TMD: Spin, Statistics and the Spin–Statistics Theorem — The Mechanical Origin of Spin and Statistics in Triadic Mesh Dynamics

This work develops three interconnected pillars of Triadic Mesh Dynamics (TMD): emergent spin, the statistical behaviour of particles, and their unification in the TMD spin–statistics theorem.In TMD, spin arises as a local orientational rhythm of triads in the discrete network, while particle statistics follow from topological constraints on sharing orientation between triads.We show that only two stable classes of orientational dynamics exist: locked configurations corresponding to fermions and shared configurations corresponding to bosons.This dichotomy leads to a fully mechanical explanation of the link between spin and statistics, replacing the axiomatic structure of quantum field theory with a geometric–topological mechanism.The result is a physically transparent interpretation in which spin and statistics emerge from the same orientational dynamics of the triadic network.