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We report on recent progress in the design of the proposed MATHUSLA LongLived Particle (LLP) detector for the HL-LHC, updating the information in theoriginal Letter of Intent (LoI), see CDS:LHCC-I-031, arXiv:1811.00927. Asuitable site has been identified at LHC Point 5 that is closer to the CMSInteraction Point (IP) than assumed in the LoI. The decay volume has beenincreased from 20 m to 25 m in height. Engineering studies have been made inorder to locate much of the decay volume below ground, bringing the detectoreven closer to the IP. With these changes, a 100 m x 100 m detector has thesame physics reach for large c$\tau$ as the 200 m x 200 m detector described inthe LoI and other studies. The performance for small c$\tau$ is improvedbecause of the proximity to the IP. Detector technology has also evolved whileretaining the strip-like sensor geometry in Resistive Plate Chambers (RPC)described in the LoI. The present design uses extruded scintillator bars readout using wavelength shifting fibers and silicon photomultipliers (SiPM).Operations will be simpler and more robust with much lower operating voltagesand without the use of greenhouse gases. Manufacturing is straightforward andshould result in cost savings. Understanding of backgrounds has alsosignificantly advanced, thanks to new simulation studies and measurements takenat the MATHUSLA test stand operating above ATLAS in 2018. We discuss next stepsfor the MATHUSLA collaboration, and identify areas where new members can makeparticularly important contributions.

An Update to the Letter of Intent for MATHUSLA: Search for Long-Lived Particles at the HL-LHC