Two-dimensional projections of the adaptive four-dimensional grid in spherical-orbit space {r, v_r, v_Ω, ψ}, depicting 192,204 trial orbits. Higher cell density indicates regions where nearby orbits diverge rapidly on-sky, requiring finer subdivision to maintain the angular tolerance ε over the observational baseline. Grid parameters (ΔT, ε) match those used in the DES SN-X3 search before any dynamics-based orbit pruning. A single value of v_r = 0 is sufficient for this search, reflecting the relatively much larger importance of on-sky velocity for relatively short time baselines.