Pi Normality Conjecture

Do we know that every possible finite sequence exists in pi?

Somewhat related:https://github.com/philipl/pifsIf the expansion of pi is normal then all your data is already in it

Since pi never repeats it should actually contain any sequence of numbers possible though, right? So if you encode your source code as number thet argument should hold up.

Every possible bit of useful stuff already exists in pi; you just need to know the bit index to retrieve it (in O(n) time, O(1) space).This is because pi is almost certainly unbiased and irrational, thus it repeats at random forever, which means that all possible finite subsequences are eventually generated.

It's a commonly held misconception that Pi is proven to be normal - it is NOT (it is a conjecture as of now) [1] [2]. Proving normality of number is a very hard problem, and hardly any numbers outside of purposefully constructed ones (such as Champernowne's constant [3]) are proven normal.In fact it's not even proven that every digit occurs infinitely many times in the decimal expansion of Pi. [4]So <a href="https://github.com/philipl/pifs" rel="no

Exactly anything you can think of can be represented as a segment of pi's infinite decimal expansion.

GP didn't say "infinite," they said "normal" [1]. If Pi is normal, as conjectured, then it does contain every possible sequence.1. https://en.wikipedia.org/wiki/Normal_number

Dumb question, but is any arbitrary string of digits with length N, somewhere in pi?

Does pi compress? It must if it is only numbers, but only by a half?

Isn't everything already published in the digits of Pi?