🔢 Sum of Three Squares - Lattice Points on Spheres: Legendre Zeros, Gauss Class-Number Formula and the 4/3 pi R^3 Count (2D)

Count integer points with x^2+y^2+z^2 = n: bar chart of r3(n) with Legendre's gaps at 4^a(8b+7), checked against the Gauss-Hurwitz class-number formula and the 4/3 pi R^3 volume law, with layer-by-layer circle counts.