@dga471, looking over this thread again, I did not describe it precisely correctly. Rather than the proof of compressibility is uncomputable. Instead, this is example of an implementation that would work if and only if we had a complete halting oracle. This does not prove that all other implementations would fail too. Of course, all other implementations would fail, and we can prove this, but that is another poof.
Just to be sure I’m not propagating any errors here. I’m leaving this not of the framing error here, and going to fix the wording in the main post.