Pandeism is the belief that God is the Universe28. Obviously, by this definition pandeism is in perfect accord with the pandeist theorem proven in this work. If a standard model omniscient God exists - something that can never be proven or disproven by means of either pure reason or experimental observation - then it is certain that God is the self-encoded Universe or else God must fail in omniscience and seems unlikely to be able to satisfy any reasonable physical model for omnipresence or omnipotence, both of which are manifest attributes of a God that is all places and times and events.
Pandeism, then, is a consistent special case of deism in general, where deistic beliefs in a creator God or a dualistic God of any sort are contradicted by the theorem and hence impossible. Pandeism, like deism, has no specific theistic creed or scripture that defines the belief as a system, so there is freedom so far to consider a God that is the sentient Universe, or a God that is the non-sentient Universe, or to further attempt to specify God by ascribing attributes that do not appear, at least, to contradict the necessary minimal set.
Any such attributes, of course, are ultimately subject to the test of reason, and may prove to be difficult or impossible to accommodate in any reasonable (conditional) model of pandeity. Sentience is one of the most challenging of the possible assertions - most people who choose to believe in God would like to believe in a personal God, that is, one that is sentient and capable of the same sort of high level cognitive function that humans are. However, if God is the Universe, this becomes a very difficult assertion to sustain, for reasons directly connected to information entropy and the compression of information necessary to sustain at least our plausible models of awareness.
Here the issue is simple: We know that God cannot use any high-level symbolic encoding of God's own complete state, because the process of encoding introduces entropy compared to the bare irreducible self-encoded state data in God. Just as you cannot, with your brain, have high level cognitive knowledge of every elementary particle in every neuron in your brain, God suffers the same sort of difficult. However, just as you with your relatively small number of connections have considerable intelligence and processing power (all of it coarse grained and fuzzy, averaging over all sorts of microscopic detail in order to arrive at general inferences and apparent truths) it is not completely implausible that the microscopic structure of the Universe itself forms one way or another an enormous brain that is capable of very high level thought; indeed one can interpret all of the mechanical operations of the visible Universe as the manifest thoughts of that brain.
Because of the uncertainties of information scaling in a possibly unbounded Cosmos in a possibly unbounded Universe of possibly unbounded dimensionality, I personally have been unable to work out whether or not this sort of sentience is or isn't plausible. We have already observed in our local part of the Cosmos that sufficiently complex physical systems exhibit surprising and unexpected degrees of self-organizing critical behavior, and self-similarity is another poorly understood buy empirically well-verified phenomenon in both mathematics and physics, where e.g. the Mandelbrot set is a fairly well known example of self-similar embedded structures of systematically increasing complexity in a very simple ruleset applied to a small ``universe'' of points. The information entropy of the Mandelbrot set is in one sense zero, as it is generated from a very compact deterministic ruleset, but in another sense its fractal disorder, increasing without bound on the microscale, can function as entropy for many purposes. Another apropos example is a random number generator, which can generate ``information entropy'' of a sort from a zero entropy finite state mathematical algorithm.
When the state information available to set up a ``random number generator'' scales to infinity, one has to confront the ordering of limits - does the psuedoentropy available to the system scale towards ``real entropy'' sufficiently fast that things like thought and awareness and discovery can emerge from a deterministic self-encoded zero entropy system? No theory I'm aware of is yet capable of addressing this issue.
This leads us to our final, perhaps most interesting, non-theistic system.