Atomic Curvature and Periodic Stability under the Aperture–Well Unification Theory (AWUT)

The Aperture–Well Unification Theory (AWUT) is applied to nuclear structure using first-principles geometric derivations from the same constants that govern galactic rotation. Wederive binding energies B/A from stitched Red-bubble geometry without empirical nuclear fit-ting. The curvature index C = A2/3(1 + ΠP ) emerges from 5D projection geometry with Purpleoverlap ΠP computed from proton-neutron arrangements. Using only the universal constantsη = 4.482, ξ = 3.10, and the 4/3 stitched area factor from galactic fits, AWUT predicts theFe–Ni stability peak and reproduces binding energies with RMS residual of 0.8 MeV per nu-cleon. Magic numbers (2, 8, 20, 28, 50, 82, 126) emerge naturally from 5D rail quantization withthe single-twist constraint (Planck-Stop). This links cosmic and nuclear scales through unifiedgeometric principles.