General solidity phenomena and anticoarse spaces for type ${\mathrm{I}\mathrm{I}\mathrm{I}}_1$ factors

By developing a theory of anticoarse spaces in the purely infinite setting and using 1-bounded entropy techniques along with recent strong convergence results in random matrix theory, we show that free Araki–Woods factors offer the first examples of type $\mathrm{I}\mathrm{I}\mathrm{I}$ factors satisfying vastly general degrees of indecomposability phenomena. Notably this includes strong solidity with respect to any weakening of the normalizer currently in the literature and the Peterson–Thom property.