  We show that the single trace heterotic N-point tree-level gauge amplitude
A_HET can be obtained from the corresponding type I amplitude A_I by the
single-valued (sv) projection: A_HET=sv(A_I). This projection maps multiple
zeta values to single-valued multiple zeta values. The latter represent a
subclass of multiple zeta values originating from single-valued multiple
polylogarithms at unity. Similar relations between open and closed string
amplitudes or amplitudes of different string vacua can be established. As a
consequence the alpha'-expansion of a closed string amplitude is dictated by
that of the corresponding open string amplitude. The combination of
single-valued projections, Kawai-Lewellen-Tye relations and Mellin
correspondence reveal a unity of all tree-level open and closed superstring
amplitudes together with the maximally supersymmetric Yang-Mills and
supergravity theories.
