PLASMA
In the literature: partially resolved
Nature and spectral slope of sub-ion-scale turbulence
In plain words
Below the size of ion orbits, the solar-wind magnetic fluctuation spectrum steepens. Whether these fluctuations are a kind of wave or a collection of thin current sheets, and why the slope has its value, are open.
Precise statement
Between ion and electron gyroscales the magnetic spectrum follows $E(k) \sim k^{-\alpha}$ with $\alpha$ about 2.8. Determine whether the fluctuations are kinetic Alfven waves, whistler waves or sheet-like structures, and derive $\alpha$ (theory proposals include $7/3$, $8/3$ and 3). An answer is a theory matching measured $\alpha$, polarization and anisotropy.
What would settle it
Simultaneous spacecraft measurements of spectral slope, polarization and wavevector anisotropy matched by one theory and by kinetic simulations.