  High-order perturbative calculations for thermodynamic quantities in QCD are
complicated by the physics of dynamical screening that affects the soft,
long-wavelength modes of the system. Here, we provide details for the
evaluation of this soft contribution to the next-to-next-to-next-to-leading
order (NNNLO) pressure of high-density, zero-temperature quark matter (QM),
complementing our accompanying paper in arXiv:2103.05658. Our calculation
requires the determination of the pressure of the hard-thermal-loop (HTL)
effective theory to full two-loop order at zero temperature, which we go
through in considerable detail. In addition to this, we comprehensively discuss
the structure of the weak-coupling expansion of the QM pressure, and lay out a
roadmap towards the evaluation of the contributions missing from a full NNNLO
result for this quantity.
