Finitely generated simple left orderable groups with vanishing second bounded cohomology

The uploaded paper proves Theorem 1.2: for every quasi-periodic labelling ρ, H^2_b(G_ρ; R)=0, via a concrete argument using homogeneous cocycles, central extensions, and carefully constructed 2-boundedly acyclic subgroups with global fixpoints, culminating in Proposition 5.1 and the proof of Theorem 1.2 . By contrast, the candidate solution relies on an unsubstantiated “commuting-conjugates” criterion and an overgeneral low-degree dictionary equating vanishing H^2_b with absence of homogeneous quasimorphisms; this conflates distinct phenomena (the paper itself notes that injectivity of H^2_b→H^2 from the absence of quasimorphisms does not force H^2_b=0) . The model also misattributes the main vanishing theorem to a different preprint. Hence: paper correct; model’s proof sketch is not reliable.