From Cosmological Viscosity to the Strong Interaction Scale Resolution of Dirac's Hierarchy, Proton Mass, and Zero-Parameter Nuclear Binding in the OHV Framework
Year: 2026
Type: preprint
Abstract: Dirac’s Large Numbers Hypothesis highlights an unexplained 39-order-of-magnitude chasm between gravitational and electromagnetic interactions at the femtometer scale. Within the Optico-Hydrodynamic Vacuum (OHV) framework, we demonstrate that this hierarchy can be formulated as a non-linear Liouville-Yukawa phase screening condition across the boundary of a localized baryonic soliton in a continuous compressible substrate. Using the fundamental dimensionless longitudinal-to-transverse wave speed ratio eta(cosmo) = c(s)/c = 0.004182 and the strictly frozen Hubble attenuation radius R(H) = 1.2843 x 10^26 m (4162.1 Mpc, calibrated on Type Ia supernovae), we characterize the screening boundary action S(screen) = 89.8612 and prove analytically that the macro-micro bridge invariant equals the exact geometric form factor of a spherical soliton, I(bridge) = 310 / pi = 0.94248. This locks the proton mass M(p) to the proton charge radius a(0) = 0.8414 fm and cosmological parameters with 0.051% precision (0.42% at the nominal reference scale R(H)^(ref) = 1.2796 x 10^26 m). Furthermore, projecting the 1D longitudinal coupling onto the 3D Euclidean space diagonal (eta(3D) = sqrt(3) * eta(cosmo)) yields both the fine-structure constant scale alpha^(-1) (OHV) = eta(3D)^(-1) - 1 = 137.056 (0.015% accuracy) and a nuclear binding energy law free of continuous regression parameters, anchored at the discrete structural shell closures ^4He (A(base) = 4) and ^56Fe (A(peak) = 56). Evaluated across stable isotopes from AME2020, the model achieves a 95.0% median accuracy (mean error 3.3-3.7%) and passes 500-iteration bootstrap and permutation significance controls (p < 0.002) for shell closure residual structures.
Author: Paygachkin, Sergey Yurevich
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223690978