Science does the objective observable universe....and so it follows naturally and logically that it does not know about the transcendent. However anyone who is sincere and mature wrt religious practice will have proof of the existence of spirit and transcendent consciousness...but there is no science involved as it is not objective and generally not able to be shown to others. If one wants to experience the proof, it requires a total commitment to a mature religious discipline...
I am not a mathematician, Ben, so I don't give much figs about "proof" or with "proving". The world is more than just mathematical equations or mathematical models. When you say "proof", I would view "proof" being a mathematical issue, not a scientific issue. Nor am I a theoretical physicist, which put more emphasis on proof than evidences.
My experience with science is more precise dealing with Applied Science, because of the courses I had completed (Civil Engineering and Computer Science). And because of that practical application to physical science, I am more incline to what can be verified, through testing or evidence.
You do know that there are differences between "proof" and "evidence", don't you?
Some would use these two words interchangeably, like judges and lawyers in the courtrooms, but when lawyers talk about "proof" what they are really saying is "evidence". If lawyer were ACTUALLY talking about "proof", they would be writing complex mathematical equations on a white board before the judge and jury.
What they are presenting in the courtroom, are "evidences", not proof, that something had occurred (like a crime or civil offense).
But I am certainly not a law student, so it doesn't matter what language they used, they can use it interchangeably. (That's strictly not true, because how we say thing matters a lot in court room.) But you have to remember this debate is a debate between science and religion, not a law court room.
Both mathematicians and scientists understand this distinction between the two.
Can you write a mathematical equation for (or draw a mathematical model of) the existence of spirit or the transcendent consciousness? That's what I would be asking you, if I wanted or requested "proof" from you.
I know what you are talking about, I just wanted to point out you are using incorrect term in your reply.
But getting back to your reply.
Yes, science don't deal with transcendent consciousness or the existence of spirit, because both are not falsifiable. No scientists couldn't possibly find evidences for either one of them, but they are also "not testable".
But (of course, there's always a "but") I think spirit and transcendent consciousness are just as "faith-related" as that of Abrahamic religions. You cannot objectively test; you can believe that it is possible, and it doesn't matter how mature the believers are, it is still taken on blind faith.