Rigidity of modules over one-dimensional complete intersection domains

Let $(R,\mathfrak{m})$ be a one-dimensional complete intersection domain. A finitely generated $R$-module is rigid if its higher Tor with every relevant partner vanishes as in the surrounding discussion. Rigidity conjecture. Then every finitely generated $R$-module is rigid. The source notes this is known for one-dimensional hypersurface domains, while the complete-intersection generalization remains open.