Isn't that what the movie Contact was about?
In all seriousness, I think if we did receive something, it would be classified immediately, and the government, or governments, will move very swiftly with a heavy hand to silence the discovery. At the very least until they know exactly what it is, what it is conveying, and how to respond.
That said, I think that if it got out, a lot of people would absolutely lose their snot. Completely. It would be chaos in some places.
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