Zero Closure Was Four-Dimensional: An Interpretive Note on the Geometry and Algebra of Sum x_n^2 = 0

An interpretive note. No new theorems are claimed. Known results are rearranged under the single closure condition Sum x_n^2 = 0 in order to fix what is determined by it and what is not. Claim 0 shows that central projection reduces the many-body zero-closure problem to a single quadratic equality constraint, and that this reduction survives complexification: writing z = q + ip, zero closure is equivalent to |q|^2 = |p|^2 together with q.p = 0, so at fixed C the solution set is the Stiefel manifold of orthonormal 2-frames. Claim 2B states the title of the paper: the basic representation is the four-dimensional (r, t, R, Q), on which zero closure imposes the light cone r^2 - t^2 - R^2 - Q^2 = 0. Claims 4 to 9 collect the geometric statements (parallelotopes satisfy the signed closure, the inertia ellipsoid saturates at multipole l