  How does nuclear binding emerge from first principles? Our current best
understanding of nuclear forces is based on a systematic low-energy expansion
called chiral effective field theory. However, recent {\it ab initio}
calculations of nuclear structure have found that not all chiral effective
field theory interactions give accurate predictions with increasing nuclear
density. In this letter we address the reason for this problem and the first
steps toward a solution. Using nuclear lattice simulations, we deduce the
minimal nuclear interaction that can reproduce the ground state properties of
light nuclei, medium-mass nuclei, and neutron matter simultaneously with no
more than a few percent error in the energies and charge radii. We find that
only four parameters are needed. With these four parameters one can accurately
describe neutron matter up to saturation density and the ground state
properties of nuclei up to calcium. Given the absence of sign oscillations in
these lattice Monte Carlo simulations and the mild scaling of computational
effort scaling with nucleon number, this work provides a pathway to
high-quality simulations in the future with as many as one or two hundred
nucleons.
