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In quantum order finding, a phase $s/r$ produces amplitude $Q^{-1}{\sum }_{x=0}^{Q-1}{e}^{2\pi ix(s/r-j/Q)}$ after an inverse quantum Fourier transform. Its nearest grid point has probability at least $4/{\pi }^2$, by bounding the sine ratio of this finite geometric Fourier amplitude. The initial modular orbit state is an equal-weight superposition of the $r$ phase eigenstates, so the phase label is uniform.