Assess the student's ability to construct explicit infinite families of compact, smooth 4-manifolds exhibiting exotic (homeomorphic but nondiffeomorphic) smooth structures by performing cork twists; require clear handlebody/Kirby descriptions of each manifold, identification and embedding of suitable corks, rigorous proofs of nondiffeomorphism using Seiberg–Witten invariants, and explicit computation of those invariants (including chamber/wall-crossing considerations) to distinguish the smooth types. State assumptions and background theorems used.