Infinitesimal Punctures, 3: Infinitesimally Punctured Structures. S-MultiSpace and S-MultiStructure, Hybrid Variational Principles, and Topological Matter

This volume elevates the framework to a unified structural and meta-geometric level. Drawing on Smarandache multi-space concepts and Neutrosophic logic, it develops a rigorous theory of S-MultiSpaces and S-MultiStructures in which multiple geometric regimes coexist within a single manifold. Neutrosophic differential geometry, hybrid connections, and generalized curvature tensors are constructed, together with modified Gauss–Codazzi relations and Smarandache variational principles.

This volume situates infinitesimally punctured geometry within a broader mathematical landscape that includes topology, holonomy, generalized algebras, and spectral reconstruction of geometry. It provides the formal completion of the trilogy, demonstrating how the structural triad underlying punctured manifolds leads to a coherent, logically consistent framework for matter, fields, and spacetime.