Thanks. What I am getting from this is that pi is believed to have this property, but proving this is still an unresolved problem.
Could be. But if you wanted to shoot for the Hutter prize, you'd probably need to include the client binary and the downloaded data to actually measure the "size" of the decompressor.
If you have to fetch one or more dictionaries to decompress the file anyway, why not just include the dictionary with the file you need to decompress?
Because the model (=="dictionary") is 70B floats -- 280GB naively, 40-70GB aggressively quantized (which might reduce compression rate). If your file is big enough that the marginal compression win over other methods makes this space-effective, sure. But that's a very narrow case.