Linear scaling of $T_c$ with attraction in isolated flat bands
In plain words
For flat bands theory predicts a superconducting temperature proportional to the pairing attraction, much larger than the exponentially small value of ordinary metals when the attraction is weak, and no experiment has tested this scaling directly.
Precise statement
For an isolated flat band of width $W << U$ ($U$ the effective attraction), mean-field and Berezinskii-Kosterlitz-Thouless theory predict $T_c \sim U$ times a band-geometric factor, compared with $T_c \sim W \exp(-1/(N(0) U))$ in dispersive bands, $N(0)$ the density of states. Determine whether $T_c$ scales linearly with $U$ in a moire flat-band superconductor where the interaction is tuned, for example by gate-screening distance or dielectric environment. An answer is the measured exponent of T_c versus U.
What would settle it
$T_{c}$ measured versus screening-layer distance or dielectric environment in moire devices with independently estimated $U$ and fixed band structure.