  We review the basic assumptions and spell out the detailed arguments that
lead to the bound on the Regge growth of gravitational scattering amplitudes.
The minimal extra ingredient compared to the gapped case - in addition to
unitarity, analyticity, subexponentiality, and crossing - is the assumption
that scattering at large impact parameters is controlled by known
semi-classical physics. We bound the Regge growth of amplitudes both with the
fixed transferred momentum and smeared over it. Our basic conclusion is that
gravitational scattering amplitudes admit dispersion relations with two
subtractions. For a sub-class of smeared amplitudes, black hole formation
reduces the number of subtractions to one. Finally, using dispersion relations
with two subtractions we derive bounds on the local growth of relativistic
scattering amplitudes. Schematically, the local bound states that the amplitude
cannot grow faster than $s^2$.
