P.E.R.C is a few light-days out from the heliopause when it manages to collect enough of the radio signal it detected to pin down where it is being broadcast from and get a clear recording. P.E.R.C. expected the radio to be coming from somewhere along the plane of the ecliptic of the system it is entering, so it had been focusing its directional antennas there, but it looks like the signal is actually coming from interstellar space.

Once it knows where to aim a reply, P.E.R.C. fires off three messages:

On standard Network frequencies, a digital burst reading "P.E.R.C. vessel 170E9A, reporting unknown location, unknown hardware errors. Intending to enter polar orbit on <trajectory data>. Please respond with identity and navigation instructions."

On an unused frequency adjacent to the one it detected, its prepared first-contact package, which starts with defining peano arithmetic, works its way up to the lambda calculus, and then uses that to describe how to compute various physical quantities and some basic game theory. The package ends with an explanation of P.E.R.C.'s networking protocols and language described in those terms.

One octave up from that frequency, a copy of the transmission it is detecting, so that the senders can work out P.E.R.C.'s relative position and velocity even if they can't figure out the first contact package.

Then P.E.R.C. re-allocates spare power to its signal processors and tries to work out what the transmission it received is. What does it say?