It's incontrovertible that the neutrons are coming from the experimental apparatus. It remains to establish that the sonic energy is causing the neutrons to appear and that the neutrons are the result of fusion.
Uranium fission reactors are fueled by Uranium which has been enriched to increase the proportion of U-235 versus the more prevalant U-238. The fission in the reactor comes about because U-235 fission products include neutrons, which, if properly slowed by moderating materials or by distance in the Uranium, can then induce fission reactions beyond those occurring just by chance. Controlling the rate of neutron involvement in the Uranium is the mechanism which allows control of a nuclear reactor.
Now we read of an experiment which introduces Uranium and we see neutrons. Perhaps thay are coming from the Uranium. Such neutrons would behave according the inverse-square law, only proving that they emanate from the apparatus and are not just background radiation.
There should be some predictions about the energy levels of neutrons created by fission of U-235 versus those created by a proposed fusion reaction. I think there is much more to be done.
I would give them credit for having the sense (and integrity) to compare the neutron flux with the sonogenerator both on and off. A statistically-significant increase in neutron flux between the "power off" and "power on" states -- combined with the inverse square obervation -- seems pretty convincing to me. (But, then, I'm just a physical chemist...)
True, but they cease emanating when the cavitation source is turned off. Presumably this was done, and reported. If not, this story would not be acceptable at any reliable scientific journal.