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Your are falling into a hole ...

Your two points has no bearing on the fact that a necessary precondition for the theorem is not being fulfilled. If a theorem says "A is true provided B and C are true" and if C is not true then A is undefined. That's it. End of discussion.

And you never posed any of the questions that you are now belatedly asking. But the answers are:
1. Yes, including some theoretical modelling and some empirical observations
2. No, and if i did the results would have been worse, at least from a theoretical perspective
3. Yes, and in fact reconstruction errors can be observed as low as fs/4


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