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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 AI-generated research project on fusion rings and their categorifications over C\mathbb C, with data extending through rank twelve. The project reports unrestricted Grothendieck-ring classifications in ranks two, three, and four, a complete multiplicity-free classification through rank twelve, and classifications or partial classifications at higher multiplicities. The released census contains 1,434,0421{,}434{,}042 rings in ranks three through twelve; ten categorification questions remain open within its stated bounds. The resources include research manuscripts, categorical models, exclusion arguments, verification code, and an interactive atlas. One categorical model per ring suffices for our classification problem; classifying all realizing categories up to equivalence is a further task. We summarize the current scope, compare it with AnyonWiki, and link to the online constructions catalogue and unresolved cases. The project's original research content was generated by AI under human direction; independent human verification remains pending.

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 depositSupersededOct 17, 2026
  2. v2Submitted by Sebastien PalcouxSubmitted as a new versionCurrentOct 26, 2026