Quadratic Strong-Operator Paving over Arbitrary Maximal Abelian Subalgebras

We prove the quadratic strong-operator paving conjecture of Popa and Vaes. For every $0<\epsilon <1$, every self-adjoint element of a von Neumann algebra admits strong-operator paving over each maximal abelian subalgebra with at most $5\times 10^8{\epsilon }^{-2}$ projections. The bound is uniform over representations and requires no separability or conditional-expectation assumption.