We give a variational proof of a version of the Yau-Tian-Donaldson conjecture for twisted Kähler-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.
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Berman et al. (2015) studied this question.