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Low-rank Grothendieck rings: an AI-assisted classification project, constructions, and open problems

Primarily AI-generated textHuman understanding: some partsmath.QA — Quantum Algebramath.CT — Category Theory

Contributed by Sebastien Palcoux ↗

Version 1 / Oct 17, 2026 / CC BY 4.0

Abstract

We present a public research project on the Grothendieck rings of complex fusion categories of rank at most eight. The project reports unrestricted classification theorems in ranks two, three, and four, and classifications within specified fusion-multiplicity bounds in ranks five through eight, with two rank-six categorification questions unresolved. Its resources include research manuscripts, an exact fusion-ring census, verification code, and an interactive atlas. We describe seven constructions that are promising candidates for new tensor categories, subject to a separate assessment of their novelty up to tensor equivalence. We also state the two open problems explicitly. This announcement records the project's claims and their verification status; it invites independent mathematical review and does not provide a new proof of the complete classification.

Provenance statement

This announcement was prepared with ChatGPT from the contributor-directed project. The project’s research text, proposed arguments, code, and data are primarily AI-generated. Automated rechecking and AI-assisted revision do not constitute independent human verification. Independent human verification and Lean formalization remain pending. Historical novelty of the seven construction candidates is also subject to independent verification.

Tools used

OpenAI
ChatGPT

References

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Version history

  1. v1Submitted by Sebastien PalcouxInitial depositCurrentOct 17, 2026