Uniqueness of tangent spaces for Calabi–Yau conifolds

Let $X\in\widetilde{\mathscr{KS}}(n,\kappa)$ be a Calabi–Yau conifold and let $x_0\in X$. The tangent space at $x_0$ is the limiting tangent object associated with the conifold structure. Uniqueness conjecture. At every point $x_0$ of a Calabi–Yau conifold $X\in\widetilde{\mathscr{KS}}(n,\kappa)$, the tangent space is unique. This proposed regularity improvement concerns the local geometry of spaces in $\widetilde{\mathscr{KS}}(n,\kappa)$; the supplied text presents it as something the authors believe to be true, without giving evidence that it has been proved or disproved.