  We completely classify the possible extensions between semistable vector
bundles on the Fargues-Fontaine curve (over an algebraically closed perfectoid
field), in terms of a simple condition on Harder-Narasimhan polygons. Our
arguments rely on a careful study of various moduli spaces of bundle maps,
which we define and analyze using Scholze's language of diamonds. This analysis
reduces our main results to a somewhat involved combinatorial problem, which we
then solve via a reinterpretation in terms of the euclidean geometry of
Harder-Narasimhan polygons.
