The PNP Theory of Cause and Effect

We derive causality from first principles within the Point–Not–Point (PNP) framework. At its core lies the topological irreducibility of the fundamental $(1)$ mode: the simplest closed oscillation of a scalar field $U$ exhibiting a $\pi$ phase inversion, or "bounce." This $\mathbb{Z}_2$ invariant enforces loop persistence and forbids extinction without a phase slip. We explicitly ground this mode in the discrete solution space of source-free Maxwell dynamics (the toroidal hydrogenic spectrum). From this physically motivated topology, we prove that such a mode cannot remain static, formalizing cause–effect not as a postulate, but as the inevitable action of the field propagator on a persistent topological sector.