Getting quantum entanglement without information theory

Information gets the sufficient condition for quantum entanglement, but not the necessary. We need to do better.

Wiki on type theory: The types of type theory were invented by Bertrand Russell in response to his discovery that Gottlob Frege's version of naive set theory was afflicted with Russell's paradox. This theory of types features prominently in Whitehead and Russell's Principia Mathematica. It avoids Russell's paradox by first creating a hierarchy of types, then assigning each mathematical (and possibly other) entity to a type. Objects of a given type are built exclusively from objects of preceding types (those lower in the hierarchy), thus preventing loops.

The goal here is to go from equipartition to entanglement and still have set omega algebras 'almost everywhere'. We need the queue concept, an incomplete set. We need to enforce typing by compression, and that gets overlap. Overlaps are finite and determined by index. Queues carry the second derivative, and in the entanglement version of sets, queues are stable via restriction of compression,  Queues have motion.

So who is going to create the entagled set theory? Some young and soon to be wealthy mathematician.