Nilpotent Defect Cores: Hierarchy, Obstruction and Singular Geometry

This monograph develops a structural framework for defect geometry, beginning with nilpotent defect cores and advancing through carrier geometry, sheaf-theoretic globalization, stratified correction theory, microlocal defect geometry, and defect-face bridge analysis. The theory is organized in three stages: local defect algebra, global defect geometry, and microlocal defects. At the bridge level, the manuscript establishes full Route A closure, determines the structural boundary of Route B in the actual three-dimensional prototype, and records an exact collar-local model in which the model-specific bridge tasks P1-P4 are fully closed. The remaining analytic frontier is explicitly isolated for arbitrary target geometric models beyond that exact model.