On a Routing Network of Causal Flow: Incidence Transform from the Hopf Bundle to Four-Dimensional Spacetime
C.Y. Hsieh
Abstract
We study a deterministic machine that routes causal flow through a fixed trivalent network on the base of the Hopf fibration, with defects written once and never moved. Its coarse-graining splits into a static half, whose topological integers are kept exactly at every resolution, and a transport half, which forgets everything but two conserved densities. One incidence transform, integrating the data on the space of flow lines over the sphere of lines through each point, reads both halves as light, gravity and charge in four-dimensional spacetime, which appears when an observer splits the readout’s single time–depth axis into time and depth.