We have an immortal soul through the eternal recurrence
Max Tegmark in Scientific American's May 2003 issue wrote an article on "Parallel Universes" in which he presents the argument that existences identical to our own recur infinitely over infinite space. He describes a few different levels of universes, but one of the simplest is that our big banged "universe may in fact be a local space-time "bubble", and that an infinite number of other such bubbles exist. Anyway, the basic premise of the eternal recurrence hypothesis proceeds from the assumption that the probability of a world coming into existence exactly like our own is finite. If either time or space are infinite then mathematics tells us that our existence will recur an infinite number of times.
Assuming this is true, then our existence survives the death of our flesh in this existence. What survives over and over, at each moment of our lives, simultaneously throughout the infinite cosmos is the pattern of our life as we lived it and shall always live it. In short, if the eternal recurrence hypothesis is correct, then we do in fact survive rigor mortis.