Bootstrapping the String Kawai-Lewellen-Tye Kernel

We show that double-copy maps for amplitudes in effective field theory are severely constrained at four points by self-consistency and locality six points. The resulting kernel depends only on two parameters as well a specific symmetric function $s$, $t$, $u$ interpolates between the original Kawai-Lewellen-Tye (KLT) string double copy open closed period integrals. Amplitudes copied with this map must obey either monodromy relations or Kleiss-Kuijf (KK) Bern, Carrasco, Johansson (BCJ) relations; there no other options. Our construction elucidates ``single-valued projection'' property of Riemann zeta-function values four-point copy.