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

Abstract: 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 $\mathrm{III}$ 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.