Infinitely many indecomposable totally reflexive modules over non-Gorenstein local rings

Let $R$ be a non-Gorenstein local ring. A finitely generated $R$-module is totally reflexive if it has G-dimension zero. Infinitely many indecomposable totally reflexive modules conjecture. Suppose that there is a nonfree totally reflexive $R$-module. Then there are infinitely many isomorphism classes of indecomposable totally reflexive $R$-modules. This conjecture concerns the representation theory of non-Gorenstein local rings; the paper's abstract proves the assertion for commutative noetherian henselian non-Gorenstein local rings, while the statement above is presented without those additional hypotheses.