Topological Residue, Readout Functor, and the Layered Origin of the Fine-Structure Constant

Within the GDUM layered architecture, topological residue and geometric residue belong to entirely distinct ontological layers. The topological residue (Kⁿ², Kⁿ²_em) is defined on the Layer-1 pre-geometric layer: it is the homotopy-lifting obstruction arising from the covering section's deviation from the ideal integrable CST benchmark. It does not depend on any metric information such as the metric tensor, curvature, or spacetime coordinates; it is invariant under continuous topological deformation and constitutes the theory's native, underlying deviation structure. By contrast, the geometric residue belongs entirely to the Layer-2 emergent spacetime: it is the metric perturbation of the metric, curvature, and connection relative to a reference geometry. Geometric deviation is a derived, representational residue: it can be generated either by projecting the underlying topological residue, or by purely metric deformation that contains no topological obstruction. Therefore: the topological residue is the source; the geometric residue is the image; and there is no one-to-one invertible mapping between them.