Yes, they have said what filter shape they're aiming at. And there is no reason why any of the *sound quality* aspects of what they promise can't be matched by open alternatives. Physics and Maths don't distinguish.
When it comes to hardware, and mass manufacture, big companies can get benefits of scale. But that evaporates when you're talking about software or thought.
So far as I can see, every part of the sound quality side of what MQA claims could be done by open alternatives. Not only 'free' as in 'no charge' but 'free' in the sense that anyone using it could check and improve as well as detect problems.
If you think about it, in a matter of just a few days, a few people here have already largely got the same results using sensible approach based on the same idea that some of the standard LPCM Shannon Space is currently wasted and can be discarded or used in a slightly different way. Just that the ways we've come up with are simpler to impliment, and free. But we already have scaling down the sizes of files, etc, by a factor of about 4.
If I could do this, lots of others can probably do better. I'm not a particularly good programmer. Just someone who starts with the awareness that these things can be done, and some grasp of what might be useful approaches.
All that said, I suspect that trying to match something as extreme as the 'behaviour of air' would be problematic in reality anyway. Nice as marketing puff, though.
But given microphones, amps, and ADCs that good, what follows could still use an open approach.