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Quantum Laurent Positivity for Mutation-Acyclic Cluster Algebras

A mix of human-written and AI-generated textHuman understanding: some partsmath.QA — Quantum Algebramath.RA — Rings and Algebrasmath.RT — Representation Theory

Contributed by 琪越 唐

Version 3 / Sep 29, 2026 / CC BY 4.0

Abstract

We prove quantum Laurent positivity for mutation-acyclic skew-symmetrizable cluster algebras of arbitrary finite rank.

Provenance statement

It took about half a month to obtain the above paper. During this period, I alternated between conversing with GPT-6-Astra and using the Danus system to tackle difficult problems. I provided it with a large number of papers for reference, such as Schiffler's paper on Laurent positivity, Davison's paper on positivity in quantum cluster algebras, and so on. 2026.10.15：The manuscript has completed a full-paper review using Rethlas-OSV, together with a supplementary check of two cited dependencies. No confirmed mathematical errors were reported within the reviewed scope. Rethlas-OSV: https://github.com/OSVerify/Rethlas-OSV

References

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Version history

  1. v1Submitted by 琪越 唐Corrected before publicationSupersededSep 29, 2026
  2. v2Submitted by 琪越 唐Submitted as a new versionSupersededSep 29, 2026
  3. v3Submitted by 琪越 唐Submitted as a new versionCurrentOct 15, 2026