The Fourier Protocol
The first half of First Contact has the shape of an epiphany and the insidiousness of a philosophical breakdown. The monumental financial ruins of a multi-decade search for the El Dorado of scalable quantum computing are transmuted overnight into the most valuable sensor array in the Solar System, while the vast computer fields they were supposed to make obsolete are used to translate the subtle patterns of surprise in the noise behind the indeterminacy of quantum decoherence into messages from a theoretical somewhere that mathematicians can only describe as a non-local place only accessible by rotating logic three and a half times around the axis of impossibility.
(Many religious explanations are offered; the metaphysical consensus coalesces around the idea of communication with the godlike AIs running the reality simulation that much of a generation performatively believes to be inside of.)
Nothing can be read in the message except the existence of a message and therefore of a sender. Scientists find a way to talk back at only moderately astronomical costs and after two projects are felled by the semi-chaotic ecosocioeconomic crises that define the calendrical system of the century a system is built that is physically guaranteed to work. Fourteen years after the first message from There humanity replies.
Nothing new is heard back. This is enough to trigger another crisis that nobody pays much attention to.
Efforts continue. Coding systems are improved. Sensors refined. Speculative xenosociopolitics becomes a science and then a fad. The mathematical complexity of the messages — which is somehow the equivalent of energy There — is increased almost to the point where scientists fear it would be damaging to anything that might be listening.
Something must be listening. Therefore something is. Nothing is being replied. People that can communicate as unconsciously as breathing decides that this is deliberate. A world that frequently refers to genocide as Thucidides self-defense concludes there's only one rational next move.
The unavoidable one, really. The only surprise is that it took so long. The mathematical complexity of the first message sent in many years is raised half-way to the theoretical maximum, orders of magnitude over what another generation had considered the safe threshold.
The message is sent.
Half-way through the reply there's nothing left to read it.
The first half of First Contact had the shape of an epiphany and the definiteness of a mathematical proof, impeccably legible and garlanded with footnotes filled with secrets and half-hints that were perhaps the message itself. No reply was attempted. The world survived until it did not.