Spectral Sirens: Reading Redshift From Features in the Compact-Object Mass Distribution

This paper asks a single question and computes its answer. If the source-frame mass distribution has a known feature, such as a gap edge or a peak, the detector-frame distribution locates the redshift; how sharply can a stated feature be located with stated event counts? 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 w50 = 0.10, w1000 = 0.02, med = 0.54, rhoA = 9.72e+54. The feature can be located to a redshift width that shrinks roughly as the square root of the event count, reaching a few hundredths at a thousand events. The estimator is centred near the population mean redshift in this simplified model; realistic selection effects would need the full hierarchical treatment. 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.