Thanks for your questions! I was one of the people who worked on the project. To answer your questions:

> Is it fair to say that their claims about spatial resolution being >>> existing EEG options are jumping the gun? If I understand correctly, you need to be targeting individual 1mm^2 regions with individual acoustic lenses, which means 17,000 channels would required 17,000 separate, uniquely-tuned ultrasound emitters, yes? Even if that's possible without messing up the data (the MHz range is big, but is it that big?) it seems like a trivial impossibility to fit that in one headset -- even the standard 32-64 EEG channels alone seem like a long shot. But maybe I'm overly cynical, or one emitter could be used to usefully excite multiple regions at once?

Since the system is linear, you could use a single probe to focus at multiple spots. Each focus would be at a slightly different modulation frequency.

> Another oddity in that paper is that it reads like we're trying to find persistent signals in the brain, like a needle in a haystack, whereas my understanding was that the field is moving decisively towards tracking signal changes over time in a given region. Is my intuition correct that accounting for a moving target would add considerable complexity to this approach?

This method would indeed let you track signals that change over time. Lock-in-amplifiers can output time-varying signals.

A modern clinical ultrasound probe have something in the range of 128 to 512 elements only. But despite that you get a real-time video stream at a lot higher resolution than a 512 pixel postage stamp.