WAN-CHAN

WAN-CHAN is a program and research pipeline designed by TANUKI-CD to produce novel tensor rank results for various algebras over finite fields using agentic AI, Conflict-Driven Clause Learning (CDCL), and Lean-backed machine verification. The goal of the program is to settle tensor rank questions that have existed in the literature for a long time, the answers to which have only recently become accessible due to advancements in artificial intelligence and computer-assisted proof technology.

The main idea is simple: a team of 4 agents, each playing a different role in the proof process, use CDCL to prove that a decomposition of a certain rank is impossible, or to find such a decomposition. One agent owns the CaDiCaL process itself and adds constraints; one proves new constraints to use in CDCL; one formally verifies these results with Lean and explains why the formalization is semantically correct; finally, one last agent performs a literature review and identifies inputs that might be helpful towards the proof. A full outline of the process can be found in the PROCESS.md file.

WAN-CHAN is not an acronym--at least, I haven't thought of a backronym yet. The name is taken directly from the Japanese word わんちゃん, which is an affectionate term for a puppy. WAN-CHAN may be thought of as a puppy "fetching" the tensor rank of multiplication or another bilinear map in a given algebra. The idea for the program has come from multiple tensor rank results, including exact ranks and bound, which I have proved using rudimentary predecessors to this process. The setup was so successful that I decided to turn it into a larger quest, and thus WAN-CHAN was born. A list of the algebras for which it is planned to find the exact tensor rank of multiplication may be found in the ALGEBRAS.md.

This program is currently a work in progress. The process may be changed or fine-tuned to some extent, but I expect it to remain mostly the same. When half a dozen results or so are produced and fully certified, I will write a paper on the program and the tensor ranks it has produced and post it to arXiv as a formal introduction to the new research process and the new tensor rank results it will have produced. Until then, the results contained in this repository must be considered pre-release material and are not yet guaranteed to be correct, complete, or final.

Current progress

4 / 30 tensor ranks determined (13.3%)

████░░░░░░░░░░░░░░░░░░░░░░░░░░ 13.3%

Algebra	Previous range	Exact rank	Proof files	Date completed
C_6(2)	11-12	12	C_6_2	10/10/26
T_6(2)	13-14	14	T_6_2	10/10/26
P_6(3)	14-15	15	P_6_3	10/11/26
P_6(2)	16-17	17	P_6_2	10/12/26

License

The contents of this repository, excluding the references directory, are provided under the MIT License. References have their own licenses, which should be checked before use.