Muon Bunch Density and Decay Heating at a Muon Collider Against the Density Ceiling

This paper computes the characteristic densities of the bunches of a multi-TeV muon collider from published operating parameters and compares them, quantity by quantity, with the Aldred density ceiling of 9.72e+57 kilograms per cubic metre, the neutron-branch bound at prescription coefficient one eighth. The headline comparison gives a margin of 60.6 orders of magnitude between the operating point and the ceiling: muon bunches are among the densest lepton bunches ever designed, yet their mass density remains 60.6 orders of magnitude below the ceiling; the design is instead dominated by muon decay, whose heating and radiation load follow from the dilated lifetime computed here. Every number is obtained from the deposited calculation, which uses only published device parameters, internationally tabulated constants, and algebra stated in full. The result is negative in the useful sense: it shows that the ceiling imposes no constraint on the system as designed or operated, identifies the empirical and engineering limits that act instead, and states precisely what change in operating parameters would be required before the ceiling could matter. The study is a computation from stated assumptions; nothing in it is a measurement.