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arXiv · 2611.01007

A Computational Verification of the Markov Uniqueness Conjecture for $z\leq 10^{500000}$

Hu Tan·Ying Zhang
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Abstract

We describe a finite computational verification of Markov Uniqueness Conjecture for normalized positive integer solutions of $x^2+y^2+z^2=3xyz$ with $z \leq 10^{500000}$. The archived run reports $239\,536\,376\,556$ triples with distinct maximal coordinates.The method combines a disjoint tree decomposition, certified fixed-point range bounds, a deterministic 48-bit candidate screen,and replay modulo $2^{128}$. We give the mathematical justification and a reproducibility procedure covering package checks,retained-data auditing, and a full rerun. The conclusion depends on correct execution of the exhaustive screen and replay; the retained audit does not regenerate the deleted screening buckets.

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BibTeXRIS

Hu Tan, Ying Zhang. 2026-10-31. A Computational Verification of the Markov Uniqueness Conjecture for $z\leq 10^{500000}$. https://arxiv.org/abs/2611.01007

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