The 3.5 keV X-ray Line, Priced: Required Sterile-Neutrino Parameters, Blank-Sky Exclusion Factors, and the Cost of the Atomic Alternatives

Recomputation of the sterile-neutrino lifetime and mixing angle required by the reported 3.5 keV X-ray line fluxes in stacked galaxy clusters, M31 and the Galactic centre (sin^2(2theta) = 5.4-8.2 x 10^-11, lifetime 5.0-7.5 x 10^27 s); the flux the same parameters predict for blank-sky fields and the per-class exclusion factors (29 fiducial, 5.8 conservative, from the published XMM-Newton blank-sky limits); and the K XVIII and sulfur charge-exchange contributions priced as fractions of the claimed flux (0.03-0.12 and 0.05-0.30 in stacked clusters). No single (mass, mixing angle) point survives all four target classes; the surviving window has width zero. AI assistance (Dave) was used in preparation; the full computation script is included.