  We revisit the tree-level closed superstring amplitude and identify its
alpha'-expansion as series with single-valued multiple zeta values as
coefficients. The latter represent a subclass of multiple zeta values
originating from single-valued multiple polylogarithms at unity. Moreover, the
alpha'-expansion of the closed superstring amplitude can be cast into the same
algebraic form as the open superstring amplitude: the closed superstring
amplitude essentially is the single-valued version of the open superstring
amplitude. This fact points into a deeper connection between gauge and gravity
amplitudes than what is implied by Kawai-Lewellen-Tye relations. Furthermore,
we argue, that the Deligne associator carries the relevant information on the
closed superstring amplitude. In particular, we give an explicit representation
of the Deligne associator in terms of Gamma functions modulo squares of
commutators of the underlying Lie algebra. This form of the associator can be
interpreted as the four-point closed superstring amplitude.
