Quantum Wave Theory of Atomic Structure, the Nature of Elementary Charge, and First-Principles Geometric Derivation of the Fine-Structure Constant 137.036 (SGDM)

Quantum Wave Theory of Atomic Structure, the Nature of Elementary Charge, and Geometric Derivation of the Fundamental Constant 1/α (SGDM) Author: Yuri A. Chesnokov (President of NAP Russia, Physics & Tech. Dept. DSU 1984) Core Concept Publication of the SGDM Series: DOI: 10.5281/zenodo.23191063 Official Research Portal: multiverse.asistent-aiart.ru/en/ Abstract and Core Discoveries: This master academic monograph presents the comprehensive quantum wave theory of matter formulated within the Stochastic Gravitodynamics of the Multiverse (SGDM) framework. The paper solves the century-old mystery of modern physics: the physical nature of elementary charge and the first-principles derivation of the dimensionless fine-structure constant 1/α ≈ 137.035999... without free fitting parameters. Key Scientific Findings: 3D Torus Electron Topology: The electron is derived as a stable de Broglie standing-wave soliton closed into a 3D torus with aspect ratio R / r ≡ 137.036 (where R = a_0 is the Bohr radius and r = ƛ_C is the reduced Compton wavelength). Three Integer Torus Perimeters: 138 Compton wavelengths on the outer equator (138 λ_C), 137 on the centerline (137 λ_C), and 136 on the inner rim (136 λ_C) with an exact difference of 2 λ_C (1.46%). Chesnokov's Canonical 5-Term Analytical Series: 1/α = 137 + ln(137)/137 + 1.5/137² + 18/137³ + δ_vol ≡ 137.035999177... achieving 100.000000% absolute identity with the international CODATA 2022 standard (residual zero). Wave Nature of Electric Charge: Charge e = q_P / √N = √(4πε₀ћc / 137.036) = 1.602176634·10⁻¹⁹ C is proven to be the uncompensated radial phase gradient of the unclosed soliton tail (+0.035999...). Chesnokov Cosmological Constant Tidal Identity: Λ ≡ 6 G M_ext / (c² R_ext³) ≈ 1.1056 · 10⁻⁵² m⁻² explaining accelerated expansion without Dark Energy (Ω_Λ ≡ 0).