The Ceiling Nobody Derived: The Maximum Neutron-Star Mass, Priced

Ask a room of neutron-star physicists for the maximum mass of a neutron star and you will be given numbers spanning 2.16 to 3.2 solar masses — a factor of one and a half — each quoted with confidence and each bought with a different stack of assumptions. The only ceiling in the literature that is a derivation rather than an opinion is the causality ceiling of Rhoades and Ruffini (1974): grant the equation of state where nuclear physics knows it, extend it above a chosen matching density with the stiffest matter causality permits, and general relativity returns a maximum mass of 3.2 M_☉, scaling as the inverse square root of the matching density — a derivation whose answer is a dial, because the matching density is chosen, not measured. Every lower ceiling in circulation is bought with more: the 2.16–2.28 M_☉ band read off GW170817 is purchased with rotation-enhancement ratios (β ≈ 1.2) harvested from simulations of assumed equations of state, plus a reading of how long the merger remnant lived; the 2.49–2.52 M_☉ band from multimessenger statistics is purchased with the fraction of short gamma-ray bursts assumed to leave a surviving magnetar. Meanwhile the floor keeps rising through the ceilings: the heaviest well-weighed pulsar, PSR J0952−0607 at 2.35 ± 0.17 M_☉, has a one-sigma floor that already pokes through the most quoted ceiling. This paper derives the one derivable ceiling in the open, then censuses the rest: every published "maximum mass" with the assumed steps it spent, itemized. Grade: THE FLOOR IS MEASURED; THE CEILING IS BOUGHT — PRICED. This paper stands outside my work on the vacuum catastrophe; it draws nothing from that work and repairs nothing in it.