  Accurate knowledge of the thermodynamic properties of zero-temperature,
high-density quark matter plays an integral role in attempts to constrain the
behavior of the dense QCD matter found inside neutron-star cores, irrespective
of the phase realized inside the stars. In this Letter, we consider the
weak-coupling expansion of the dense QCD equation of state and compute the
next-to-next-to-next-to-leading-order contribution arising from the non-Abelian
interactions among long-wavelength, dynamically screened gluonic fields.
Accounting for these interactions requires an all-loop resummation, which can
be performed using hard-thermal-loop (HTL) kinematic approximations.
Concretely, we perform a full two-loop computation using the HTL effective
theory, valid for the long-wavelegth, or soft, modes. We find that the soft
sector is well-behaved within cold quark matter, contrary to the case
encountered at high temperatures, and find that the new contribution decreases
the renormalization-scale dependence of the equation of state at high density.
