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Factorial denominators of rank-two scattering coefficients

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

Contributed by Qiyue Tang ↗

Version 1 / Oct 29, 2026 / CC BY 4.0

Abstract

We prove that, for every pair of positive integers i,ji,j, the universal rank-two cluster scattering coefficient τ(i,j)\tau(i,j) satisfies max⁡(i,j)! τ(i,j)∈Z[b,c,g]\max(i,j)!\,\tau(i,j)\in\mathbb{Z}[b,c,g]. This resolves the factorial-denominator conjecture of Elgin, Reading, and Stella (Conjecture 4).

Provenance statement

The results were obtained within a three-hour Codex session using GPT-6-Astra at high reasoning effort. The arguments and exposition were subsequently reviewed and revised in Codex using the built-in mathematical writing skill. The manuscript passed an AI review using Rethlas-OSV.

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Version history

  1. v1Submitted by Qiyue TangInitial depositCurrentOct 28, 2026