Hadronic Structure from Hopf Vortex Topology: Magnetic Moment Ratio, Deuteron Binding Energy, Effective Radius, and the Hadronic Shell as a Galactic-Scale Analogue

The Primordial Energy Wave (PEW) framework models nucleons as Hopf vortices on a torus with R/r = φ (golden ratio), with ξp = 0.367 fm. This article derives three hadronic observables from first principles, with no free parameters, and introduces a fourth contribution (new in v2): (1) μn/μp = −2/3 [A★★★] from SU(2)isospin. Agreement: 97.3%. Residual 2.7%. (2) BD = 3π/φ³ = 2.2246 MeV [B★★] from Chern-Simons action on S³. Agreement: 99.987% (0.3 keV). (3) reff(D) = ξp·φ⁴ = 1.755 fm [B★★] from Bethe-Peierls + OPEP tensor. Agreement: 99.97%. (4) The hadronic shell correction [B★★]: the three residuals are interpreted as the contribution of the distributed amplitude field ò(r) surrounding each nucleon vortex — the hadronic shell — in direct analogy with the galactic operculum shell of Article 7. The shell fraction δshell ~ 1/κ²p ≈ 4% provides a unified PEW explanation of the 2.7% magnetic moment discrepancy and the sub-per-cent deuteron residuals. (5) The universal shape hierarchy [B★★]: sphere (J→0, stars) → Hopf torus (hadronic J, nucleons) → spiral operculum (galactic J, galaxies), governed by R = J²/(GM³r). Numerical check: RSun ≈ 2×10⁻⁶ ≪ 1 (sphere ✓); Rproton ≈ 2×10¹⁹ ≫ 1 (torus ✓). MSC: 81V35 · 81T13 · 22E70 · 85A15 PACS: 21.10.Dr · 21.45.-v · 14.20.Dh · 21.30.-x · 98.35.Df