Effective non-vanishing conjecture for regular pairs

Let $(d;a)=(d_1,\ldots,d_c;a_0,\ldots,a_n) \in \mathbb N^c \times \mathbb N^{n+1}$ be a regular pair such that $a_i \ne 1$ and $d_j \ne a_i$ for any $i,j$. Assume $c \le n$ and $\operatorname{gcd}(a_0,\ldots,a_n)=1$. The quantity $\delta(d;a)$ is the arithmetic invariant associated with the regular pair, and $G(a_0,\ldots,a_n)$ is the Frobenius number, namely the largest integer not representable as a nonnegative integral combination of $a_0,\ldots,a_n$. Effective non-vanishing conjecture.

$$\delta(d;a) \ge G(a_0,\ldots,a_n).$$

This purely arithmetic statement would imply Ambro--Kawamata's conjecture for smooth weighted complete intersections and is presented as an independently interesting connection between regular pairs and the Frobenius coin problem. Its resolution status is not specified in the source.