The criteria would be successful survival, where survival could either be the extant itself or its reproductive progeny. This is a behavioural dynamic relevant to subatomic particles and life forms and astronomical masses even as their capacities and behaviours are vastly different. Each hierarchically functional interactive system or level of being has its own distinct dynamic Integrity. Our goal is not to say that some of existence is conscious and the rest not but rather that existential persistence of Integral systems is accomplished through a variety of mechanisms, distinct yet interactive. Consciousness as we experience it is an outgrowth of abilities inherent in the primal constructs of existence.
All responsive systems can satisfy the new definition.
By adding Apollonian relationships to standard Pythagorean ones we discern new ways of modelling EM relationships as closed toroids, spin as a yaw function, and others relationships including superstring symmetry and quark architecture. We are required to formulate a post-Godel perspective that places interaction potential as the superior quality of existence rather than information acquired from past interactions.