It really is gone. You can predict what you think it might have been, but you can't know what it was.

it's gone in a single still frame

but across many consecutive frames, the information is spread out temporaly and can be recovered (partially)

the same principle of how you can get a high resolution image from a short video, by extracting the same patch from multiple frames

https://en.wikipedia.org/wiki/Video_super-resolution

No, it's not "restoring detail". The information is gone.

It is predicting what the information might maybe have been like.

you are arguing with math proofs here, the information is not gone, if it was a real video (as opposed to adversarily generated video)

I'm struggling with the idea that you can use maths to recover information from a video that simply was not present in the video.

I get that what you're describing can statisically "unblur" stuff you've blurred with overly-simplistic algorithms.

I can provide you with real-world footage that has "natural" motion blur in it, if you can demonstrate this technique working? I'd really like to see how it's done.

That looks interesting. Is there ready-made software that can do this? Doesn't have to be easy to use just useable with a time commitment of a few days.