  Our limited understanding of the physical properties of matter at ultra-high
density, high proton/neutron number asymmetry, and low temperature is presently
one of the major outstanding problems in physics. As matter in this extreme
state is known to only exist stably in the cores of neutron stars (NSs),
complementary measurements from electromagnetic and gravitational wave
astrophysical observations of NSs, combined with terrestrial laboratory
constraints and further theoretical investigations, hold the promise to provide
important insight into the properties of matter in a region of the quantum
chromodynamics phase space that is otherwise inaccessible. This
multidisciplinary endeavor imposes the following requirements for facilities
and resources in the upcoming decade and beyond:
  * A next generation of gravitational wave detectors to uncover more double NS
and neutron star-black hole mergers;
  * Sensitive radio telescopes to find the most massive and fastest spinning
NSs;
  * Large-area, high-time-resolution and/or high angular resolution X-ray
telescopes to constrain the NS mass-radius relation;
  * Suitable laboratory facilities for nuclear physics experiments to constrain
the dense matter equation of state;
  * Funding resources for theoretical studies of matter in this regime;
  * The availability of modern large-scale high performance computing
infrastructure.
  The same facilities and resources would also enable significant advances in
other high-profile fields of inquiry in modern physics such as the nature of
dark matter, alternative theories of gravity, nucleon superfluidity and
superconductivity, as well as an array of astrophysics, including but not
limited to stellar evolution, nucleosynthesis, and primordial black holes.
