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I'm sorry, that article is far too long to tell me what you are trying to say. All I can gather is, I was wrong

tl;dr Random data may appear to have patterns, but those patterns do not repeat, so they cannot be compressed.

Ah, but they can repeat! There is a finite chance that any sequence of any length will occur in a random sequence.

So while a compression alg applied to a very large amount of random data is unlikely to reduce the size, it is quite possible to achieve some compression on smaller blocks.

Any given _example_ of a random sequence may have less than maximum entropy, and so may be compressible, but a truly random sequence _in general_ will not be compressible. So you can make a compression algorithm that will compress random data in some cases but it will never be able to compress any arbitrary random data. Does this help?

You should take a look at the almost 15 year old (and unsolved) "Random Compression Challenge"

http://marknelson.us/2012/10/09/the-random-compression-chall...

That is still your problem and you need to take responsibility for it. It is wiser to learn and know what you're talking about, don't just add ambient, useless, incorrect noise.

Saying something true but burying it is not wise either.

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