Contraction algebra conjecture for analytic types of threefold flops

Suppose that $Y\to Y_{\mathrm{con}}$ and $Z\to Z_{\mathrm{con}}$ are flopping contractions of a single curve in smooth projective $3$-folds, to points $p$ and $q$ respectively. Associate to these contractions the contraction algebras $\mathrm{A}_{\mathrm{con}}$ and $\mathrm{B}_{\mathrm{con}}$. Contraction algebra conjecture. The completions of the stalks at $p$ and $q$ are isomorphic if and only if

$$\mathrm{A}_{\mathrm{con}}\cong\mathrm{B}_{\mathrm{con}}.$$

This conjecture asserts that the contraction algebra distinguishes the analytic type of a flop. Its status is not established by the supplied text.