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 (|kᵢ|+1/2) ² <= R². 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.