Katznelson's negative answer conjecture for Bohr and topological recurrence

A set $S\subset\mathbb{N}$ is a set of Bohr recurrence if it meets every Bohr set, and a set of topological recurrence if it is a set of topological recurrence in the dynamical sense.

Katznelson's conjecture. There is a set $S\subset\mathbb{N}$ which is a set of Bohr recurrence but not a set of topological recurrence.

This is the negative answer to Katznelson's question. The paper presents it as an open question following its disproof of the higher-order analogue.