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

Let $R$ be a Gorenstein local ring. Countable $\operatorname{CM}$-representation type means that $R$ has only countably many isomorphism classes of indecomposable maximal Cohen–Macaulay modules.

Hypersurface conjecture. If $R$ has countable $\operatorname{CM}$-representation type, then $R$ is a hypersurface.

This is a folklore conjecture dating at least to the 1980s. It is known when $R$ has finite $\operatorname{CM}$-representation type and when $R$ is a complete intersection with algebraically closed uncountable residue field, but remains open in general.