We derive the shell capacity sequence Cn = 2n2 from a geometric definition of shells via the shell-closure condition on a spiral corridor traversing a cone interior. The closure condition determines two geometric quantities: the step fraction δn = 1/n (the fraction of a full revolution represented by one step at the n-th shell) and the cone deficit angle αn = 1 − 1/n (related by αn = 1 −δn). These imply Nn = n tile positions per revolution. The derivation requires one additional structural assumption: that the n-th shell contains exactly n concentric revolutions. This assumption is stated explicitly and its geometric origin is discussed; its derivation from first principles is deferred to subsequent work. Given this assumption and the two-state perpendicular structure of the physical class, the closure condition yields Cn = 2n2 for n ≥ 2, matching the electron shell capacities of the chemical elements and the prior algebraic derivation in the literature.