WeaveCube: A Feasibility Study of Exact Shared-Word Construction for Rubik's Cube Solving

We study the feasibility of exact shared-word construction in WeaveCube, a Rubik's Cube research system developed within the two-phase solver lineage. The project calls this organization the Lee Weave Method: conditions retain a common move-word identity, exact necessary restrictions reduce a candidate relation, and explicit combinations or complete witness families are formed only when needed. We formalize the scope required for sound restriction and distinguish verified witnesses from exhaustive negative results. In a planted-positive 5+5 mechanism experiment, two banks of 577,368 words define 333,353,807,424 conceptual index pairs; joint signatures restrict this relation before small candidate sets are materialized. Two ordering policies, evaluated in an adaptive-fixed-adaptive sequence on the same eight cases, each found replay-verified witnesses; median condition counts were 8, 10, and 8. A separate historical local-closure experiment reports 15.4988 s for a vectorized first-witness configuration versus 36.8624 s for the geometric mean of two full-closure controls, while a later total-economics experiment did not show a lower total wall after preparation overhead. Neither result establishes a general speedup. Separately, a frozen operational driver historically returned replay-checked solutions for 24 deterministic, hash-derived, 25-move scrambles. A new reproduction run using the same sealed corpus and frozen D6 asset serialized all 24 complete solution words and replayed each again natively; an independent fixed-frame 54-sticker implementation with no CubeLab/WeaveCube import also replayed all 24 scramble-solution pairs to the solved state. Historical timings remain attached only to the original run. These results should be read primarily as a feasibility demonstration: the proposed shared-word construction can be implemented and can produce valid solutions in the tested settings. They do not establish reliable coverage of arbitrary cube states, consistently short solutions, computational scalability, or competitive performance relative to mature solvers. The architecture nevertheless exposes concrete questions about coverage, scaling, construction policy, and solution quality for future study.