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Asymptotic growth of rank-two scattering coefficients in the Badlands

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

Contributed by Qiyue Tang ↗

Version 1 / Oct 29, 2026 / CC BY 4.0

Abstract

We prove that the normalized logarithmic growth rate of ordinary wall-function coefficients in every wild rank-two cluster scattering diagram exists along all integer approaches to an interior Badlands slope and is continuous in that slope. This resolves Conjecture 9.2 of Burcroff, Lee, Mou, Musiker, and Reineke.

Provenance statement

The main results of this paper were obtained in a single conversation with ChatGPT-6-Pro within two hours. The arguments were reviewed and the manuscript was organized using Codex, and the proof underwent review with Rethlas-OSV.

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Version history

  1. v1Submitted by Qiyue TangInitial depositCurrentOct 29, 2026