  We report on recent progress and next steps in the design of the proposed
MATHUSLA Long Lived Particle (LLP) detector for the HL-LHC as part of the
Snowmass 2021 process. Our understanding of backgrounds has greatly improved,
aided by detailed simulation studies, and significant R&D has been performed on
designing the scintillator detectors and understanding their performance. The
collaboration is on track to complete a Technical Design Report, and there are
many opportunities for interested new members to contribute towards the goal of
designing and constructing MATHUSLA in time for HL-LHC collisions, which would
increase the sensitivity to a large variety of highly motivated LLP signals by
orders of magnitude.
