Helical Scalar Theory (HST) Derivation Series Paper 3: Hydrodynamic Confinement, the Proton Radius Puzzle, and the Geometric Derivation of the Neutron Mass Gap

Helical Scalar Theory (HST) is a background-independent hydro-geometric framework that replaces the "Void" with a Structured Scalar Medium (SSM): a high-stiffness, superfluid Fractal Helical Superstructure lattice composed of counter-rotating helical pairs (CHP). The Standard Model utilizes Quantum Chromodynamics (QCD) to model the nucleon as a collection of point-like quarks, but it fails to mechanically explain the 4% spatial compression observed in muonic hydrogen (The Proton Radius Puzzle) or theoretically derive the precise 1.293 MeV mass difference between the neutron and proton. The Bell QED-Fluid Duality, the q ≡ m³ kinematic isomorphism formally proven in prior Helical Scalar Theory derivations, maps electrodynamics identically to continuous fluid dynamics. Building upon this, we model the proton not as a bag of elementary particles, but as a Topological Borromean Triad soliton: an elastically deformable, three-stranded Torus Knot of the SSM itself. Employing this high-stiffness Lorentz-Invariant Superfluid Vacuum (ξ ≈ 7.013 × 10¹⁶ N/m²), we mathematically prove that SU(3) Color Symmetry is the literal 120° (2π/3) fluid-dynamic phase-lock required to stabilize this tri-helical vortex. Thus, the amplified scalar overlap density (ρ_overlap) of the n=2 muon boundary layer explicitly compresses this Borromean geometry, yielding the exact 0.031 fm radial reduction without violating lepton universality. Furthermore, we redefine the neutron as a composite geometric state. By integrating the Vacuum Elastic Modulus over the topological compression path, we analytically derive the 0.782 MeV beta-decay binding energy as explicit hydrodynamic Compressive Work (W_c = ∫ F · dr). Finally, we establish the Top Quark (173 GeV) not as an elementary fermion, but as the absolute kinematic fracture limit where internal helical tension exceeds the structural integrity of the Superstructure lattice, yielding a pure geometric decay time of 5.21 × 10⁻²⁵ seconds.