I think most of the criticism on random data compression is too far sweeping and absurd. For example saying that it's impossible to compress random data because if it were possible you could compress data forever and make any file a single bit... is basically reductio ad absurdum.
I don't see anyone making that claim (and I certainly didn't in my article where I specified a limit of 1k.) People like to bring up the pigeonhole principle as if it's a mathematical proof that there can never be a practical algorithm for compressing random data. But the truth is if there's so many different ways to represent data then we might never run into a situation where it's actually relevant.
The other fault I see in these comments is the knee-jerk reaction over using a PoW-inspired algorithm for set reduction. Why is that? Could it be because blockchain technology is no longer in your favourite hype cycle and you need to signal to all your tech buddies that you're in the know by bandwagoning like everyone else? PoW is far superior to other ways to reduce the sets and has the added bonus that nonces are more compressible.
The point that I got to with this research is having 14 bits left over per set to save offsets after filtering results. I was running some code yesterday and noticed that using 3 x 3 bit fields to save the number of zero bit information in the hashes produced low offsets. I think that this could be compressed with the same simple quotient idea I already wrote about to fit in the 14 bits so that you could quickly filter and recover the sets and dereference the original data.
This would reduce 1024 bytes to around 1015~ which would be more than enough to solve the 20+ year compression challenge and refute claims that random data can't be compressed. Of course, the cluster that I built to run my code is too slow and I'm getting tired of waiting. So I will need a break from this. In the mean time you can stick to the insults and other predictions in the comments. As we all know from experience: hacker news is a positive and constructive community that is excellent at predicting the future.