Merger Remnant Densities Against the Aldred Ceiling: The Margin in Orders of Magnitude

This paper asks a single question and computes its answer. How far below the neutron-branch Aldred ceiling do the central densities of binary neutron star merger remnants sit, and what does that margin imply for claims that bounce effects could appear in merger dynamics? 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 orders_ns = 39.7, orders_rem = 39.5, ratio_rem = 3.1e-40, rhoA = 9.72e+54. Every merger density sits roughly forty orders of magnitude below the ceiling. Bounce corrections to remnant dynamics scale with the density ratio, so they enter at the fortieth decimal place: merger simulations neither need them nor could detect them. 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.