One Neutron, Two Clocks: A Ten-Second Defect in the Lifetime, Priced

The neutron is the simplest radioactive thing there is — one particle, alone, falling apart into a proton, an electron, and an antineutrino — and nuclear physics cannot agree on how long it lives. Two methods measure its lifetime. The bottle method traps ultracold neutrons in a vessel and counts the survivors: the traps read 877.75 seconds, with an error bar under a third of a second. The beam method flies neutrons down a pipe and counts the protons their deaths produce: the beam reads 887.7 seconds, give or take two. The two clocks differ by 9.95 seconds — one percent of the neutron's life, four and a half times the combined error bars — and they have differed, stubbornly, for twenty years, through new traps, new beams, blinded analyses, and audits of every budget line either side can name. A one-percent hole in the ledger of the best-understood decay in nuclear physics is not a detail. The lifetime sets the universe's helium fraction, calibrates the weak force's own bookkeeping, and anchors the unitarity accounts of the quark-mixing matrix. This paper prices the defect and the three doors proposed to explain it: a dark decay channel that would hide one death in ninety from the beam's proton counter, priced against the narrow mass window it must live in and the neutron stars it must not soften; a mirror-neutron oscillation that would leak trapped neutrons into invisibility, priced against the laboratory bounds on the oscillation itself; and plain systematics, priced at what each side's honesty would cost. Every door has a price tag. None of them is free, and the defect stands until one is paid. Grade: DEFECT STANDS — THREE DOORS, ALL PRICED, NONE FREE. This paper stands outside my corpus's vacuum ledger; it neither spends that ledger nor repairs it.