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The curve is the differentiable phase-dispersion (lower = more coherent fold). Markers: true P, P/2 (the Lomb–Scargle peak), 2P, and the diurnal aliases. Narrow bandwidth = the real, spiky landscape: nearly flat everywhere with razor-thin dips, so gradient descent has no slope to follow and stalls. Wide bandwidth = smooth but the dips wash out and shift to aliases. Either way, gradient descent almost never finds the true period — which is why period search uses dense grid scans, not optimization.