Weak Lensing Magnification of Standard Sirens: Scatter, Bias, and the Delensing Dividend

This paper asks a single question and computes its answer. How large is the weak-lensing scatter on siren luminosity distances as a function of redshift, what bias does a flux-limited selection impose, and how much does delensing with a foreground galaxy map recover? 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 sd1 = 1.7, sd3 = 3.3, bias3 = 0.17, rhoA = 9.72e+54. Distance scatter reaches 1.7 per cent by redshift one and 3.3 per cent by redshift three in this scaling, while the selection bias, at 0.17 per cent by redshift three, remains small but systematic: it does not average away with event count. Delensing recovers a substantial fraction of the scatter. 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.