What if an hypothesis claimed that X should never occur, and X occurs?
Wrong question. X has a probability of occurring under some hypothesis H. How that's determined varies according to formulation. If P(X|H) is, say, based on historical data then we can reason about P(H|X) by observing a series of X. If, however, P(X|H) is purely speculative, then P(H) as a prior must have some factual basis. (It does not, in your formulation.) Observing P(X|H) over many X in a way that seems to contract H means that the speculated method of reckoning P(X|H) is where the error lies.
This is covered under two of the fatal flaws I already pointed out in your argument. Do not simply continue to make the same errors. Further, the specific way in which you formulate P(X|H) has been separately shown to be untenable. That's one or two other previously-identified fatal errors.
Further, under no circumstances does a statistical inference that concludes X cannot happen constitute proof that X did not happen. If X happened, the probability that it should happen under whatever circumstances prevailed is simply irrelevant.
If we can get past the sharp shooter issue...
We will not "get past" the issue in the way you want, which is to disregard that you're committing it and that it's a fatal flaw in your argument. You assign significance to X, and thus to P(X|H), only after you observe what X is. There is no statistical tap-dance that makes that not an error.
as far as I can tell, mathematics says that H is probably wrong.
- Gotta go. I'll be back
"As far as [you] can tell" ignores several fatal errors beyond the two or three you've focused on this afternoon. You laid out your argument in a comprehensive fashion and I gave you a comprehensive response. There were a dozen individually fatal errors that you have not even acknowledged much less rejoined. No, you can't say that once you get past a couple of initial errors, the rest just falls into place. You don't get to leap over all your critics' subsequent objections and land at the desired conclusion.