# A counterexample to the Bernhard-Jablan unknotting conjecture

## TL;DR

This paper presents a specific knot that disproves the Bernhard-Jablan unknotting conjecture by demonstrating that crossing changes do not reduce the unknotting number as previously conjectured.

## Contribution

The authors provide the first known counterexample to the Bernhard-Jablan unknotting conjecture, challenging assumptions about crossing changes and unknotting numbers.

## Key findings

- Counterexample knot with property that crossing changes do not lower unknotting number
- Disproof of the Bernhard-Jablan unknotting conjecture
- Implications for knot theory and unknotting processes

## Abstract

We show that there is a knot satisfying the property that for each minimal crossing number diagram of the knot and each single crossing of the diagram, changing the crossing results in a diagram for a knot whose unknotting number is at least that of the original knot, thus giving a counterexample to the Bernhard-Jablan Conjecture.