Peculiar Velocities and the Nearby Siren Floor: Where Redshift Stops Being Distance

This paper asks a single question and computes its answer. For the nearest sirens, the host peculiar velocity is a large fraction of the recession velocity; at what redshift does that term fall below one per cent, and what Hubble constant floor does it set for a single nearby event? 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 z1pct = 0.083, z2pct = 0.042, frac001 = 8.3, rhoA = 9.72e+54. A single siren at redshift 0.01 carries a peculiar-velocity term of several per cent no matter how well its distance is measured. The term falls below one per cent only beyond the redshift printed in the abstract, which defines the useful nearby floor for single-event cosmology. 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.