The extremal zero configurations equidistribute: wrapped-angle std approaches pi/sqrt(3)=1.8138 (uniform value; measured 1.834/1.808/1.820 at n=32/64/128), arc-occupation fractions match the uniform measure, and nearest-neighbor gaps approach 2pi/n (normalized min gap 0.96-0.99; at n=120 normalized gaps lie in [0.94,2.19] with std 0.11). Since the exact lattice configuration has energy exactly 3/2, the Theta(n) extremal energy lives in O(1/n)-scale fluctuations invisible to the weak limit of the zero measure: the fixed-measure variational route (rounds 1-2 next-direction, this round's route 2) is degenerate as stated, and the correct limit object is a translation-invariant unit-intensity point process on R. Supporting heuristic (not a theorem): Laplace asymptotics give only O(sqrt n) energy for any smooth non-uniform limiting density. Angle statistics only (no exact-convolution evaluation); numerical, optimizer-based.