Birational rigidity implies K-stability

Prove that every birationally rigid Fano variety is K-stable.

Background

The paper studies two properties of Fano varieties: birational rigidity, which concerns uniqueness under birational modifications into terminal Mori fiber spaces, and K-stability, which is equivalent to the existence of a Kähler–Einstein metric. Although these notions arise from different areas, the paper notes that both are related to singularities of suitable divisors on Fano varieties.

The conjecture asserts a general implication from birational rigidity to K-stability. The paper proves this implication for well-formed and quasismooth Fano 3-fold weighted complete intersections, but leaves the assertion unresolved for arbitrary birationally rigid Fano varieties.