but this is a joke hahaha

Basically the work will be give me starting index from which, next N digits are = "45334138023580". Finding the first digit can take ages while verification is O(1)ish.

Imagine that to provide storage systems similar to IPFS, but the blockchain network only stores the metadata and no data!

*split it*into N several chunks and I share it with N different people. Or with the same people, but I share it at N different dates. Say I charge them $10 a month for doing that, and I don't pay you anything.

Am I violating your copyright? Are you entitled to do that?

To make it funnier: Say instead of the .xz, I "compress" it via π compression [1]. So what I share with you is a pair of π indices and data lengths for each of them, from which you can "reconstruct" the audio. Am I illegally violating your copyrights by sharing that?

Store stable diffusion model in the π file system (https://github.com/philipl/pifs)

"Almost zero overhead in terms of data storage"

I think we've largely just decoupled the fun and goofy projects from the mainline projects; I think businesses have less of a sense of humor than engineers.

[1] https://github.com/Herzult/SimplePHPEasyPlus [2] https://github.com/philipl/pifs [3] https://github.com/hubsmoke/bro [4] https://github.com/jneen/balls

If we find a way to compute Pi's decimals quickly enough, this FS will become the next big thing :)

That is so cool.

And I beg pardon if I sounded dismissive of the OP; it's a great explanation and interesting exploration, thanks.

- [1] πfs - the data-free filesystem

practically yes, but

In fact it's not even proven that every digit occurs *infinitely* many times in the decimal expansion of Pi. [4]

So https://github.com/philipl/pifs is wrong in claiming that all byte stream will exist somewhere in Pi (it's not proven). Also it's worth calling out that even if Pi was Normal it will likely take more space to store the indices of two location as it will for original data itself (for at least majority of the integers), so it's not much of a "compression" strictly speaking. It's easy to see how this will work out for a known normal number - Champernowne's constant [3] -> Unlike Pi, Champernowne's constant is guaranteed to contain all the possible natural number sequences, but storing just the starting index of them in this constant is going to take much longer than the entire number itself (e.g., number "11" start at index 12 (1-indexing), number "12" starts at index 14, and so on - the size of index increases much faster than integer being looked up itself).

[1] https://mathworld.wolfram.com/NormalNumber.html

[2] https://math.stackexchange.com/a/216578

[3] Champernowne's constant (in base 10) is the concatenation of all positive integers and treating them as the decimal expansion (following "0."): 0.12345678910111213... It can be trivially seen that it contains all natural number strings. It is also proven to be Normal in base 10 (which is a stronger property). See https://en.wikipedia.org/wiki/Champernowne_constant for details.

[4] https://en.wikipedia.org/wiki/Normal_number#Properties_and_e...