Singularity of the spectrum of typical minimal smooth area-preserving flows in any genus

The uploaded paper proves Theorem 1 (typical locally Hamiltonian flows with only simple saddles have purely singular spectrum) by reducing to special flows over IETs with symmetric logarithmic roofs, verifying a rigidity-plus-exponential-tails criterion (Theorem 4), and then pulling back via the Katok measure class; see the statements of Theorem 1 and Proposition 2.1 and the reduction in §2.3, and the tails criterion in §4.1 together with §5.3–§8 where the tails are constructed from trimmed derivative bounds along rigidity towers . The candidate solution outlines the same route: reduction to IET special flows with symmetric logs, application of the CFKU singularity criterion (rigidity + exponential tails), and the pullback via the period/Katok measure class; this matches the paper’s strategy and ingredients. A minor imprecision is that the candidate states per-discontinuity symmetry C_i^+ = C_i^-; the paper’s symmetry class SymLog(T) requires only equality of total left and right coefficients (plus an AC part), which still yields the same spectral conclusion via cohomological adjustments . Overall, both are correct and essentially the same proof.