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: Jacques Hadamard | Statement: [prime number theorem, provedIndependentlyBy, Jacques Hadamard]

Target entity: Jacques Hadamard
Context triple: [prime number theorem, provedIndependentlyBy, Jacques Hadamard]

• A. Jacques Hadamard chosen
  Jacques Hadamard was a prominent French mathematician known for his fundamental contributions to number theory, complex analysis, and partial differential equations, including the prime number theorem and the concept of well-posed problems.
• B. Georges Valiron
  Georges Valiron was a French mathematician known for his influential work in complex analysis and the theory of entire and meromorphic functions.
• C. Émile Picard
  Émile Picard was a prominent French mathematician known for his fundamental contributions to complex analysis and algebraic geometry, including Picard's theorems.
• D. Maxime Bôcher
  Maxime Bôcher was an American mathematician known for his work in differential equations and analysis, and for his influential role in early 20th-century American mathematics.
• E. Arnaud Denjoy
  Arnaud Denjoy was a French mathematician known for his contributions to real analysis, particularly in the theory of integration and trigonometric series.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target predicate: provedIndependentlyBy
Context triple: [prime number theorem, provedIndependentlyBy, Jacques Hadamard]

• A. independentlyFormulated chosen
  Indicates that multiple entities arrived at the same or similar idea, result, or formulation without influencing or relying on each other.
• B. wasFirstProvedBy
  Indicates that a particular statement, theorem, or result was originally and for the first time demonstrated or established as true by a specified agent.
• C. independenceProvedBy
  Indicates that the independence of something (such as a statement, axiom, or system) is established or demonstrated by a particular proof, method, or agent.
• D. originallyIndependentOf
  Indicates that one entity was initially separate from, and not derived from or influenced by, another entity at the outset.
• E. independentlyDevelopedBy
  Indicates that something was created or developed by an entity without collaboration, influence, or shared effort with others.
• F. None of above.