From Merger Rates to Siren Yield: What the Current Detector Network Should Deliver Per Year

This paper asks a single question and computes its answer. Combining published local merger rates with the current network's stated sensitive volumes, how many binary neutron star and black hole mergers per year should be detected, and how many of the neutron star events should yield a usable siren measurement? Working in a flat LambdaCDM background and carrying the bounce-frame density ceiling explicitly — the Aldred Limit, rho_A = rho_Pl (m/m_Pl)^2/(8 pi C), with the neutron branch at 9.72e+54 g per cubic centimetre — the calculation gives the headline values bns = 3.3, bns_usable = 1.6, bbh = 187, rhoA = 9.72e+54. The arithmetic predicts a few binary neutron star detections per year at current sensitivity, with roughly half of those usable as sirens, against of order two hundred black hole detections. This matches the observed scarcity of bright sirens and explains it without invoking any anomaly: the volume is simply small. Every number reported here comes from the deposited computation script, which states its assumptions in full. This study is simulated and computed from stated assumptions and published catalogue values; it is not a measurement.