  We use harmonically trapped systems to find the leading gradient corrections
of the supefluid local density approximation (SLDA) - a density functional
theory (DFT) describing the unitary Fermi gas (UFG). We find the leading order
correction to be negative, and predict the q^2 coefficient of the long-range
static response c = 1.5(3) - a factor of two smaller than predicted by
mean-field theory - thereby establishing a new and experimentally measurably
universal constant.
