Radius Sweep of Fully-Inscribed Unit-Cell Counts on a 4-Dimensional Lattice: An Enumeration Table from R = 0.5 to 10.0 with a Reproducible Formulation

We count the number of unit 4-cells on the 4-dimensional integer lattice that are fully inscribed in a 4-dimensional hyperball of radius R, i.e. the cells satisfying sum (|k_i|+1/2)^2 <= R^2. We tabulate N0(R) for R = 0.5, 1.0, ..., 10.0, together with the circumscribing diameter 2R and the stacked-cell diagonal length 2 rho(R), and give a reproducible algorithm and an accompanying CSV. In particular N0(1)=1, N0(2)=9, N0(3)=137. This is a purely geometric / integer-lattice enumeration and asserts no correspondence to physical constants.