raulchiclano/Dynamic-Background-Hypothesis: DBH v5.0 Beta: Mass Hierarchy and Structural Invariants Unification

We present the Beta version of the Dynamic Background Hypothesis (DBH) v5.0, a refined unified field framework that transitions from a descriptive model to a predictive structural theory. This release completes the unification of the mass sector, demonstrating that mass hierarchies emerge from first-principles vacuum rheology rather than from free parameters. Key breakthroughs included in this version: Mass Hierarchy & Natural Units Identification of the electron as the natural unit of mass ($M_e \approx 1/\phi$), establishing the functional zero of the substrate's energy scale. Structural Mass Ratios Emergence of the proton–electron ratio (~1836) as a consequence of geometric extension and confinement rigidity, rather than constituent mass addition. Law of Vacuum Containment Formalization of mass not as an intrinsic property, but as the integrated energy debt required to stabilize topological defects below the substrate's rupture threshold. Dimensional Evasion Mechanism Demonstration that the hadronic scale jump ($\sim 10^3$) arises from a transition in effective stress dimensionality, from 0D (point-like) to 1D (string-like) configurations. Structural Invariants & Parameter Robustness Computational validation of a bare elastic invariant (~79.00) with sensitivity below 0.13 % under variations of vacuum stiffness ($\beta$) and confinement strength ($\sigma$). Gauge Dressing Hypothesis (Ongoing) Evidence that the numerical scale associated with the fine structure constant ($\alpha^{-1} \sim 137$) may emerge as a gauge-dressed manifestation of the elastic invariant in a three-dimensional vacuum. The full field-theoretic formalization of this correspondence remains an active line of investigation. This release provides the complete computational and conceptual framework for the mass sector, establishing the DBH as a self-consistent, predictive, and thermodynamically grounded approach to fundamental physics.