EARTH
In the literature: open
Where and how much does helium rain out inside Jupiter and Saturn?
In plain words
At high pressure, helium may stop mixing with hydrogen and sink as droplets, releasing heat. This could explain why Saturn is warmer than expected and why both atmospheres lack helium.
Precise statement
Determine the pressure-temperature extent of hydrogen-helium immiscibility in Jupiter and Saturn and the amount of helium depleted from the outer envelopes (the Galileo probe measured helium mass fraction about 0.234 versus a protosolar value near 0.27). An answer is an immiscibility curve and evolutionary model that fits both planets' atmospheric helium, luminosity and gravity.
What would settle it
Ab initio and shock-compression determination of the H-He miscibility gap combined with evolution models fitting both planets.