 Asymptotic minimum speed of an unbound Kepler orbit

For a positive-mass object in the inverse-square attractive field with potential zero at infinity, energy conservation gives $v^2(r)=2E/m+2GM/r$. Along the outgoing unbound branch, speed decreases toward the displayed limiting value. It is positive for a hyperbola and zero for a parabola. This is an infimum approached at infinite separation, not a finite-radius stopping point or the local escape velocity.