Third-Generation Detectors as Siren Machines: A Yield and Precision Forecast From Stated Rates

This paper asks a single question and computes its answer. With stated merger rates and horizon distances for Einstein Telescope and Cosmic Explorer class instruments, how many usable sirens per year follow, and what Hubble constant precision does that yield imply under stated counterpart fractions? 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 nev = 2517, bright = 50, sig = 0.68, rhoA = 9.72e+54. The yields are large: hundreds to thousands of detections per year, with tens of bright sirens annually under a two per cent counterpart fraction. The combined Hubble constant precision reaches the sub-per-cent level in the central case, at which point calibration and lensing systematics, not event count, set the limit. 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.