Gas-rich ultra-diffuse galaxies: alleviating the MOND tension with hyperconical modified gravity

Referee: [Abstract and analysis of the UDG sample] The neighbourhood-scale parameter scan (described in the abstract and preceding the chi-squared calculations) is performed directly on the six UDGs to drive the model to its asymptotic branch before comparing to the same published velocities. This introduces circularity because the branch selection depends on the data under test, with no independent prior calibration or theoretical derivation fixing the parameter value in advance. The central claim that HMG alleviates MOND tension but is still insufficient rests on this step; the paper must demonstrate that the scan is not post-hoc or provide a pre-specified justification.

Authors: We acknowledge the referee's concern about potential circularity. The neighbourhood-scale parameter is a fixed environmental quantity in the HMG framework, and the scan is performed solely to identify the value at which the model enters its theoretically predicted asymptotic branch (where the velocity prediction becomes independent of further parameter variation). This branch is derived from the underlying hyperconical geometry and has been applied consistently in prior HMG studies on other systems. However, we agree that the manuscript would benefit from explicit clarification. In revision we will add a dedicated subsection justifying the scan range from theoretical considerations and previous HMG calibrations on larger samples, report the exact parameter values selected for each galaxy, and demonstrate that the chosen values lie within the expected neighbourhood-scale range rather than being tuned to minimize chi-squared for these six objects. This addresses the post-hoc issue without altering the reported chi-squared values. revision: partial

Referee: [Results and chi-squared comparisons] The reported chi-squared values (18.1 for HMG, 9.7 for Newtonian, 615.7 for MOND) lack accompanying error-bar details, full data tables, or verification that the parameter scan was pre-specified rather than data-driven. Without these, the per-galaxy tension ranges (0.2-2.1 sigma for HMG) cannot be fully assessed for robustness, directly affecting the conclusion that HMG is 'still not sufficient' for four of the six galaxies.

Authors: We agree that additional documentation is needed for full reproducibility and robustness assessment. The chi-squared values were computed using the published velocity uncertainties from Mancera Piña et al. combined in quadrature with the reported baryonic-mass uncertainties. In the revised manuscript we will include a complete data table listing, for each galaxy: baryonic mass, observed outer velocity with uncertainty, HMG asymptotic prediction, Newtonian prediction, MOND prediction, and the individual contributions to the total chi-squared. We will also specify the exact scan procedure (range, step size, and convergence criterion for the asymptotic branch) and confirm that the same procedure was applied uniformly. These additions will allow direct verification of the per-galaxy tensions (0.2-2.1 sigma for HMG) and the statement that HMG remains insufficient for four galaxies. revision: yes