That assumption is empirically supported, but is, as of now, conjectural and unproven. In fact, our ability to prove facts about the distribution of digits in p

That assumption is empirically supported, but is, as of now, conjectural and unproven. In fact, our ability to prove facts about the distribution of digits in pi is so weak that we can't even rule out statements such as "after a certain point, all digits of pi represented in base 10 are either 0 or 1."