{"ok":true,"article":{"slug":"terminal-symmetry-as-a-decision-resource-statewise-refinement-for-anytime-verifi-c7a72d6c","title":"Terminal Symmetry as a Decision Resource: Statewise Refinement for Anytime Verified Construction","url":"https://arxiv.org/abs/2608.11318","canonical":"https://www.aimode.news/article/terminal-symmetry-as-a-decision-resource-statewise-refinement-for-anytime-verifi-c7a72d6c","sourceName":"arXiv cs.LG","summary":"arXiv:2608.11318v1 Announce Type: new Abstract: Many sequential construction tasks exhibit exact symmetry at completion while their execution remains directed and history-dependent. We develop a decision-resource view of terminal symmetry: process evidence supplies directionality, terminal correspondence transports that structure across equivalent outcomes, realized-state evidence refines its current decision relevance after transitions, and a fixed verifier certifies execution. This decomposition yields transport--refine--certify. \\method{} instantiates the principle with an episode-fixed transported process structure, its state-restricted process rank, a state-dependent residual rank refreshed after accepted transitions, and an ordinal rank meet whose top-$k$ set is exactly the union of the two proposal prefixes. The meet provides a completion guarantee under prefix coverage and attains the tight worst-case verifier-query bound under the corresponding prefix information model; a two-state construction predicts a strict post-transition dynamic--static separation. Across CAD assembly, Mini-Programs, and exact-fill packing, statewise refresh improves anytime AUC by up to $6.77$, $21.75$, and $8.68$ points, respectively. On 1,135 target-removal episodes from the official GRN OOD scenes, \\method{} attains the lowest mean capped verifier cost at all three scales among the compared GRN and CDGS-style planners. The statewise signal also transfers across aggregation and scheduler organizations. Terminal symmetry thereby becomes a reusable decision resource for directed construction.","category":"AI","image":null,"lang":"en","publishedAt":"2026-08-13T04:00:00+00:00","createdAt":"2026-08-13T04:30:12.663308+00:00"}}