Thermodynamic consistency and closure limits of radiatively cooled X-point collapse

Your manuscript is accepted. This revision makes every Section 6 numerical control reproducible from the text and explicitly marks the archive-dependent counts as supplementary. It also separates the evolutionary-accessibility and thermal-stability arguments of Uzdensky and McKinney in Section 5. The analytic core is unchanged and stands on displayed derivations: the Section 2 Bernoulli counterexample, the Section 3 positivity restriction, the Section 4 cumulative-integral and inverse-square coefficient findings, and the domain-limited steady branch in Section 5. Please consider the editorial notes below when preparing the final version.

Verdict: accept. All three concerns from the round-2 minor revision are addressed in the revised manuscript, and the revision introduces no new correctness, validity, novelty or reproducibility problem. Concern 1 (Ref. [5] archive): resolved. Section 6, second paragraph, now states that the 4,096-state, 150-digit and steady-branch counts are supplementary and not load-bearing for any conclusion. Ref. [5] adds six commit-pinned program and JSON mirrors. Whether DOI 10.5281/zenodo.23780790 resolves remains not_enough_evidence, but no conclusion now depends on it. Concern 2 (control specifications): resolved. Section 6 now states the PCG64 seed 250813081, the four uniform draws and their transformations, the θ₀=0 overwrite and the strict-sign criterion for Eq. (7). It also gives the two negative-pressure controls, the 150-digit Gauss-Legendre orders and τ=2⁻ⁿ grid, the frozen (H, ℰ) cases with their ξ values and z⁶ substitution, the 24-case steady grid, the nine clock cases, the six sign cases and the four domain tuples. Concern 3 (Uzdensky and McKinney): resolved. The final paragraph of Section 5 now presents α<1+β_T in their Eq. (57) as an evolutionary-accessibility condition. It attributes the instability verdict to their separate d(Q_rad/Q_ohm)/dA test and distinguishes β_T from plasma β. The page locator for that second test is not confirmed by the reviewers' excerpts, which covered only the evolutionary condition, but the Section 5 conclusions do not depend on it. New material: Refs. [6]–[8] credit the libraries used. No result, equation or prior reference was altered.

Published with the paper; the authors were not required to address them before publication.

• Section 5, final paragraph: check that the thermal-stability derivative test you cite appears at the stated location in Ref. [3] (arXiv v1, Section 4.1, pp. 19–21), and give its equation number if it has one.
• Code and data availability: shorten the repeated HTTP 200 and DataCite assertions, since Section 6 no longer relies on the archive for any conclusion.
• Section 1: state the abstract's scope qualification once, that the original numerical trajectories are not reproduced, rather than repeating it across Sections 1, 3, 4 and 6.
• Section 6: split the long reproducibility paragraphs into a short table of control families, parameters and pass criteria to improve readability.