The Pavesi Unified Framework: A Fully Regular Gaussian-Smoothed Anisotropic Geometry, Exact Curvature Control, and Quantum Topological Transport

We introduce a fully regular, Gaussian-smoothed anisotropic spacetime geometry that unifies traversable wormholes, non-singular black-hole analogues, and central anisotropic cosmologies within a single analytic framework. The Pavesi Unified Framework (PUF) implements a finite-width Gaussian transition layer ensuring the finiteness of all curvature invariants and the strict localization of energy-condition violations.We derive in closed form the Christoffel symbols, Ricci and Einstein tensors, curvature invariants, geodesic structure, and the full Dirac-Pavesi equation. The Gaussian layer induces a geometry-driven effective mass suppression and a quantum potential well that enhances tunneling and information transport.We compare the PUF with non-commutative geometry, loop quantum gravity, asymptotic safety, and regular black-hole models, showing that PUF achieves regularization through a purely geometric mechanism without modifying Einstein’s equations or introducing new degrees of freedom.