Finite groups with logarithmic Weisfeiler–Leman dimension

This preprint constructs finite groups of nilpotency class two and exponent three with centre equal to the derived subgroup of order 27, and proves logarithmic lower and upper bounds for their Weisfeiler–Leman dimension. The bounds cover both counting Versions I and II in dimensions at least two, both distinguishing pairs in the stated class and identifying a group in that class among all finite groups. The construction uses representations of the three-arrow Kronecker quiver, almost split sequences and a character-sum transfer to groups. The archive includes Lean sources for the main theorem and the four logarithmic endpoints, with dependency and scope records. Kernel checking is distinguished from a complete formalization of every intermediate argument in the prose. Research directed and curated by Matthew Liston. The mathematics, proofs, formalization and manuscript preparation substantially involve AI systems; paper-specific attribution and checking limits are disclosed in the paper and archive. No independent human proof verification, external endorsement or peer review is claimed. Licensing: original manuscript and documentation CC BY 4.0; original code MIT. The archive provides the exact file-level license mapping. Manuscript revision: 22 October 2026. Research director's note — Matthew Liston: This project is motivated by philosophical exploration and curiosity about AI-assisted research. My aim in sharing these results is to make them available for scrutiny, correction and further development, so that others can build on whatever proves useful to mathematics and science. Correspondence: atemporalwalk@gmail.com.