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Isn't it common to be able to re-open court cases? That (technically, legally) sidesteps ne bis in idem (aka double jeopardy), but it requires that substantial new evidence is brought. So basically it adds that barrier, and the barrier becomes higher for every new attempt.

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No, it's not common to reopen court cases if the jury finds a person innocent. You can certainly reopen court cases where someone was found guilty, but that's not double jeopardy.

Juries make guilty/not guilty findings, not innocence.

What's the technical distinction between "not guilty" and "innocent?"

IANAL, but

Innocent = "We, the jury, are certain the defendant didn't do it."

Not guilty = "The prosecution did not convince us, the jury, that the defendant did it."

And because our criminal justice system is not set up to establish innocence, only to check if there's enough evidence to prove guilt, we don't use the term "innocent" for decisions.

You’re a statistician, aren’t you?

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