How do Seyfert coronae make neutrinos while hiding gamma rays?
In plain words
The nearby active galaxy NGC 1068 emits far more energy in neutrinos than in gamma rays, which suggests the particles are made in a dense, hot region next to its black hole that absorbs the gamma rays.
Precise statement
For NGC 1068 (neutrino luminosity $\sim 3e42\ \mathrm{erg}/\mathrm{s}$ at 1.5-15 TeV, with a GeV-TeV gamma-ray flux far lower), determine where and how protons are accelerated to $\sim 1e14\ \mathrm{eV}$ within $\sim 10\ \text{to}\ 100$ gravitational radii of the black hole (turbulent acceleration, magnetic reconnection, accretion shocks), and whether the model predicts how neutrino luminosity scales with intrinsic X-ray luminosity across Seyferts. Answer: a model giving $L_{\nu}/L_{X}$ and the spectral shape, tested against the Seyfert sample.
What would settle it
Detection of neutrinos from several further Seyferts with fluxes matching the predicted $L_{\nu}/L_{\mathrm{X}}$ scaling, and MeV gamma-ray observations of the cascaded emission.