PreprintCC BY 4.0arXiv
A Computational Verification of the Markov Uniqueness Conjecture for z≤ 10500000
Abstract
We describe a finite computational verification of Markov Uniqueness Conjecture for normalized positive integer solutions of x2+y2+z2=3xyz with z ≤ 10500000. 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 2128. 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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BibTeX
@misc{tan2026computational,
title = {{A Computational Verification of the Markov Uniqueness Conjecture for $z\leq 10^500000$}},
author = {Hu Tan and Ying Zhang},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.01007},
eprint = {2611.01007},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.01007},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Computational Verification of the Markov Uniqueness Conjecture for z≤ 10^500000
AU - Hu Tan
AU - Ying Zhang
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.01007
UR - https://arxiv.org/abs/2611.01007
AB - 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 ≤ 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.
ER -