The hypersurface conjecture for Gorenstein rings of countable Cohen–Macaulay type

Let $R$ be a standard graded Gorenstein ring of countable Cohen–Macaulay type, meaning that it has only countably many indecomposable graded Cohen–Macaulay modules up to shifts. Hypersurface conjecture. The ring $R$ is a hypersurface. The finite-type analogue is known: standard graded Gorenstein rings of graded finite Cohen–Macaulay type are hypersurfaces. Using the concept of super-stretched, this conjecture is known for standard graded rings of dimension at most one, but remains open in higher dimensions.