The diffeomorphism conjecture for the 16- and 17-vertex triangulations of the K3 surface

Let $(K3)_{16}$ and $(K3)_{17}$ denote the 16-vertex and 17-vertex triangulations, respectively, of the K3 surface. K3 triangulation diffeomorphism conjecture.

$$(K3)_{16}\text{ and }(K3)_{17}\text{ are diffeomorphic}.$$

The smooth type of $(K3)_{17}$ is canonical, whereas the smooth type of $(K3)_{16}$ was unknown in the source context. Since piecewise-linear and smooth manifolds correspond in dimension four, resolving this conjecture would determine whether these two triangulations represent the same smooth 4-manifold.