- Updated: August 19, 2026
- 2 min read
Terminal Symmetry as a Decision Resource: Statewise Refinement for Anytime Verified Construction
Terminal Symmetry as a Decision Resource
Many sequential construction tasks exhibit exact symmetry at completion while their execution remains directed and history‑dependent. In this article we present a decision‑resource view of terminal symmetry, where 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.
The proposed method, Transport‑Refine‑Certify, instantiates this principle with an episode‑fixed transported process structure, a 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.
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, the 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, making terminal symmetry a reusable decision resource for directed construction.
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Andrii Bidochko
CTO UBOS
Andrii Bidochko is an AI entrepreneur and researcher focused on AI agents, reinforcement learning, and autonomous systems. He writes about the technologies shaping the future of machine intelligence, from frontier models and agent architectures to real-world AI applications.