideal lattice of a finite prerequisite poset rather than unconstrained action strings. We give an exact local-to-global theory of order sensitivity on this state space. First, we prove that any two admissible paths with the same endpoints differ by a finite sequence of elementary diamond swaps. Second, for edge-additive path valuations, we show that path-independence is equivalent to vanishing diamond curvature, yielding an endpoint potential with a canonical Möbius parameterization on the ideal lattice. Third, we prove that a local diamond field is induced by an edge-based path model if and only if it satisfies cube consistency, with uniqueness after fixing a reference-tree gauge. Under reduced-state longitudinal assumptions, supported reference paths identify reference-path scores, whereas local order effects require two-sided support of both orders on each diamond. These results yield exact planning consequences, including an order-insensitivity bound and dynamic programming on the truncated ideal lattice.
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