What interaction binds electrons into pairs in the cuprates
In plain words
In a superconductor electrons form pairs (Cooper pairs) that move without resistance; in ordinary metals lattice vibrations supply the attraction, but in cuprates the source of the attraction is not agreed upon.
Precise statement
Identify the dominant pairing interaction behind $d_{(x^{2}-y^{2})}$ superconductivity in hole-doped CuO2 planes (candidates: antiferromagnetic superexchange $J \sim 0.13\ \mathrm{eV}$ and spin fluctuations, charge-transfer fluctuations, phonons, or a combination). An answer is a microscopic mechanism that predicts $T_c(p)$ and the gap magnitude across cuprate families within a factor of order one and passes material-specific tests (isotope effect, pressure dependence, family dependence of T_c,max).
What would settle it
A controlled calculation from a materials-specific model that reproduces $T_{\mathrm{c}}(p)$ in several families, together with spectroscopy showing that the identified boson spectrum accounts for the measured gap function.