Ideally, what you want is a single SAT value among a remainder universe of UNSATs.

Sometimes the best you can achieve at any given point is a lower bound and an upper bound range, like "greater than 3 but less than 9."

Of course I simplified in my post but it started out with a pretty broad range of a lower and upper bound, then narrowed further, then narrowed further, then narrowed further, etc...until the specific final result achieved K=7=SAT while every K<7=UNSAT & every K>7=UNSAT. I think it ran for a full week alone on K between 6 and 7.

As amazing as Claude is to seemingly make unprecedented progress, it is even more likely to blow the most insane levels of smoke up your ass before you've legitimately reached that point.

"You should publish right now! Don't wait! There is no reason to wait!"

Like seriously, Claude was outputting something closely resembling (non?)peer pressure on me to not just keep this information to myself - and this was before all the recent math-related breakthroughs started becoming public.

It was also - most notably - before it had actually verified what it was saying it had calculated. I was the one pushing for more verification, more contemplation, more proofs of claims. And though Claude is better at this stuff now, it's definitely not not still happening.

I think I made the right choice then and I will consider being more open now that others have taken the burden of proving that, no it can actually sometimes do the incredible things its claimed its done for you.

My wife remains skeptical - she is/was seriously concered that I was under AI psychosis for believing that I had made such progress - and I can't even fault her for that. It sounds crazy to say it.

If anyone is reading this and is actively involved with FHE, especially someone from Zama or related group, I'd very much love to chat privately. I have many other "innovations" I've been working on since.