I came across the Bigelow contest that had a sizeable prize for to people submit articles / essays arguing beyond a reasonable doubt that consciousness survives physical bodily death - here is a link to the top 3 winners: https://www.bigelowinstitute.org/index.php/bics-afterlife-pr...
There's some good material in there.
I don't know what a proof would look like, but often the experiences involve being disembodied, so a reproduced and reproducible experiment where someone having a near death experience can accurately describe something they couldn't have had prior knowledge of, or guessed, or sensed (heard) in a coma, or found out after waking but before describing, that would be proof. Anecdote is not enough.
There are indeed multiple cases that follow that pattern that have been recorded and in papers (see an example below) - I think they're called "Peak in Darien" cases. The pattern is:
- Person has a near-death experience whilst unconscious - Something happens whilst they are unconscious that they would have no natural means of knowing - Same person comes back and has knowledge of what happened
Here's a paper from Bruce Greyson - https://med.virginia.edu/perceptual-studies/wp-content/uploa...