Gimenez–Sengupta–Srinivasan conjecture on Betti numbers of arithmetic monomial curves

Let $({\bf m})=m_0,\ldots,m_n$ be an arithmetic sequence of positive integers, and let $C({\bf m})\subset\mathbb A_k^{n+1}$ be the associated affine monomial curve, with homogeneous coordinate ring $k[\Gamma]$. Betti-number conjecture. All the Betti numbers of $k[\Gamma]$ are determined by $n$ and the value of $m_0$ modulo $n$. The claim proposes that these homological invariants depend only on the length of the arithmetic sequence and the residue class of its first term, despite the defining ideal also involving the common difference and the actual sequence.