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We calculate Sorkin's spacetime entanglement entropy of a Gaussian scalar field for complementary regions in the 2d cylinder spacetime and show that it has the Calabrese-Cardy form. We find that the cut-off dependent term is universal when we use a covariant UV cut-off as in [1]. In addition, we show that the relative size-dependent term exhibits complementarity. Its coefficient is however not universal and depends on the choice of pure state. It asymptotes to the universal form within a natural class of pure states.