Nodal angle resolved photoemission spectra taken on overdoped La$_{1.77}$Sr$_{0.23}$CuO$_4$ are presented and analyzed. It is proven that the low-energy excitations are true Landau Fermi-liquid quasiparticles. We show that momentum and energy distribution curves can be analyzed self-consistently without quantitative knowledge of the bare band dispersion. Finally, by imposing Kramers-Kronig consistency on the self-energy $Sigma$, insight into the quasiparticle residue is gained. We conclude by comparing our results to quasiparticle properties extracted from thermodynamic, magneto-resistance, and high-field quantum oscillation experiments on overdoped Tl$_2$Ba$_2$CuO$_{6+delta}$.
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