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: Carl Gustav Jacob Jacobi | Statement: [Jacobi’s four-square theorem, prover, Carl Gustav Jacob Jacobi]

Target entity: Carl Gustav Jacob Jacobi
Context triple: [Jacobi’s four-square theorem, prover, Carl Gustav Jacob Jacobi]

• A. Carl Gustav Jacob Jacobi chosen
  Carl Gustav Jacob Jacobi was a 19th-century German mathematician renowned for his fundamental contributions to elliptic functions, number theory, and differential equations.
• B. Johann Eduard Jacobsthal
  Johann Eduard Jacobsthal was a 19th-century German architect known for his contributions to historicist architecture and his work on building restoration and design in Germany.
• C. Alfred Clebsch
  Alfred Clebsch was a 19th-century German mathematician known for his influential work in algebraic geometry and invariant theory.
• D. Ernst Eduard Kummer
  Ernst Eduard Kummer was a 19th-century German mathematician renowned for his foundational work in number theory, particularly on ideal numbers and Fermat's Last Theorem.
• E. Peter Gustav Lejeune Dirichlet
  Peter Gustav Lejeune Dirichlet was a 19th-century German mathematician renowned for his foundational contributions to number theory and analysis, including Dirichlet's theorem on arithmetic progressions.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target predicate: prover
Context triple: [Jacobi’s four-square theorem, prover, Carl Gustav Jacob Jacobi]

• A. proved
  Indicates that one entity has demonstrated the truth or validity of another entity (such as a statement, theorem, or claim) through logical or evidential means.
• B. proofRole
  Indicates the specific function or responsibility an entity has within the structure or presentation of a proof.
• C. wasFirstProvedBy chosen
  Indicates that a particular statement, theorem, or result was originally and for the first time demonstrated or established as true by a specified agent.
• D. coProclaimed
  Indicates that two or more entities jointly made or issued the same formal declaration or announcement.
• E. partiallyProvenFor
  Indicates that something has been shown to hold or be true for part of a domain or set of cases, but not yet for all cases.
• F. None of above.