Title: Elucidation of the subcritical character of the liquid--liquid transition in dense hydrogen

Abstract: The liquid-liquid phase transition in high-pressure Hydrogen is a problem of longstanding and controversy. The recent Nature paper by Cheng et al. [vol. 585, p. 217] makes a set of strong claims to the effect that all the previous density functional theory molecular dynamics (MD-DFT) and quantum Monte Carlo calculations of that transition are incorrect because of finite size effects and, in the MD-DFT case, short run times. The basis of those claims is their use of large systems and long durations for classical MD driven by a machine-learnt potential (MLP) which they developed. The straightforward test of their claims is to do MD-DFT on systems as large or larger than Cheng et al. used and for significantly longer durations than in the previous MD-DFT simulations. We have done so and find that neither diagnosis of theirs (size effects, duration limits) is correct. Instead, we find that the MLP does not drive MD in fidelity with the underlying DFT electronic structure that it is supposed to replicate. The result is that the MLP-driven MD results are artifactual, not systematically connected to the theoretical underpinning on which the MLP was trained.