What I'm looking for specifically however is, as we have seen, almost impossible to effectively describe.
Nonsense. It's the Christian soul. You really haven't even done much to conceal the fact that that's what you're trying to prove exists. What you've had difficulty doing -- and rightly so -- is concealing that endeavor by vigorous obfuscation and equivocation. Your critics here and elsewhere are well attuned to your verbal shenanigans. In your more honest moments you admit all of this, and tell us you refrain from using the word "soul" because you don't want to be so easily seen to beg the question. But here we are.
I've been claiming that modern science tends to believe that each particular self...
Modern science does not conceive of the self as particular, divisible, or individual. That's the Christian soul, not science's model of the self.
...but no one in the field seems to be asking the question about the "self" that I first raised: would your self exist if your parents had never met?
And that's because they're talking about the scientific model of the self, which is vastly different than your thinly-veiled notion of the Christian soul. This is a chronic problem for you. You are intellectually unable to conceive of a model of the self that is even slightly different than the Christian soul. This is one of the main reasons your argument fails. All your attempts to falsify the scientific model have incorrectly assumed it shares most of the properties of the Christian soul. It does not.
Here, we all agreed that it would not; but, we have also agreed (I think) that if we could create a brain with your DNA, we would not bring your particular self back to life.
No.
This is a bald-faced lie, Jabba. It's a lie you've told repeatedly, and you have been told in no uncertain terms -- every time you tell it -- that it is a lie. Because of that, we have to conclude it is a deliberate lie that you have no intention whatsoever of stopping telling. Your wanton desire to lie both to and about your critics seems to be why a lot of people consider you beyond salvation.
I haven't found anyone that is studying consciousness talking about that issue.
Because your model is not an issue in the study of the mind. You are the only one trying to prove the existence of a soul by means of Bayesian statistics. Everyone else is smarter. They're following the evidence, not some last-ditch effort to get attention.
Does anyone here think they know what I mean by 'brand new," and "out of nowhere and thin air"? If so, does anyone agree with me?
You mean the religious concepts, and I suspect you can find many religious people who will agree with you. But that, however, is not at all a mathematical proof for immortality. That's not even a rational line of reasoning for immortality.
Also, does anyone here know what modern science thinks about [this issue?
Modern science has no evidence that your model of the soul is what constitutes the self. Your question presupposes your model is not patently absurd.
What are the physical factors that determine a "who" that can never be recreated?
The physical factors that determine the self are a functioning brain. There are no other factors. The physical factors cannot be recreated because individual brains cannot be exactly reproduced.