Diagonal supercompact Radin forcing
  Motivated by the goal of constructing a model in which there are no $\kappa$-Aronszajn trees for any regular $\kappa>\aleph_1$, we produce a model with many singular cardinals where both the singular cardinals hypothesis and weak square fail. 
Omer Ben-Neria, Chris Lambie-Hanson, and Spencer Unger
math.LO