APM Nuclear Shells from Holonomy: QMU Curvature–Torsion Quantization, Nuclear g-Factors, and the Vajra Periodic Mapping

This paper develops a complete, QMU--ledger closed nuclear shell model derived directly from Aether holonomy.  A single curvature quantization rule, \[ Iκ,s = s - 1, \] generates the full nuclear shell hierarchy: spins \[ ja,s = s - 12, jb,s = s - 32, \] degeneracies \[ N_s = 4s - 2, \] and cumulative closures \[ N≤ S = 2S^2, \] which reproduce the magic numbers when proton and neutron shells are counted together.  These relations arise entirely from the geometry of closed loxodromic Aether modes. Torsion is introduced as a companion invariant, \[ Iτ,s,x = ± Δs,x, \] and acts as a geometric control parameter.  It produces: $a/b$ subshell splitting, isotopic shifts in nuclear g--factors, the onset of nuclear deformation when torsion becomes comparable to curvature. The shell g--factor is obtained from the same holonomy machinery that governs the electron and proton, \[ gs,x = 2Rs,x [ 1 + {χ_x(cκ(s-1) + cτIτ,s,x)}{16π^2} ], \] where χₓ = e²/eₑmax² and Rs,x is a geometric projection factor.  Nuclear magnetic moments follow directly as \[ μs,j,x = gs,x\,χ_x\,j\,magm_x. \] The paper provides QMU--closed analyses for ⁴He, ¹⁶O, ⁴⁰Ca, ¹⁷O, ⁴¹Ca, and ¹³¹I, including moment ratios such as \[ {μ̃({}⁴¹Ca)}{μ̃({}¹⁷O)} ≈ 5/3, \] which arise directly from the holonomy spin ladder. A holonomy--to--Vajra mapping algorithm is introduced, showing that the block widths and wave structure of the Vajra and Pauling--sphere periodic tables follow from the same curvature closures 2S² that govern nuclear shells.  Electronic periodicity is therefore a projection of nuclear Aether holonomy. The appendix derives torsion gradients and second differences, \[ Gs,x = Δs+1,x - Δs,x, H(τ)s,x = Δs+1,x - 2Δs,x + Δs-1,x, \] and uses them to construct a QMU deformation indicator, \[ Ds,x = {cτΔs,x}{cκ(s-1)}, \] showing how spherical, moderately deformed, and strongly deformed regimes appear naturally from holonomy.  A Nilsson-like energy ledger is constructed, demonstrating how deformed nuclear spectra and band structures arise from the torsion pattern of Aether centerlines. Finally, a QMU binding-length functional and QMU nuclear-radius scaling are proposed, both derived solely from the curvature index S and the torsion imbalance Δs,x.  These provide a roadmap for QMU--only predictions of nuclear masses and radii in future work. Overall, the paper establishes that nuclear shells, magnetic moments, electronic periodicity, deformation, and geometric energy scaling all emerge from a single holonomy principle in the Aether Physics Model.