Prompt Collapse Thresholds in Binary Neutron Star Mergers and Their Shift Under the Density Bound

When two neutron stars merge, the remnant either collapses promptly to a black hole, survives briefly as a hypermassive star held up by differential rotation, or endures, and the boundary between those fates is a threshold total mass near 2.9 solar masses that gravitational-wave astronomy now uses as an equation-of-state probe. This paper computes the correction the neutron-branch density bound makes to that threshold. Remnant central densities of two to four times saturation density give correction fractions from 5.76e-41 to the three-times-saturation value of 8.64e-41, bounding the shift of the threshold mass at 2.51e-40 solar masses. The prompt-collapse threshold measures the nuclear equation of state and rotation alone; the density bound cannot move a merger remnant across the boundary in either direction. Simulated from stated assumptions, not measured.