  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.
