On Kanai’s conjecture for frame flows over negatively curved manifolds

The paper proves Kanai’s conjecture (under strict 1/4-pinching and C^{1/√δ} regularity of the Kanai horizontal distribution) by constructing a flow-invariant conformal structure on Eu via the dynamical curvature F and holonomy groups, then invoking known rigidity to obtain real hyperbolicity, with an integrability alternative only in dimensions 4 and 8. The candidate solution sketches a different route through the unstable shape operator U^+, Schur’s lemma, and the Riccati equation; however, it makes a critical incorrect claim that 1/4-pinching implies uniform quasi-conformality on Eu and overstates ergodicity in odd dimensions (ignoring the known n = 7 caveat). It also misstates the representation-theoretic exceptions. These issues are substantive gaps, so the model’s proof is not correct as written, while the paper’s argument is coherent and matches its stated results.