Herzog–Srinivasan periodicity conjecture for monomial-curve Betti numbers

Let $K$ be a field, let ${\mathbf a}=(a_1<\cdots<a_n)$ be a sequence of positive integers, and let $I({\mathbf a}+j)$ be the defining ideal of the affine monomial curve parametrized by $t\mapsto(t^{a_1+j},\ldots,t^{a_n+j})$. For each finitely generated $K[x_1,\ldots,x_n]$-module $M$, write $\beta_i(M)=\dim_K\operatorname{Tor}_i^{K[x_1,\ldots,x_n]}(M,K)$ for its $i$-th total Betti number. Herzog–Srinivasan conjecture. The Betti numbers of $I({\mathbf a}+j)$ are eventually periodic in $j$ with period $a_n-a_1$. The paper's abstract states that this conjecture is proved, so the eventual periodicity claim is now a theorem rather than an open conjecture.