The higher-dimensional Erdős distinct-distances conjecture

For every fixed d ≥ 3, any n ≥ 2 distinct points in ℝ^d determine at least $c_dn^{2/d}$ distinct distances, with $c_d\gt 0$ depending only on dimension. This matches the integer-grid order and resolves the higher-dimensional Erdős distinct-distances conjecture with a constant-factor bound.