  We introduce the concept of non-Archimedean metrics attached to a
transcendental pseudoeffective cohomology class on a compact K\"ahler manifold.
This is obtained via extending the Ross-Witt Nystr\"om correspondence to the
relative case, and we point out that our construction agrees with that of
Boucksom-Jonsson when the class is induced by a pseudoeffective $\mathbb
Q$-line bundle.
  We introduce the notion of a flag configuration attached to a transcendental
big class, recovering the notion of a test configuration in the ample case. We
show that non-Archimedean finite energy metrics are approximable by flag
configurations, and very general versions of the radial Ding energy are
continuous, a novel result even in the ample case. As applications, we
characterize the delta invariant as the Ding semistability threshold of flag
configurations and filtrations and prove a YTD type existence theorem in terms
of flag configurations.
