how do we know the BPP formula for $\pi$ is valid?

how do we know the BPP formula for $\pi$ is valid?

i recently read about the Bailey–Borwein–Plouffe formula for calculating
the n*th* digit of Pi. I'm curious to how can we be sure that the formula
is always accurate or correct?! Even if we can verify for every Pi digit
discovered till now with a "standard formula", how do we know that the
formula is correct after those digits?
Also, what's the implication of these kind of BPP formulas for other
"divine"/fundamental constants? can we learn anything else about the value
of such constants and our universe through these? Any insight into the
"supreme fascist" mind?