Terminal Symmetry as a Decision Resource: Statewise Refinement for Anytime Verified Construction

A recent paper on arXiv (2608.11318) presents a decision-resource perspective on terminal symmetry within sequential construction tasks. The authors introduce a principle known as transport-refine-certify: evidence from processes offers directionality, terminal correspondence conveys structure among equivalent outcomes, realized-state evidence enhances decision relevance post-transitions, and a fixed verifier ensures execution certification. This approach is exemplified through an episode-fixed transported process structure, state-restricted process rank, state-dependent residual rank, and an ordinal rank meet, where the top-k set is the combination of two proposal prefixes. The meet guarantees completion under prefix coverage and achieves a strict worst-case verifier-query limit. This paper is classified as a cross-type announcement and is accessible on arXiv.