Residual Geometry (RG 0.4.6): Structural Residuals, Resolution, and Reconstruction

This work develops a structural framework for analyzing how distinctions, relations, and residual information are preserved, transformed, or lost under changes of scale, representation, and resolution. It introduces a typed geometry of structural transitions, including horizontal and inter-level transport, boundary continuation, global consistency, and reconstruction from incomplete information. Particular attention is given to singular limits, structural ambiguity, the distinction between representation and physical realization, and the conditions under which local structures can be consistently assembled into a global system. The framework combines formal mathematical constructions, conditional results, and open problems, providing a foundation for further investigation of geometric, dynamical, and information-theoretic structures.