The short-progression exclusion for the Loneliness Spectrum

Let $n\geq2$ and let $v_1,\ldots,v_n$ be positive integers, each at most $1.501n$. Define

$$\operatorname{ML}(v_1,\ldots,v_n)=\max_{t\in\mathbb{R}}\min_{1\leq i\leq n}\Vert tv_i\Vert.$$

Short-progression exclusion conjecture. One has

$$\operatorname{ML}(v_1,\ldots,v_n)\neq\frac{3}{3n+2}.$$

The claim is presented as a proposed first step toward extending the spectrum results to larger ranges of speeds. It is not established in the stated passage and remains open.