The knot-and-link generation conjecture for exotic smooth structures on $E(2)$

Let $M=E(2)$ be the compact 4-manifold, and consider its distinct exotic smoothness structures. Knots and links are used to generate smooth structures on $M$ via knot surgery.

Knot-and-link generation conjecture. All distinct exotic smoothness structures of the compact 4-manifold $M=E(2)$ can be generated by knots and links.

This conjecture concerns the contribution of different differential structures to the formal gravitational path integral. The source does not provide evidence resolving the conjecture, and its status is therefore open.