Article 4: Vortex Stability and Structure in the PEW Framework: Rigorous Foundations, Self-Adjoint Extensions, and the Hierarchical Dance of Cosmic Vortices

The Primordial Energy Wave (PEW) framework models all physical entities as topological vortex configurations of a single complex scalar field Ψ = ÷exp(iθ). Previous articles established the Lagrangian, derived the gravitational constant (κ²=8π), and computed the fine-structure constant (α_em = 1/137.018, within 0.013% of CODATA). The present article addresses two foundational questions left open: why do these vortex solutions persist, and what is the precise geometric structure of their cores?We first formalise the boundary conditions at the vortex core (ρ→0) using the theory of self-adjoint extensions of singular differential operators, drawing on the Infinitesimally Punctured Geometry (IPG) framework of…