windows. Can we do justice to this information? Specifically, can we devise concrete signatures for quark matter and color superconductivity in “neutron star” interiors, or for phase transitions during or in the immediate aftermath of supernova explosions or “neutron star” mergers?

Conceptual and Algorithmic Issues
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Opportunities
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### See the Effects of Chiral Fermions

Thanks to some very ingenious recent work we now know how to implement chiral symmetry in a precise way in lattice QCD, suitable for numerical integration. As a result many fundamental questions become accessible, including

-   quantitative spectroscopy of the pseudoscalar mesons. Since the masses of the octet are most sensitive to the values of small light quark masses, the meson masses can be used in principle to determine the light quark masses, which then become inputs to calculations of flavor $SU(3)$ breaking and isospin violation, including “electromagnetic” mass differences;

-   questions of phase structure. As has already appeared in our earlier discussions, chiral symmetry restoration is a major feature distinguishing different phases, and conditions the properties of collective modes at the phase transitions, it is important in these contexts to implement it accurately;

-   study of axial baryon number violation. Axial baryon number (more 