Explore cutting-edge research on binary neutron star mergers and quark deconfinement phase transitions in this 48-minute scientific lecture. Delve into numerical relativity simulations that demonstrate how hadron-quark phase transitions can be investigated through multimodal post-merger gravitational wave spectroscopy. Learn how these transitions suppress one-armed spiral instability in merger remnants, creating an anti-correlation between l=2, m=1 gravitational wave mode energy and the energy density gap between phases. Discover how measuring signal-to-noise ratios of specific gravitational wave modes could help constrain phase transition energy density gaps, advancing our understanding of the state of matter formed during binary neutron star mergers - a key objective in multimessenger astronomy.