Area convergence of Voronoi cells on spiral lattices

The paper proves j^{1-2α}|V(z_j,S)| → 2πα (with an O(j^{-1/2}) relative error) by linearizing to a suitable lattice and controlling Voronoi areas under a precise perturbation scheme. The candidate solution correctly identifies the nearest-neighbor scale and obtains a disk-sandwich for the union of cells, but then makes an unjustified leap: from S(J)=πJ^{2α}+O(J^{2α−1/2}) it concludes |V(z_J)|=S(J)−S(J−1)=2παJ^{2α−1}+O(J^{2α−3/2}). Without additional regularity to control successive errors, this step does not follow; the boundary-error term can dominate the first difference. Hence the model’s proof is incomplete for the claimed limit and error term, while the paper’s argument is complete and correct.