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: Poincaré conjecture | Statement: [Ricci flow, usedInProofOf, Poincaré conjecture]

Target entity: Poincaré conjecture
Context triple: [Ricci flow, usedInProofOf, Poincaré conjecture]

• A. Poincaré conjecture chosen
  The Poincaré conjecture is a landmark problem in topology that characterizes the three-dimensional sphere among three-dimensional manifolds and was famously solved by Grigori Perelman in the early 2000s.
• B. Navier–Stokes existence and smoothness problem
  The Navier–Stokes existence and smoothness problem is a fundamental unsolved question in mathematical fluid dynamics that asks whether three-dimensional fluid flow equations always have smooth, globally defined solutions.
• C. Hodge Conjecture
  The Hodge Conjecture is a major unsolved problem in algebraic geometry that predicts which cohomology classes on a non-singular projective complex variety arise from algebraic subvarieties.
• D. Yang–Mills existence and mass gap problem
  The Yang–Mills existence and mass gap problem is a fundamental unsolved question in mathematical physics that asks for a rigorous proof that quantum Yang–Mills theory exists and exhibits a positive mass gap, and is one of the seven Millennium Prize Problems.
• E. Millennium Prize Problem
  The Millennium Prize Problem is one of seven famous unsolved mathematical problems designated by the Clay Mathematics Institute, each carrying a $1 million reward for a correct solution.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target predicate: usedInProofOf
Context triple: [Ricci flow, usedInProofOf, Poincaré conjecture]

• A. usedInProofStyle
  Indicates that one entity is employed as a method, technique, or approach within the proof style or strategy of another entity.
• B. requiresProofOf
  Indicates that one entity must provide formal evidence or documentation to validate or authorize another entity.
• C. typicalProofUses chosen
  Indicates that a proof characteristically or commonly employs a particular method, technique, or component.
• D. usedInPartOf
  Indicates that something is utilized or plays a functional role within a specific component or subpart of a larger whole.
• E. areUsedIn
  Indicates that certain entities serve as components, tools, or resources within a particular process, context, or application.
• F. None of above.