I give you a precise formula for calculating the expected signing key from the validation key, initial time and message timestamp, and you reply that you still can't tell which key was used to sign which message. Clearly we have a communication problem, but I don't have any idea how to bridge the gap.
As for "knowing this technology", I have no idea how systemd actually implements this. I only presented one possible implementation based on the design requirements. Obviously, since I made the implementation up on the spot, I can't point you to any papers; everything there is to know is in this thread.