Hard gaps in maximum constraint satisfaction problems?
Prasad Raghavendra in the STOC'08 best paper proved a dichotomy conjecture for approximating Max-CSP assuming the Unique Games Conjecture. This is not how he presented it originally, but he did give talks presenting things this way a couple of years later, e.g., at the IAS, where it was videotaped:
http://www.math.ias.edu/seminars/abstract?event=36669

The difference from showing SNP-hardness is that here we talk about quantitatively optimal results.