The end is the beginning is the end, hence that part in the closing statement "Of course completely theoretical, and just a random pondering on the nature of the end-beginning."

The only problem is by the time we get the data to prove the theory it will be useless, how will we encode it if all the matter is dissolved into energy then back to matter again?

Send it out as a stream of photons outside the boundaries of the possible expansion zone of the next cycle? Honestly no idea there.