Solvable Initial Value Problems Ruled by Discontinuous Ordinary Differential Equations

The paper proves two key facts: (i) if f is solvable (Baire–1 and with closed discontinuity sets on all closed subdomains), then the f-removed sequence stabilizes at a countable stage (Theorem 9, via the Cantor–Baire stationary principle, Theorem 6), and (ii) the unique solution of the IVP can be obtained analytically by a concrete transfinite search-and-glue construction ((α)Monkeys approach) that converges to the solution (Theorem 10) . The candidate solution correctly rederives the countable termination of the removed-set process using standard Baire–1 facts and a rational-balls injection argument, which is compatible with the paper’s Theorem 9 and Lemma 2 (meagerness/Fσ of discontinuities) . However, its final “construction” of the solution is circular: it defines ranks using the unknown solution y and assumes uniqueness/continuity on layers to “glue” solution segments, instead of providing the analytic, non-circular transfinite procedure that the paper develops ((α)Monkeys). Thus, while the candidate’s termination argument is fine, it fails to supply the analytic transfinite construction required by Theorem 10. The paper’s argument is complete on both points; the model’s solution is incomplete/wrong on the constructive step.