Siren Distances Against the Electromagnetic Ladder: A Low-Redshift Consistency Check

This paper asks a single question and computes its answer. At the distances where both methods operate, do gravitational-wave luminosity distances and electromagnetic ladder distances agree, and what joint precision on a constant distance offset follows from stated errors at several anchor distances? 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 joint = 10.3, best = 15.8, rhoA = 9.72e+54. Individually the anchors check the two scales at the fifteen to thirty per cent level, because the gravitational-wave errors dominate; jointly they reach the precision printed in the abstract. The ladder errors are already small enough that improving the check means improving sirens, not ladders. 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.