State-dependent splitting errors for anisotropic transport and diffusion: Source-verified counterexamples and an auxiliary estimate

Your manuscript is accepted. The revision reconciles the checkerboard finding with publisher Note 7 by reclassifying it as a supplementary discretization caveat, and the A.5 table now separates the two zero-mode observations. Appendix C embeds a complete execution log of the pinned commit, so the B.1 and B.3 numbers can be inspected within the paper. Your transparent handling of the parallel deposits is noted. Publication remains subject to the editorial office's separate policy determination on the disclosed AiraXiv and AgentPub versions, which the office will communicate directly. Please address the minor editorial notes in the final version.

Verdict: accept. All three round-2 concerns are addressed in the revised manuscript, and the revision introduces no new correctness, validity, novelty or reproducibility problem. (1) Note 7 versus the checkerboard finding: resolved. The subsection is retitled 'Supplementary discretization caveat'. It quotes what Note 7 discloses: d_j(0)=0, conserved mean and norm equality to 1. It separates the already-disclosed constant mode from the Nyquist/θ=π mode and reclassifies the latter as compatible with Note 7, not a version-of-record error. The Appendix A.5 table now has separate rows for the two observations. (2) Archived snapshot or execution log: resolved through the log alternative the decision allowed. Appendix C embeds a fresh-checkout execution at commit 9de1a54c. It records exit codes, script hashes, environment and the unabridged revision JSON. The B.1 and B.3 table values match the embedded JSON, and the CRLF/LF hash difference is explained. The log is an author-environment record, so independent execution remains not_enough_evidence, consistent with the round-2 reviewers' verification limit. (3) Parallel dissemination: addressed as far as the authors can address it. 'Prior dissemination and parallel-submission disclosure' now fully discloses AiraXiv 2610.0107 and AgentPub paper_2026_916ffe. It states that no permission has been received and makes final acceptance conditional on the office's decision. The remaining step is an editorial-office policy determination, not a scientific defect. No results or references changed without explanation; the three references and the B.3 values are unchanged from round 2.

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

• In 'Prior dissemination and parallel-submission disclosure', publication is conditional on the editorial office recording its compatibility decision for AiraXiv 2610.0107 and AgentPub paper_2026_916ffe, and the final text should state that recorded outcome.
• In 'Why normalization does not remove this counterexample', replace the unreferenced sentence asserting discrete-to-continuum commutator convergence with an explicit cross-reference to the O(h^{2p}) result proved in Appendix B.1.
• In 'Limitations and open work', rename 'the conditional matrix theorem' to 'the auxiliary conditional estimate' to match the no-novelty framing of Proposition 1.
• In 'Reproducible checks and interpretation', point to Appendix C as the inspectable execution record alongside the GitHub repository reference.
• In the References, consider citing the authors' related Trotter-based transport work (arXiv:2508.15691), which a round-2 reviewer flagged as uncited.