A Unified Quantum-Gravity Theory of Geometric Monism: Structured Spacetime Manifolds and Topological-Sector Screening

Addressing the ontological divide between general relativity and quantum mechanics, this paper constructs a geometric-monism framework in which the unique fundamental physical reality of the universe is the four-dimensional smooth, orientable Lorentzian manifold. Elementary particles are interpreted as stable configurations of localized high-curvature gravitational solitons of spacetime, and matter waves as spacetime-curvature perturbation fields excited by soliton motion. Relying on a topological-sector coexistence mechanism and an observation-induced topological locking effect, path-integral methods are used to elucidate the physical nature of quantum superposition and wavefunction collapse in quantum measurement. Starting from a higher-curvature gravitational action, the geometric-dynamical field equations are derived, the paradigm of an independent matter stress–energy tensor is discarded, and wave–particle duality together with the de Broglie relation is derived self-consistently along a purely geometric route. A conditional scaling prediction for the mean spacetime curvature of the electron is given; its static-soliton premise receives no support within the static vacuum sector (Appendix B), and the prescribed turn to the time-dependent sector has now been executed: a universal family of long-lived oscillon-type curvature solitons is shown to exist in the f(R)-equivalent scalaron slice, the classical-family extrapolation to the electron workpoint is excluded by the Kaup bound by at least nineteen orders of magnitude, and the curvature-window prior [0.01, 1] is conditionally calibrated. The fixing of particle masses accordingly devolves to the topological-locking module. Several readily implementable, rigorously falsifiable precision-physics experimental schemes are designed. Upholding spacetime-geometry determinism, the theory ascribes quantum statistical-probability effects to the observation system's inability to access the full global topological information, achieving a globally self-consistent unification of spacetime, matter, gravity, and the quantum-measurement framework.