We study the space of open string effective field theories by combining the
constraint of unitarity and monodromy relations for the four-point amplitude.
The latter is a reflection of an underlying disk correlator with singularities at the
boundary. By assuming maximal SUSY, the resulting bootstrap isolates Wilson
coefficients to at least 10^{−4} of the Type-I superstring. Furthermore, utilizing our
geometric approach, we obtain the critical dimension of 10 from the low energy
coefficients alone. Remarkably, relaxing SUSY but requiring the massless states
to carry four-dimensional helicities, the Wilson coefficients are again constrained
to superstring values within 10^{−4}. Thus we conclude that type-I string theory
is the unique solution to the monodromy bootstrap with either maximal susy
or vector external states. We also introduce Tachyons to the bootstrap and
demonstrate for the scattering of external vectors, the bosonic and superstring
span the allowed region. Allowed regions for closed string effective field theories
are obtained by implementing the KLT relations.