  We give a variational proof of a version of the Yau-Tian-Donaldson conjecture
for twisted K\"ahler-Einstein currents, and use this to express the greatest
(twisted) Ricci lower bound in terms of a purely algebro-geometric stability
threshold. Our approach does not involve the continuity method or
Cheeger-Colding-Tian theory, and uses instead pluripotential theory and
valuations. Along the way, we study the relationship between geodesic rays and
non-Archimedean metrics.
