Pizzato–Sano–Tasin Frobenius bound for regular pairs

Let $(d;a)$ be a regular pair, with $d=(d_1,\ldots,d_c)$ and $a=(a_0,\ldots,a_n)$, and define

$$\delta(d;a)=\sum_{i=1}^c d_i-\sum_{j=0}^n a_j.$$

Assume that $c\leq n$ and $a_i\neq 1$ for every $i$. Let $F(a_0,\ldots,a_n)$ denote the Frobenius number of the weights.

Pizzato–Sano–Tasin conjecture. Then

$$\delta(d;a)\geq F(a_0,\ldots,a_n).$$

This numerical conjecture translates effective non-vanishing for the relevant weighted complete intersections into a Frobenius-semigroup inequality. The paper proves the corresponding geometric result in codimension at most three; the conjecture is attributed to Tasin in the source.