I once had an idea for a file transfer system based on digits of pi that sounds the same as this idea.

You'd give everybody DVDs of digits of pi (or they could calculate them themselves) , and then transfer files faster by just sending them the offset into pi.

At the time I thought it could work with a big enough bank of digits of PI on both sides. If transfer was expensive, and calculating digits was cheap then you could give everyone an infinite supply of digits of pi and have a nearly infinite compression system.

I discovered that often the offset into pi is much larger than the data you are sending. Turns out it's an expensive way to sent things.

Also, it turns out that this area was already well understood. There are no free lunches with entropy.

But it was a fun idea to kick around.