  We consider the mass-critical generalized Korteweg--de Vries equation
$$(\partial_t + \partial_{xxx})u=\pm \partial_x(u^5)$$ for real-valued
functions $u(t,x)$. We prove that if the global well-posedness and scattering
conjecture for this equation failed, then, conditional on a positive answer to
the global well-posedness and scattering conjecture for the mass-critical
nonlinear Schr\"odinger equation $(-i\partial_t + \partial_{xx})u=\pm
(|u|^4u)$, there exists a minimal-mass blowup solution to the mass-critical
generalized KdV equation which is almost periodic modulo the symmetries of the
equation. Moreover, we can guarantee that this minimal-mass blowup solution is
either a self-similar solution, a soliton-like solution, or a double
high-to-low frequency cascade solution.
