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: Jacobi differential operator | Statement: [Jacobi polynomials, areEigenfunctionsOf, Jacobi differential operator]

Target entity: Jacobi differential operator
Context triple: [Jacobi polynomials, areEigenfunctionsOf, Jacobi differential operator]

• A. Jacobi operator chosen
  The Jacobi operator is a linear differential operator central to the theory of elliptic functions and integrable systems, named after the mathematician Carl Gustav Jacob Jacobi.
• B. Jacobi matrix
  A Jacobi matrix is a tridiagonal matrix, often symmetric, that arises in numerical analysis and mathematical physics, particularly in the study of orthogonal polynomials and eigenvalue problems.
• C. Jacobi bracket
  The Jacobi bracket is a bilinear operation generalizing the Poisson bracket in differential geometry, central to the theory of Jacobi manifolds and Hamiltonian systems.
• D. Jacobi last multiplier
  The Jacobi last multiplier is a mathematical tool introduced by Carl Gustav Jacob Jacobi for integrating systems of differential equations by providing an integrating factor that simplifies them to solvable form.
• E. Jacobi
  Jacobi is a German surname most famously associated with the 19th-century mathematician Carl Gustav Jacob Jacobi, known for his foundational work in elliptic functions and number theory.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target predicate: areEigenfunctionsOf
Context triple: [Jacobi polynomials, areEigenfunctionsOf, Jacobi differential operator]

• A. isMassEigenstateOf
  Indicates that one entity is a quantum state with a definite mass that results from diagonalizing the mass operator (or mass matrix) associated with the other entity.
• B. orthonormalityRelation
  Indicates that a set of vectors are mutually orthogonal and each has unit length with respect to a given inner product.
• C. isSelfAdjoint
  Indicates that an operator is equal to its own adjoint (conjugate transpose), meaning it has the same effect as its Hermitian transpose in the given inner product space.
• D. CPEigenstate
  Indicates that a quantum state is an eigenstate of the combined charge-conjugation and parity (CP) symmetry operator, remaining unchanged up to a phase under the CP transformation.
• E. isHermitian
  Indicates that an operator or matrix is equal to its own conjugate transpose, ensuring real eigenvalues and orthogonal eigenvectors.
• F. None of above. chosen