CM
In the literature: open
Does metallic hydrogen superconduct, and at what temperature
In plain words
Because hydrogen atoms are so light their vibrations are fast, and theory predicts that metallic hydrogen could superconduct near or above room temperature.
Precise statement
Determine whether metallic solid hydrogen (molecular or atomic phase, pressure above $\sim 4\,\mathrm{Mbar}$) superconducts and measure $T_c(P)$; calculations give $T_c$ from about 100 K to above room temperature depending on phase and pressure. An answer is a resistive and magnetic transition at a calibrated pressure, or a bound excluding superconductivity above a stated temperature.
What would settle it
Four-probe transport and magnetic measurements on metallic hydrogen in a diamond anvil cell showing a field-dependent transition.