I just don't see how you can prove or even make a logical case for any supernatural phenomena.
Please keep trying, I'm open to argument.
How about the phenomenon of your existence?..its something that you have zero scientific evidence for; zero mathematical formulas for; zero evidence of any kind for...
But you are so intimate with that knowledge that the moment you say "I do not exist" you see the absurdity of your statement and know yourself to be a liar.
That is what we call an intuitive truth ..a truth beyond nature..a supernatural truth.