  The space of Wilson coefficients of EFT that can be UV completed into
consistent theories was recently shown to be described analytically by a
positive geometry, termed the EFThedron. However, this geometry, as well as
complementary numerical methods of semi-definite programming, have so far
focused on the positivity of the partial wave expansion, which allows bounding
only ratios of couplings. In this paper we describe how the unitarity upper
bound of the partial waves can be incorporated. This new problem can be
formulated in terms of the well known $L$-moment problem, which we generalize
and solve from a geometrical perspective. We find the non-projective
generalization of the EFThedron has an infinite number of non-linear facets,
which in some cases have remarkably simple descriptions. We use these results
to derive bounds on single couplings, finding that the leading derivative
operators are bounded by unity, when normalized by the cut-off scale and loop
factors. For general operators of mass dimension $2k$ we find the upper bound
is heavily suppressed at large $k$, with an $1/k$ fall-off.
