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: Cauchy problem | Statement: [Cauchy–Kovalevskaya theorem, relatedTo, Cauchy problem]

Target entity: Cauchy problem
Context triple: [Cauchy–Kovalevskaya theorem, relatedTo, Cauchy problem]

• A. Cauchy problem chosen
  The Cauchy problem is a fundamental type of initial value problem in partial differential equations, where one seeks a solution satisfying prescribed data on a given initial surface.
• B. 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.
• C. Dirichlet problem
  The Dirichlet problem is a fundamental boundary value problem in potential theory and partial differential equations, asking for a function that solves a specified PDE inside a domain while taking prescribed values on the domain’s boundary.
• D. Lectures on Cauchy’s problem in linear partial differential equations
  "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.
• E. d’Alembert’s formula
  d’Alembert’s formula is a classical solution method for the one-dimensional wave equation that expresses the displacement of a vibrating string in terms of its initial shape and velocity.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.