Algebraic form of the cyclotomic numerical semigroup conjecture

Let $\operatorname{\mathbb{k}}$ be an algebraically closed field, and let $R$ be a graded domain of Krull dimension one over $\operatorname{\mathbb{k}}$. Call $R$ cyclotomic when its Hilbert series is cyclotomic. Algebraic form of the cyclotomic numerical semigroup conjecture. Every cyclotomic graded domain of Krull dimension one over an algebraically closed field is a complete intersection. Graded one-dimensional domains over an algebraically closed field are semigroup algebras, and submonoids of $\mathbb{N}$ reduce to numerical semigroups after dividing by their gcd; thus this is an algebraic reformulation of the preceding conjecture and remains open.