The Elasto-Hydrodynamics of the Proton: Absence of Membrane, Barometric Respiration, and Electronic Valve through the E=PV Law

The Standard Model of particle physics treats the proton either as an immutable rigid structure or as a blurred cloud of mathematical probabilities, running into insoluble contradictions such as the "proton radius puzzle". Drawing upon the Kenophobia paradigm, this paper demonstrates that the proton is a purely hydrodynamical entity lacking any rigid membrane or skin. Anchored in a fractal universe governed by the principle of Maximum Entropy Production (MEP) and Universal Darwinism, the proton is revealed to be a stationary toroidal vortex (triangular Hill’s vortex) composed of 919 e⁺/e⁻ pairs and a single central positron (totaling 1839 electron masses). Through the unified thermodynamic equation: E = Mₚ · c² = Pᵥ · V we establish how the steric volume of its Hill sphere dynamically and elastically adapts to variations in vacuum pressure Pᵥ. This fluid and fractal model: Resolves the proton radius puzzle recorded at the Paul Scherrer Institute (2010) by explaining the radius contraction from 0.877 fm (electronic spectroscopy) to 0.841 fm (muonic spectroscopy) as a direct barometric compaction (Pᵥ increasing locally from 5.33 × 10³⁴ Pa to 6.02 × 10³⁴ Pa) caused by the kinetic stress of the heavy muon. Establishes the natural respiration radius at terrestrial rest at R = 0.981 fm for a baseline pressure of the depleted Plenum of Pᵥ = 3.8 × 10³⁴ Pa. Assigns to the peripheral electron the role of a mechanical regulating valve, adjusting its orbit onto the exact interface where internal centrifugal pressure balances the confinement of the Plenum. Builds a direct fractal bridge to black hole astrophysics, modeling Sagittarius A* (Sgr A*) as a polyhedral macro-hadronic core measuring 4088 km in diameter under a critical density of 2.3 × 10¹⁷ kg/m³.