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) A (x, t) A~ (x, t) and a phase θ (x, t) (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 C₋₎₂₀₋ (x) = C₀ A (x) / Aₕ₀₂C~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 () C (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) ∝rₑ (r) 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