I checked the publications page and so far I'm not seeing any real theory here. That doesn't mean it's wrong, but it certainly feels weird. The most in-depth equation I saw in any of their linked papers is the definition of the electromagnetic field tensor.
I'm not saying you couldn't develop a fusion reactor by doing purely experimental work with bleeding-edge laser technology. But I'd feel a lot more confident if they were to produce, for example, some kind of prediction of their net power, or a relation between e.g. laser power and fusion yield, or some other quantitative prediction about something.
For example, I'm not sure what prediction they exceeded by a factor of a billion in TFA. Shouldn't you mention that somewhere?
Another poster mention's Todd Rider's thesis, a famous barrier to creative fusion. In this particular case I think the way they evade Rider is by using higher laser powers and shorter reaction times than Rider considered to be possible. One of the important exceptions Rider acknowledges (and that I remember) is ultradense fusion; ultrafast fusion seems to be at least similar in principle.
They do seem to be making quantitative predictions based on simulations. I don't think I've seen them boil it down to a simple scaling law though.
In any event, ultimately practical proven results will always trump whatever the current theory may suggest.
[0] https://www.hb11.energy/news-and-publications [1] https://aca3d9dd-3b9c-446b-8797-0ba1cdb49ccb.filesusr.com/ug...
Exponential progress does sometimes have results that seem too good to be true. In this case the progress has been in picosecond lasers, which for a while have been getting ten times more powerful every three years or so.
What's great about this is it should be pretty cheap to test. The petawatt lasers only cost tens of millions in the first place, and China is finishing up a 30PW laser which they plan to let other researchers use. If Hora is right then that should be powerful enough. Even more powerful lasers are being planned elsewhere.
HB11 isn't the only company working on aneutronic fusion. The largest is TAE (formerly Tri Alpha), with about $700 million invested. There's also Helion and LPP.