What interaction binds electrons into pairs in the cuprates?

Identify the dominant pairing interaction behind $d_{(x^{2}-y^{2})}$ superconductivity in hole-doped $\mathrm{CuO_2}$ 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 $T_c,\mathrm{max}$).

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.