Verification Of The Jones Unknot Conjecture Up To 23 Crossings

TL;DR

This paper verifies the Jones unknot conjecture for all knots with up to 23 crossings, confirming that the Jones polynomial distinguishes the unknot from other knots within this range.

Contribution

The authors computationally prove the Jones unknot conjecture for knots up to 23 crossings, extending previous verifications to a larger class of knots.

Findings

Jones polynomial distinguishes the unknot from nontrivial knots up to 23 crossings

The conjecture holds for all knots with up to 23 crossings

Provides computational evidence supporting the conjecture's validity

Abstract

The Jones unknot conjecture states that the Jones polynomial distinguishes the unknot from nontrivial knots. We prove it for knots up to 23 crossings.