The t -U -V -J model fits together three major parts of the superconductivity puzzle of the cuprite compounds: (i) it describes the opening of a d-wave pairing gap, (ii) it is consistent with the fact that the basic pairing mechanism arises from the antiferromagnetic exchange correlations, and (iii) it takes into account the charge fluctuations associated with double occupancy of a site which play an essential role in doped systems. The strengths of the interactions U , V and J in YBa 2 Cu 3 O 6.7 and La 2−x Sr x CuO 4 (x = 0.16) samples are obtained by requiring quantitative consistency between the angle-resolved photoemission spectroscopy (ARPES) measurements, the sharp collective mode at the antiferromagnetic wave vector Q AF = (π, π), and the observed inelastic neutron scattering resonance (INSR) positions of the incommensurate peaks at wave vectors Q δ = ((1 ± δ)π, π) and Q δ =