Geometric Quantification of Dimensional Translocation via Spectral Flow Anomalies in Twisted Equivariant K-Theory

Mathematical Applications of Science Fiction We present a rigorous framework for quantifying the migration of quantum states across non-compact dimensions, termed “Dimensional Translocation.” By utilizing the machinery of twisted equivariant K-theory, we construct a canonical map relating the spectral flow of a family of twisted Dirac operators to the topological charge of a dimensional rift. We introduce the Morvane-Spectral Sequence, which converges to the obstruction class of the translocation event in the cohomology of the classifying space of the gauge group. We prove that the anomaly cancellation condition for the translocation current is equivalent to the vanishing of the Dixmier–Douady class of a specific gerbe over the translocation manifold. This framework provides a geometric quantization of the leakage of information between branes in a bulk spacetime.