Causal Direction Index and Four-Dimensional Topological Causality Theorem

We establish a topological origin for the causal direction of time in four-dimensional spacetime from the Pin⁺ bordism group Ω4Pin+=Z16. We introduce the Causal Direction Index CDI(k)=Im(Z(k))=sin(πk/8), which quantifies the topological preference for time direction in each of the 16 topological sectors. We prove the 4D Topological Causality Theorem with four parts: (A) mathematical structure, (B) physical consequences, (C) weak topological constraint from RFB=∞, and (D) 4D uniqueness from the triple blockade. We establish that CPT conservation has a dual foundation: the standard chain from Lorentz invariance and a topological chain from Pin⁺ bordism, which are independent and exhibit scale stratification. We derive three falsifiable predictions: (1) neutron EDM dn=0 implies sector k=0 and no topological contribution to the arrow of time; (2) CMB TB/EB sign flip signals the Element 8 sector; (3) CPT conservation persists even if Lorentz invariance breaks, provided the Pin⁺ structure is preserved.