5 problems

For every admissible lattice point $(\chi,c)$, does there exist a closed, simply connected, spin symplectic $4$-manifold $X$ such that $(\chi_h(X),c_1^2(X))=(\chi,c)$?

Matsumoto's $11/8$-conjecture. The inequality

Universal cork conjecture. There is no universal cork, i.e. no cork $(U,f_U)$ relating every exotic pair of simply-connected, closed $4$-manifolds.

Disc embedding conjecture. The circles $f_i(S^1)$ bound disjointly embedded discs in $M$ with transverse spheres, inducing the same framing on $f_i(S^1)$ as the $f_i$.

$s$-cobordism conjecture. There is a homeomorphism