Superstring theory proposes that our universe includes fundamental strings of energy that vibrate in possibly 10(?) dimensions. To describe how this occurs in our universe, string theorists (Strominger and Witten among other prominent theorists) propose that space is composed of a particular type of CYCalabi-Yau (CY) manifold. These manifolds can accommodate the vibrations of strings in the required ten dimensions.
The problem is that there are at least 10^500$10^{500}$ possible different CY manifolds and so far there is no theoretical way to determine (if superstring theory is true) which one of these 10^500$10^{500}$ (or more) CY manifolds is THEthe CY manifold for the space of our universe. My question is: Is there any way to mathematically completely rule out even one of the possible CY manifolds as the manifold that accommodates string vibrations in our universe?