Terminal Symmetry as a Carrier of Asymmetric Process Knowledge: Statewise Refinement for Anytime Verified Construction — Paper

Abstract

Many sequential construction tasks have exact terminal symmetries even though execution is directed and depends on history. Process evidence supplies order; terminal correspondence transports it between equivalent outcomes; the realized state updates relevance. These roles define a carrier framework: transport what the outcome preserves; refine what history changes. SymBuild combines transported process and state residual ranks by ordinal rank meet; its top-$k$ prefix exactly equals their top-$k$ union, yielding a tight worst-case verifier query bound under prefix information. We evaluate SymBuild in three construction domains: computer-aided design (CAD) assembly, Mini-Programs, and exact-fill packing, and test additional framework instantiations in all four domains. SymBuild improves the area under the anytime verified success curve by up to 6.77, 21.75, and 8.68 points over Static in the three construction domains. Refresh gains recur beyond SymBuild under alternative aggregation, planning, and learned scoring methods; on Geometric Reasoning Network (GRN) target removal, direct Combined refresh has the lowest mean verifier query score at all three scales and reduces learned state evaluations by factors of 6.48-12.20 relative to refreshed population-based search. Together, these results support the carrier framework and demonstrate that SymBuild is an effective, analyzable method for anytime verified construction.

Authors 1

Yi Liu

Specification

Official page: arxiv.org/abs/2608.11318
Source:arXiv (Atom API + RSS)T1observed 6 h agohigh
Arxiv announce type: replace
Source:arXiv (Atom API + RSS)T1observed 6 h agohigh
arXiv id: 2608.11318
Source:arXiv (Atom API + RSS)T1observed 6 h agohigh
Categories: cs.LG, cs.AI
Source:arXiv (Atom API + RSS)T1observed 6 h agohigh
PDF: arxiv.org/pdf/2608.11318
Source:arXiv (Atom API + RSS)T1observed 6 h agohigh
Primary category: cs.LG
Source:arXiv (Atom API + RSS)T1observed 6 h agohigh
Published: 11 Sept 2026
Source:arXiv (Atom API + RSS)T1observed 6 h agohigh

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9

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T19

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6 h ago

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Authors: Yi Liu

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Value	Valid from → to	Status	Source	Confidence	Extractor
https://arxiv.org/abs/2608.11318	11 Sept 2026 21:02 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic

Claims are temporal and append-only: a new observation closes the previous claim (valid_to) instead of overwriting it. Conflicting claims from different sources are kept side by side and flagged — never averaged. Methodology →

11 Sept 2026
New paperPaperTerminal Symmetry as a Carrier of Asymmetric Process Knowledge: Statewise Refinement for Anytime Verified Construction
New paper: Terminal Symmetry as a Carrier of Asymmetric Process Knowledge: Statewise Refinement for Anytime Verified Construction
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arXiv (Atom API + RSS)	rss.arxiv.org/rss/cs.LG	feed	T1· Official	4 h ago	1

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