ATPEW — Unifying Space-Time, Gravity, and Quantum Mechanics through a Primordial Energy Wave (Version 10, Major Theoretical Revision)

We present Version 10 of the Aldon Theory of Primordial Energy Waves (ATPEW), a unified theoretical framework in which spacetime, gravity, quantum phenomena, and particle structure emerge from a single underlying scalar field — the Primordial Energy Wave — characterized by a real amplitude A~(x,t)\tilde A(x,t)A~(x,t) and a phase θ(x,t)\theta(x,t)θ(x,t). In ATPEW, time and gravitational dynamics arise from spatial variations of a local propagation speed C~local(x)=C~0A~(x)/A~vac\tilde C_{local}(x) = \tilde C_0 \tilde A(x)/\tilde A_{vac}C~local(x)=C~0A~(x)/A~vac. Matter corresponds to stable topological configurations (Hopf vortices) of the underlying field. Version 10 introduces major theoretical developments: • Explicit covariant Lagrangian formulation with conserved Noether phase current• Full derivation and numerical solution of the radial Euler–Lagrange equation for the vortex profile• Analytical proof of the universal near-core scaling u(ρ)∼Cρu(\rho) \sim C\sqrt{\rho}u(ρ)∼Cρ• Geometric torus closure condition fixing the proton radius• Correction of the κ² parameter relative to Version 4• Derivation of the fine-structure constant from Hopf fibration geometry (99.44% agreement)• Harmonic mass spectrum reproducing electroweak bosons and baryons with >99% agreement• Emergent gravitational constant from wave properties• Testable prediction for proton core charge density scaling ρe(r)∝r\rho_e(r) \propto rρe(r)∝r The framework remains fully falsifiable and confronts observational and experimental data across multiple regimes, including particle physics, gravitational dynamics, and astrophysical structure. This version supersedes Version 4 (January 2026) by providing the complete radial solution, geometric closure mechanism, and corrected parameter structure. Aldon, M. (2026). Unifying Space-Time, Gravity, and Quantum Mechanics through a Primordial Energy Wave. Zenodo. DOI: 10.5281/zenodo.18296240