About this ebook
This volume establishes the geometric and analytic foundations of infinitesimally punctured manifolds. It introduces the weak–strong decomposition of geometry, in which smooth differential structure coexists with defect-supported distributional curvature on measure-zero sets. Classical singularities are reinterpreted as punctures carrying finite, integrable curvature, replacing divergent invariants with well-defined distributional objects. The book develops codimension-based classification of defects, holonomy effects, regularisation via smooth metric families, and the structural Neutrosophic triad as a geometric—not yet dynamical—decomposition.
A substantial portion of the volume is devoted to operator theory on punctured manifolds, including self-adjoint extensions of Laplace-type operators, spectral stability, defect-induced bound states, and scattering without external potentials. Explicit low-dimensional toy models—punctured circles, conical planes, and point defects in three dimensions—demonstrate how geometry alone generates observable analytic consequences. This book contains no field equations and no cosmological models; its purpose is to provide a rigorous, self-contained mathematical groundwork upon which the subsequent volumes build.
