Terminal Symmetry as a Decision Resource: Statewise Refinement for Anytime Verified Construction
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.
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[Submitted on 11 Aug 2026]
Title:Terminal Symmetry as a Decision Resource: Statewise Refinement for Anytime Verified Construction
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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.
Subjects:
Machine Learning (cs.LG); Artificial Intelligence (cs.AI)
Cite as: arXiv:2608.11318 [cs.LG]
(or arXiv:2608.11318v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2608.11318
arXiv-issued DOI via DataCite (pending registration)
Submission history
From: Yi Liu [view email] [v1] Tue, 11 Aug 2026 18:08:01 UTC (400 KB)
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