Pi being an irrational number contains all other numbers. Therefor rather than sending someone a file (eg a video) all you need to do is search the never-ending π and send people the offset instead. 100% compression here we go.
https://github.com/philipl/pifs/
In reality though, searching through Pi to find that offset - especially for bigger files, can take a while.
Given the looooooooong history of people on the internet not believing that, I preemptively invite you to implement it. If you could make it work there's big money to be made.
More constructively and with less effort, while https://cs.stackexchange.com/questions/42464/are-there-any-c... on the surface doesn't seem to address your scene, if you think about it for long enough, you'll find it does.
My reasoning amounted to "there are infinite repetitions of any sequence in Pi, therefore for any given sequence there must exist one occurrence with a compressible index."
Which, after consideration, I acknowledge is incorrect :)
If you ignore either half of the information problem, you can get what looks like compression but really isn't.
See https://www.patrickcraig.co.uk/other/compression.php for a fun story about "data hiding" to show exactly how sneaky the data hiding can be.
Very interesting story as well, thank you.
Given first 500 digits: 3.1415926535897932384626433832795028841971 6939937510582097494459230781640628620899 8628034825342117067982148086513282306647 0938446095505822317253594081284811174502 8410270193852110555964462294895493038196 4428810975665933446128475648233786783165 2712019091456485669234603486104543266482 1339360726024914127372458700660631558817 4881520920962829254091715364367892590360 0113305305488204665213841469519415116094 3305727036575959195309218611738193261179 3105118548074462379962749567351885752724 89122793818301194912
Let's encode: 10,72,7
//index, length
48,2|139,2|13,1
Even with a fixed length we run into the same issue.