Triple

Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).

Phrase: Yau's proof of the Calabi conjecture | Statement: [Calabi–Yau metric, guaranteedBy, Yau's proof of the Calabi conjecture]

Target entity: Yau's proof of the Calabi conjecture
Context triple: [Calabi–Yau metric, guaranteedBy, Yau's proof of the Calabi conjecture]

• A. Calabi conjecture chosen
  The Calabi conjecture is a fundamental result in complex differential geometry, proved by Shing-Tung Yau, which characterizes when a compact Kähler manifold admits a unique Ricci-flat Kähler metric in a given Kähler class.
• B. Donaldson–Uhlenbeck–Yau theorem
  The Donaldson–Uhlenbeck–Yau theorem is a fundamental result in differential and algebraic geometry that characterizes when a holomorphic vector bundle over a compact Kähler manifold admits a Hermitian–Einstein metric, linking geometric stability with the existence of such metrics.
• C. Calabi–Bernstein theorem
  The Calabi–Bernstein theorem is a result in differential geometry that characterizes entire maximal spacelike hypersurfaces in Minkowski space as necessarily being affine hyperplanes.
• D. Nirenberg problem in differential geometry
  The Nirenberg problem in differential geometry is a classical question about prescribing Gaussian curvature on the 2-sphere via conformal deformations of the metric.
• E. Kähler–Ricci flow
  Kähler–Ricci flow is a geometric evolution equation that deforms Kähler metrics on complex manifolds according to their Ricci curvature, playing a central role in complex differential geometry and the study of canonical metrics.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.