Half-integer spin is one of the strangest facts in quantum mechanics: a fermion must be rotated through 720 degrees, not 360, to return to its original state. Standard theory postulates this; it does not explain it.
This paper derives the 720 degree restoration property, and the spin-statistics connection that follows, from the topology of how condensed structures embed in a physical substrate. The distinction between fermions and bosons becomes a geometric fact.