> I'd be interested to see what can happen without those restrictions.
If you did not have time limits you could exhaustively search through Pi looking for your data, then store just the offset into Pi.
Or if the offset got too large then Pi to the power of lots of random numbers. One of those numbers will, somewhere, have your data. But it's infeasible to search for it.
There is no universal compression algorithm, by the pigeonhole principle.
And your compression scheme won't work by the simple fact that the offset of where in Pi your data lies will, on average, take the same number of bits to store as the data itself. Ditto, with pi to the power of lots of random numbers, the offset and the power will, on average, take the same number of bits to store as the data itself.
If you did not have time limits you could exhaustively search through Pi looking for your data, then store just the offset into Pi.
Or if the offset got too large then Pi to the power of lots of random numbers. One of those numbers will, somewhere, have your data. But it's infeasible to search for it.