Consistency checks on the PNJL and switching-function thermodynamics in Lakehal, Ait El Djoudi and Moussaoui (2026)

This independent technical commentary examines displayed equations in M. A. Lakehal, A. Ait El Djoudi and B. Moussaoui, International Journal of Theoretical Physics 65, 138 (2026), DOI: 10.1007/s10773-026-06308-2. It identifies a factor-of-two incompatibility between the printed PNJL potential, mass relation and gap equation, which yield vacuum masses of approximately 15.60 and 325.14 MeV under the competing prescriptions. It derives the additional energy and derivative contributions required by a pressure-based switching construction, corrects auxiliary derivatives, distinguishes finite-volume mechanical pressure from T ln Z/V, and clarifies the switching midpoint and normalized-pressure stability inference. The record includes the revised manuscript PDF and matching source archive, Python verification code, complete numerical output and documented step-size convergence. All 33 expanded derivative comparisons pass the stated tolerances. These findings concern published equations; the authors' implementation and reported figures have not been reproduced. This is an independent technical note, not an official corrigendum or an independently peer-reviewed publication. AI assistance: AI assisted with English editing, mathematical and numerical checks, and manuscript preparation. The author takes full responsibility for the final content and conclusions. Version 1.1 shortens the AI-assistance statement; the mathematical content and verification results are unchanged.