The Absolute Barotropy Vacuum (ABV): Geometric Determinants of Fundamental Constants

This monograph presents a novel, deterministic paradigm in theoretical physics, termed the Absolute Barotropy Vacuum (ABV) or the Silver Torus Model. The work addresses one of the most profound challenges in contemporary physics: the origin of dimensionless physical constants and the mass spectrum of elementary particles. Moving beyond the probabilistic nature of the Standard Model and the complexity of quantum electrodynamics (QED) renormalization, the ABV model proposes that elementary particles are stable, toroidal torsional twists (solitons) within a high-stiffness barotropic superfluid medium (the "neutrino sea"). The central discovery of this theory is the identification of a unique geometric invariant, the Stigma constant (), derived from the silver ratio and octagonal symmetry, which serves as the fundamental scale bolt of reality. Key results and derivations presented in this work include: Analytical derivation of the fine-structure constant () and the anomalous magnetic moment of the electron (aₑ): The model achieves a precision of 10^-12, matching the most recent Penning trap experimental data (Fan et al. , 2023) without the use of free structural parameters. A Unified Baryon Mass Equation: The monograph provides a first-principles derivation of the proton and neutron rest masses with an accuracy of 10^-7 MeV, offering a mechanical explanation for isospin asymmetry and CPT symmetry through the "Silver Bolt" mechanism. Geometric Resolution of Quark Confinement: By analyzing the roots of the Silver Equation of State, the work demonstrates that quarks are complex-conjugate mass bases. Their "confinement" is shown to be a geometric necessity resulting from imaginary vibration amplitudes relative to 3D space. Neutrino Mass Spectrum: The model derives the masses of the three neutrino generations as "imaginary phase shadows" or residual slips of vacuum saturation, providing values consistent with solar and atmospheric oscillation data. By reducing the fundamental parameters of the universe to a single, rigid geometric equation of state, the Absolute Barotropy Vacuum model offers a significant simplification of physical theory (Occam’s Razor), transitioning from a probabilistic framework to a purely deterministic, geometric hydrodynamics of the vacuum.