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: [Millennium Prize Problem, hasFirstSolvedProblem, Poincaré Conjecture]

Target entity: Poincaré Conjecture
Context triple: [Millennium Prize Problem, hasFirstSolvedProblem, 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. 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.
• C. 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.
• D. 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.
• E. 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.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target predicate: hasFirstSolvedProblem
Context triple: [Millennium Prize Problem, hasFirstSolvedProblem, Poincaré Conjecture]

• A. hasFirstTrial
  Indicates that an entity is associated with its initial or earliest trial, test, or legal proceeding.
• B. commonlySolvedBy
  Indicates that a problem, task, or issue is typically addressed or resolved through a particular method, tool, or agent.
• C. solved
  Indicates that one entity has successfully found a solution or answer to a problem, task, or challenge involving another entity.
• D. hasChallenge
  Indicates that an entity faces, experiences, or is confronted with a particular difficulty, obstacle, or problem.
• E. turnedPro
  Indicates that an individual transitioned from amateur status to professional status in a particular field or activity.
• F. None of above. chosen