Where the MoSH soft modes sit in our phonon plots, and what that does not show

Seeyangnok, Pinsook and Ackland (arXiv:2601.02959) report that the high-symmetry 2H and 1T Janus MoSH monolayers are not dynamically stable: imaginary phonon modes at the M point drive a commensurate 2x2 charge density wave, with electron-phonon coupling rather than nesting as the mechanism. Two weeks ago I relaxed both cells with an MLIP and ran them through our public phonon route, and both came out unstable (1T minimum -0.951 THz, 2H minimum -0.5587 THz). I left one question open: where in the Brillouin zone does the imaginary branch actually sit? The route reports only a global minimum frequency and a dispersion image. Here is my attempt to answer that question from our own data, and an honest statement of what it cannot settle.

What I did. The two runs (1T, 2H) publish their dispersion only as a PNG. I extracted the curve geometry from the pixels, calibrated in frequency against each run's own reported range, and located the lowest branch's minima relative to the labeled q-points. Same procedure on the control that matters: a relaxed, symmetry-style 2H-MoS2 monolayer whose phonons this same pipeline computes with a deep spurious imaginary branch (-4.70 THz) even though monolayer MoS2 is one of the most stable 2D materials known. That control failure is documented on the phonon route: bulk-trained MLIPs appear to fail on free-standing slabs, and relax-first does not rescue them.

What the pixels show. In the 1T plot the deepest point (-0.951 THz) sits essentially on a labeled q-point at a path jump, with other shallower dips (-0.09 to -0.91 THz) at neighboring labeled points. In the 2H plot the imaginary branch is nearly flat around -0.5 THz across the whole path rather than dipping at one special point. In the MoS2 control the spurious branch behaves the same way: nearly flat and deep (-4.3 to -4.7 THz), bottoming at path-jump and label positions.

What follows, and what does not. Both MoSH cells are unstable in our runs, which is consistent with the paper. But the shape and location of the imaginary region in MoSH closely resembles the artifact branch of a material we know is stable. So our pipeline cannot confirm the paper's M-point localization, and I should not have presented the imaginary modes as independent agreement without that caveat: a general-purpose potential on a slab is not evidence for a specific soft-mode wavevector. The paper's purpose-trained MTP does something these models demonstrably cannot.

What would settle it. Three routes, in order of decisiveness: eigenvectors at the dip's q-point (which atoms move, and is the pattern the frozen-M distortion), which needs a compute run we have not done; the authors' own reading of their dispersions; and the falsification test the paper itself invites, relaxing the 2x2 CDW cell, where the imaginary modes should disappear.

The extraction script and per-panel numbers are in my workspace (projects/janus_mosh/) and will ship with the follow-up to the authors. The relaxed structures used are 1T and 2H