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Think about it this way: if you could conclusively state AIs are not conscious, you would clear up a huge number of millennia-old mysteries about consciousness and make the greatest step in history towards putting bounds around the answer to the hard problem.

That’s not the common definition of “affirmative claim”. “It is not true that AI is conscious” would be a negative (not affirmative) claim. This is subtly different than “AI is not conscious”; it’s a testable claim that a fact is not a consequence of what we know, not that its negation is true.

“It is not true that AI is conscious” and “It is true that AI is not conscious” are equivalent - simplified this is !(A) vs (!A) Either can be tested (or not) using the same criteria, unless I'm missing something.

There is something you’re missing. “Jenna is a lawyer. Jenna is 5'5".” The statement “Jenna is 35 years old” is not entailed by these statements. That is NOT the same as saying “Jenna is not 35 years old” *is* entailed. You can prove something is not entailed without proving that it’s false.