  Effective field theories (EFT) parameterize the long-distance effects of
short-distance dynamics whose details may or may not be known. It is known that
EFT coefficients must obey certain positivity constraints if causality and
unitarity are satisfied at all scales. We explore those constraints from the
perspective of 2 to 2 scattering amplitudes of a light real scalar field, using
semi-definite programming to carve out the space of allowed EFT coefficients
for a given mass threshold M. We point out that all EFT parameters are bounded
both below and above, effectively showing that dimensional analysis scaling is
a consequence of causality. This includes the coefficients of four- and
six-derivative interactions. We present simple extremal amplitudes which
realize, or "rule in", kinks in coefficient space and whose convex hull span a
large fraction of the allowed space.
