I know of a possible structure that could survive heat-death. It has infinity dimensions and is directed-graph based. If we mount the opcodes Exists and Forall into lambdas, each as a graph node, we can define in math nth level hypercomputing. Every node points at 2 child nodes which represent a lambda call pair, so thats 2 outgoing edges. A third edge points at what the lambda evals to. Every hypercomputing statement is an integer and most of them do more than the integers (and more than the reals and more than the surreals) number of compute steps. A hypercomputing statement takes infinites of infinites... of compute but only the integers amount of memory. So it all fits in the integers. It is therefore infinitely compressed (or more). A hypersphere of varying radius could have grooves annealed into it in the shape of these hypercompute math statements, to imprint a copy of this infinite graph onto the unified field of physics itself. We'd likely have to experiment various ways but it seems to me that some variant of this could physically exist, and as I believe the Mathematical Universe Hypothesis, I believe does physically exist.