Any cosmic-level communication would probably either be so simple that it could be explained as natural phenomena (given that we can't go there and study the me

Any cosmic-level communication would probably either be so simple that it could be explained as natural phenomena (given that we can't go there and study the mechanism in detail) or so complex that we don't even recognize it as containing a message. Interesting numbers like pi and the golden ratio occur so often in nature that we would incorporate them into a naturalistic explanation rather than supposing they had an intelligent origin. And there are probably still many fundamental numbers/relationships that we haven't discovered yet, so they would look like noise (as would the digits of pi if we weren't already familiar with it). Broadcasting fundamental constants wouldn't work. Likewise if they were to broadcast more complex information such as their genetic sequence. However, someone on Earth might eventually recognize a signal containing a human genetic sequence. That sort of leads up to a vague theory I have about communication: There is no way to encode information that guarantees an arbitrary intelligent being, no matter how smart, would be able to interpret it. We will have to develop a common language over time through deliberate interaction and feedback.