Proof that I'm immortal

[Angrboda]

A process is only self sustaining if it sustains itself, i.e. maintains it's identity as that process.  (Duh.)  Sustaining something else or becoming something else is not the same thing.  So, no, the universe isn't composed of "a never ending series of self sustaining actions" except insofar as the identity involved is only that it is matter and energy.  But simply being matter and energy is not what makes a self, so that is insufficient.  

The "I" that we identify as ourselves is more than just energy.  It is a process: matter and energy in specific configurations and undergoing specific changes.

The universe is full of personality through apparently self sustaining actions; planets in orbit, the fixed position of the stars, gravitational pull, etc; all in the midst of the break down of other systems that can no longer sustain themselves...but it's still the universe...we are a part of the universe, always have been and always will be...if you find no sense of self in that notion, so be it.

Are you hinting at the concept of a soul or something?

That's speaking metaphorically. The personality in the cosmos is not a literal personality. No, I'm stating plainly that you're wrong because I've identified something that causes you to be you that does not exist after you die. And no, the universe is not full of self-sustaining actions.