  We establish the absolute continuity of the integrated density of states
(IDS) for quasi-periodic Schr\"odinger operators with a large trigonometric
potential and Diophantine frequency. This partially solves Eliasson's open
problem in 2002. Furthermore, this result can be extended to a class of
quasi-periodic long-range operators on $\ell^2(\Z^d)$. Our proof is based on
stratified quantitative almost reducibility results of dual cocycles.
Specifically, we prove that a generic analytic one-parameter family of
cocycles, sufficiently close to constant coefficients, is reducible except for
a zero Hausdorff dimension set of parameters. This result affirms Eliasson's
conjecture in 2017.
