What radiation mechanism produces GRB prompt gamma-ray spectra?
In plain words
The first seconds of gamma rays have a spectral shape that neither the glow of hot gas nor electrons spiraling in magnetic fields (synchrotron radiation) reproduces cleanly.
Precise statement
Explain the prompt spectra (peak energy $E_p \sim 100\,\mathrm{keV}$ to a few MeV; low-energy photon index $\alpha \sim -1$, harder than the fast-cooling synchrotron value $-3/2$, with a sizable fraction of spectra harder than the slow-cooling synchrotron limit $-2/3$) and the $E_p$ versus isotropic energy (Amati) correlation, choosing among synchrotron from internal shocks or reconnection with marginally fast cooling, dissipative photospheres, and Comptonization. Answer: a mechanism and dissipation radius that reproduce spectra, variability and correlations for a large sample.
What would settle it
Joint fits of time-resolved spectra and polarization of a large burst sample by one mechanism with physically consistent parameters.