The next to last was the most interesting to me... it's gotta be an old April Fools in the NSA Technical Journal. It flatly states we've received signals from outer space, and posits a decoding of them....
I know exactly what this is though I can't remember where to find the source. It was an exercise they gave to a bunch of scientists and mathematicians to see if it was plausible that they could even decode the meaning behind an alien message, if one were ever found. (And also probably to provide some credentials for candidate experts to consult in such a scenario.) They did quite well. That said, the code itself was created by a human, so I'm not sure it has the value they think it does. One thing higher education in STEM taught me was that human thinking is actually really easy to spot. We, for the most part, really just use the same tired old tricks again and again in different contexts.
Intelligence agencies have internal decoding competitions and trainings. This sounds like one of them, simply framed around an alien transmission, and you're just looking at the answer key where it's assumed the reader is familiar with the frame.
The entire "transmission" is at the end. To be honest, of all the things we could receive from an alien source, "They transmitted basic set theory and a periodic table at us... and that's it..." would almost be the weirdest possible outcome.
Why would that be the weirdest possible outcome? This provides a demonstration of intelligence, intent and understanding that starting with objective, science-based fundamentals which can be deduced (set theory) and observed (elements) seems like an _awesome_ wide net to cast if you're trying to communicate.
It's not like they could compress a JPG and beam it over here in a way that wouldn't look like garbage.
I think "and that's it" would be the weird part. Maybe it's just because I watched Contact, but I would expect the basic demonstration of intelligence/etc to precede a more interesting message. The basic math and science transmission could be used as a Rosetta stone of sorts, to bootstrap that more interesting message. Otherwise what's the point? Maybe the aliens just want somebody else to know they existed I suppose.
"I think "and that's it" would be the weird part."
Yes, that's my point. You make the presumably-strenuous effort to broadcast to the stars, sacrificing any number of other priorities in the process, and you basically transmit the scientific equivalent of a throat clearing, and then stop? Silence is understandable, and a message like in the movie Contact is understandable, and a lot of other things are understandable, but that would just be weird.
It's obviously a crypto challenge to anyone who has ever played them. It maps way too nicely to human concepts. This is what every amateur putting together an "alien challenge" without attempting to be scientific about it ends up doing, and it's easy to tell. That's fine if you're doing it for fun, but it's obviously not real.
I've been here solved that. ACM tried to run an challenge about an "alien computer" that was obviously not alien, but ended up being very real. I was part of the team that reverse engineered it first, but the whole contest collapsed and all interest waned after we ended up finding the very-much-not-alien chip involved by accident. We did cover the initial process, but unfortunately never got around to writing the follow-up posts.
If aliens were actually found, it definitely wouldn't be announced in an unclassified document shared with everyone at NSA. Although I don't think it's a prank per se, just someone who wrote a cryptography puzzle and wanted to frame it in a cute way.