Breaking the Distance-Inclination Degeneracy: What an Electromagnetic Inclination Prior Buys a Siren

This paper asks a single question and computes its answer. The gravitational-wave amplitude couples distance and orbital inclination; how much does an inclination constraint from a jet or kilonova observation shrink the distance, and hence Hubble constant, uncertainty for a binary neutron star siren? 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 w90 = 32.2, w5 = 5.6, improve = 5.8, rhoA = 9.72e+54. An uninformative inclination leaves a distance interval several times wider than the interval obtained with a five-degree jet prior. The improvement factor between those cases is the headline number in the abstract, and it is achieved with no change to the gravitational-wave detector at all. 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.