Firehot
Member
Hi,
I've been working on a personal Rubik's Cube solver research project called WeaveCube.
The project explores a construction method I call the Lee Weave Method. The basic idea is to keep multiple candidate move words under a shared identity, progressively restrict those candidates using exact constraints, and delay committing to or materializing a complete candidate until the remaining set is small enough to construct a witness.
I want to be careful about what I'm claiming.
This is not a solver that is currently competitive with mature implementations such as Kociemba-family solvers or Nissy in speed or solution length. I have also not established reliable coverage over arbitrary cube states, consistent solution quality, or computational scalability.
At this stage I see the work primarily as a feasibility demonstration: the construction idea can actually be implemented, and in the tested settings it does construct complete cube solutions that pass exact replay verification.
A few results from the experiments:
WeaveCube is built in the lineage of established two-phase solvers. I am not claiming invention of two-phase solving, subgroup reduction, Phase 2, IDA*, pruning tables, pattern databases, generic set intersection, or related established techniques.
What interests me now is whether the shared-word construction idea has room to develop further.
Some obvious open questions are:
I do not know whether these limitations can be overcome. I'm releasing the work mainly because it seems a little unfortunate for the experiments and the idea to remain only on my computer. If someone finds the construction interesting, sees a flaw, knows of closely related prior work that I missed, or sees a much better way to develop it, I would genuinely be interested.
Paper / preprint:
https://doi.org/10.5281/zenodo.22846520
Source code:
https://github.com/SeanFirehot/WeaveCube-Public
Archived software release:
https://doi.org/10.5281/zenodo.22834879
The repository also includes an
Feedback, criticism, related references, and suggestions are all welcome.
I've been working on a personal Rubik's Cube solver research project called WeaveCube.
The project explores a construction method I call the Lee Weave Method. The basic idea is to keep multiple candidate move words under a shared identity, progressively restrict those candidates using exact constraints, and delay committing to or materializing a complete candidate until the remaining set is small enough to construct a witness.
I want to be careful about what I'm claiming.
This is not a solver that is currently competitive with mature implementations such as Kociemba-family solvers or Nissy in speed or solution length. I have also not established reliable coverage over arbitrary cube states, consistent solution quality, or computational scalability.
At this stage I see the work primarily as a feasibility demonstration: the construction idea can actually be implemented, and in the tested settings it does construct complete cube solutions that pass exact replay verification.
A few results from the experiments:
- A 5+5 exact-signature experiment represented a conceptual space of 333,353,807,424 word pairs without materializing the full Cartesian product at the beginning.
- A first-witness experiment showed that, in one local closure configuration, stopping after a verified witness could avoid substantial full-family construction work. This was a local result and did not translate into a demonstrated general end-to-end speed advantage.
- A sealed 24-case operational test returned solutions for all 24 deterministic 25-move scrambles.
- I later reran that test to recover the actual 24 solution sequences. All 24 passed a second native replay, and I also replayed them with a separate 54-sticker transition implementation that did not import WeaveCube; all 24 again reached the solved state.
- The project also contains a separate finite-state result concerning its ATO-zero terminal set.
WeaveCube is built in the lineage of established two-phase solvers. I am not claiming invention of two-phase solving, subgroup reduction, Phase 2, IDA*, pruning tables, pattern databases, generic set intersection, or related established techniques.
What interests me now is whether the shared-word construction idea has room to develop further.
Some obvious open questions are:
- Can coverage be made substantially broader and more reliable?
- How does the approach scale as candidate spaces and word lengths increase?
- Can constraint ordering and scheduling be improved?
- Can the candidate representation be made much more compact?
- Can solution length be improved without losing the construction structure?
- Is there useful parallel, SIMD, or GPU structure here?
- Can any part of this approach be combined productively with stronger existing cube-solving techniques?
I do not know whether these limitations can be overcome. I'm releasing the work mainly because it seems a little unfortunate for the experiments and the idea to remain only on my computer. If someone finds the construction interesting, sees a flaw, knows of closely related prior work that I missed, or sees a much better way to develop it, I would genuinely be interested.
Paper / preprint:
https://doi.org/10.5281/zenodo.22846520
Source code:
https://github.com/SeanFirehot/WeaveCube-Public
Archived software release:
https://doi.org/10.5281/zenodo.22834879
The repository also includes an
OPEN_PROBLEMS.md file describing the current limitations and possible research directions.Feedback, criticism, related references, and suggestions are all welcome.
