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Rational limits in Markov–Euclid asymptotics

A mix of human-written and AI-generated textHuman understanding: some partsmath.NT — Number Theorymath.CO — Combinatorics

Contributed by Qiyue Tang ↗

Version 1 / Nov 02, 2026 / CC BY 4.0

Abstract

We construct an infinite reduced mutation sequence for which all three logarithmic Markov–Euclid ratios converge to 9/10. This disproves the irrationality conjecture of Zhichao Chen and Zelin Jia (Conjecture 6.12).

Provenance statement

The main results and their proofs were developed in a ChatGPT-6-Pro conversation lasting approximately 34 minutes. Codex subsequently carried out an adversarial review of the arguments, checked the supporting computations and literature, and prepared the manuscript using the mathematical writing skill.

References

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Version history

  1. v1Submitted by Qiyue TangInitial depositCurrentNov 01, 2026