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Does every free group action that is orbit equivalent to a totally weakly mixing action also admit a totally weakly mixing representative within its orbit equivalence class?

Related: Gaboriau's theorem on L2 Betti numbers as orbit equivalence invariants, Ornstein-Weiss theorem on orbit equivalence for amenable groups, Popa's cocycle superrigidity theorem

Resolving this problem would clarify the map between spectral ergodic theory and the orbit equivalence classification program for free group actions, potentially revealing new invariants that are finer than orbit equivalence but coarser than isomorphism. A positive answer would mean total weak mixing is an orbit equivalence invariant, giving a new tool to distinguish orbit equivalence classes. A negative answer would produce exotic examples showing that free group actions can be orbit equivalent while having fundamentally different mixing structures, which would deepen understanding of how non-amenability allows more flexibility in the dynamics and would likely drive new constructions in geometric group theory and measured group theory.

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