The BoxContZonotope NP-hardness conjecture

Let $a_1,\ldots,a_m\in\mathbb{Q}^n$ and let $\nu\in[0,\infty)\cap\mathbb{Q}$. BoxContZonotope conjecture. Deciding whether there exists a rectangular box $B$ such that

$$\sum_{j=1}^m[-a_j,a_j]\subset B,\qquad \operatorname{vol}_n(B)\leq\nu$$

is $\mathbb{NP}$-hard. The problem is introduced as a further source of computational intractability in determining $\Lambda(P)$, beyond volume computation alone; no proof or resolution is supplied.