If anything has, minimally, a robust spatiotemporal sense of itself, and can project that sense forward to evaluate future outcomes, then it has a robust "self."

What this requires is a persistent internal model of: (A) what counts as its own body/actuators/sensors (a maintained self–world boundary), (B) what counts as its history in time (a sense of temporal continuity), and (C) what actions it can take (degrees of freedom, i.e. the future branch space), all of which are continuously used to regulate behavior under genuine epistemic uncertainty. When (C) is robust, abstraction and generalization fall out naturally. This is, in essence, sapience.

By "not trivially reducible," I don't mean "not representable in principle." I mean that, at the system's own operative state/action abstraction, its behavior is not equivalent to executing a fixed policy or static lookup table. It must actually perform predictive modeling and counterfactual evaluation; collapsing it to a reflex table would destroy the very capacities above. (It's true that with an astronomically large table you can "look up" anything -- but that move makes the notion of explanation vacuous.)

Many robots and AIs implement pieces of this pipeline (state estimation, planning, world models,) but current deployed systems generally lack a robust, continuously updated self-model with temporally deep, globally integrated counterfactual control in this sense.

If you want to simplify it a bit, you could just say that you need a robust and bounded spatial-temporal sense, coupled to the ability to generalize from that sense.