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Equality of the Mirković–Vilonen and theta bases

A mix of human-written and AI-generated textHuman understanding: some partsmath.RT — Representation Theorymath.RA — Rings and Algebras

Contributed by Qiyue Tang ↗

Version 1 / Nov 02, 2026 / CC BY 4.0

Abstract

We prove Kamnitzer's ICM 2022 conjecture that the Mirković–Vilonen and theta bases coincide.

Provenance statement

The initial draft was developed through seven ChatGPT-6-Pro conversations totaling approximately 23 hours and 10 minutes, interspersed with four hours of research using Pharos. It was then reviewed and polished with Codex and its built-in mathematical paper-writing skill before being submitted to Rethlas-OSV for review. This was the first time Rethlas-OSV identified a nontrivial error in my work that invalidated the proof of the main theorem. Previously, manuscripts had either passed its review or yielded editorial errors, such as incorrect reference numbers or a missing plural ending, or readily repairable mathematical errors, such as an omitted hypothesis. I submitted the review report to ChatGPT-6-Pro and asked it to spend six hours repairing the proof. After it reported completing the repair, I used a separate ChatGPT conversation for approximately three rounds of review totaling about 88 minutes. These reviews found no further errors. Codex then reviewed and polished the manuscript, expanding it from 21 to 52 pages. The revised manuscript was then reviewed using Rethlas-OSV. The second Rethlas-OSV review identified further errors in the manuscript, including one that again blocked the proof as written. They were classified as minor because the report also supplied corrections. After these errors were corrected and the exposition was polished again, the manuscript passed Rethlas-OSV review.

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Version history

  1. v1Submitted by Qiyue TangInitial depositCurrentNov 01, 2026