Bhardwaj–Narayanan–Venkataraman conjecture on lonely times

Let $V$ be an $n$-set of positive integer speeds, let $v_n$ denote the largest speed, and let $\|x\|$ be the distance from $x$ to the nearest integer. Conjecture on lonely times. For every $n\in\mathbb{N}$ and every such $V$, there is a positive integer $M$ such that, if

$$t=\frac{M}{2^{\lceil\ln_2v_n+1\rceil}(n+1)v_n},$$

then

$$\min_{v\in V}\|tv\|\geq\frac{1}{n+1}.$$

The conjecture proposes a structured time at which the origin is lonely and is described in the source as supported by simulations. Its general status is open.