Title: Nuclear Shell Structure and the Island of Stability from Topological Soliton Theory Author: Alexander Novickis (alex.novickis@gmail.com) We develop a topological account of nuclear shell structure, the binding energy curve, and the predicted island of stability within the Faddeev-Niemi soliton framework on the flag manifold $F_2 = \mathrm{SU}(3)/[\mathrm{U}(1) \times \mathrm{U}(1)]$. A nucleus with $Z$ protons and $N$ neutrons is identified with a multi-soliton configuration of Hopf charge $H = A = Z + N$. We show that the nuclear magic numbers $\{2, 8, 20, 28, 50, 82, 126\}$ correspond to topological shell closures --- configurations where adding one further unit of Hopf charge requires a qualitatively different soliton geometry, producing an energy gap analogous to the shell gaps of the conventional nuclear shell model. The first three magic numbers ($2, 8, 20$) emerge from the harmonic spectrum of the mean soliton field and match the closed-shell geometries identified in the Battye-Sutcliffe Skyrmion catalogue. The higher magic numbers ($28, 50, 82, 126$) require spin-orbit splitting, which we trace to the off-diagonal moduli space metric coupling soliton internal orientations to orbital motion --- a Berry-phase effect intrinsic to the topological structure. The semi-empirical mass formula $B(A,Z) = a_V A - a_S A^{2/3} - a_C Z(Z-1)/A^{1/3} - a_A(A-2Z)^2/A + \delta(A,Z)$ is derived term-by-term from the soliton framework (Paper XXXIV), and we extend this analysis to the superheavy region. The island of stability --- predicted by nuclear structure models around $Z = 114$, $N = 184$ --- is interpreted as the next major shell closure beyond $H = 126$, where the multi-soliton configuration recovers enhanced polyhedral symmetry. We estimate the shell stabilisation energy, compare with the Finite Range Droplet Model (FRDM) and relativistic mean-field (RMF) predictions, and identify the lattice computations required to make quantitative predictions. All results beyond the semi-empirical mass formula are conditional on multi-soliton lattice computation at large $H$; we distinguish clearly between framework predictions and computational targets. Series: Paper CXVII in the Hopf Soliton Programme