The Sign as a Rotation - Fermionic signs from the causal structure - why the arrow of time runs on through every minus (Berry phase II)

This note continues the Berry-phase line that resolved the CP-angle problem in SupplementXII. There the Berry phase of the closed triangle was the right quantity; here it is the Berryphase of the closed winding. The fermionic sign problem is resolved structurally: the minussign is not a reversal but a rotation, and the causal structure shows that it factorscompletely into a positive substrate count. The theorem of Troyer and Wiese (2005) isthereby not refuted but placed and defused: the remaining hardness is no longer afundamental sign barrier but a localised convergence or conditioning problem. Newstatements are marked NEW, proofs closed with ■, limits named honestly. All numericalresults come from exact diagonalisation of small lattices.