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: Hadamard’s work on the Cauchy problem | Statement: [Hadamard’s example of ill-posed problems, appearsIn, Hadamard’s work on the Cauchy problem]

Target entity: Hadamard’s work on the Cauchy problem
Context triple: [Hadamard’s example of ill-posed problems, appearsIn, Hadamard’s work on the Cauchy problem]

• A. Lectures on Cauchy’s problem in linear partial differential equations chosen
  "Lectures on Cauchy’s Problem in Linear Partial Differential Equations" is a classic mathematical treatise by Jacques Hadamard that systematically develops the theory of existence, uniqueness, and well-posedness for solutions to linear partial differential equations.
• B. Hadamard’s example of ill-posed problems
  Hadamard’s example of ill-posed problems is a classical mathematical construction illustrating how small changes in input data can cause large, unstable changes in solutions, thereby violating the standard criteria for well-posedness in analysis and partial differential equations.
• C. Hilbert’s nineteenth problem
  Hilbert’s nineteenth problem is one of David Hilbert’s famous list of 23 problems, asking whether solutions to regular variational problems are always analytic.
• D. Hilbert’s twenty-second problem
  Hilbert’s twenty-second problem is one of David Hilbert’s famous list of 23 problems, concerning the uniformization of analytic relations and the representation of multi-valued analytic functions by single-valued ones on suitable Riemann surfaces.
• E. Cauchy–Kovalevskaya theorem
  The Cauchy–Kovalevskaya theorem is a fundamental result in partial differential equations that guarantees the existence and uniqueness of analytic solutions to certain initial value problems under appropriate analyticity conditions.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.