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Using a new variant of photoelectron spectroscopy, we measure the homogeneousnear-nodal pairing ($\Delta$) and pair-breaking self-energy ($\Gamma_S$)processes for a wide range of doping levels ofBi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$. For all samples we find that the pairingextends above the superconducting transition T$_c$ to a scale T$_{Pair}$ thatis distinct from the antinodal pseudogap scale T$^*$ and near but slightlyabove T$_c$. We find that $\Delta$ and T$_{Pair}$ are related with a strongcoupling ratio 2$\Delta$ /k$_B$T$_{Pair}\approx6$ across the entire dopingphase diagram, i.e. independent of the effects of antinodal pseudogaps orcharge-density waves.

Coordination of the energy and temperature scales of pairing across the doping phase diagram of Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$