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: Hilbert’s tenth problem | Statement: [Entscheidungsproblem, relatedTo, Hilbert’s tenth problem]

Target entity: Hilbert’s tenth problem
Context triple: [Entscheidungsproblem, relatedTo, Hilbert’s tenth problem]

• A. Hilbert’s tenth problem chosen
  Hilbert’s tenth problem is a famous unsolved question in mathematics that asked for a general algorithm to determine whether any given Diophantine equation has an integer solution, and whose negative answer helped establish fundamental limits of computability.
• B. Entscheidungsproblem
  The Entscheidungsproblem is a foundational decision problem in mathematical logic that asks whether there exists a general algorithm to determine the truth or falsity of any given first-order logical statement.
• C. Hilbert’s second problem
  Hilbert’s second problem is one of David Hilbert’s famous list of 23 problems, asking for a proof of the consistency of arithmetic from a finite set of axioms using finitary methods.
• D. Hilbert’s seventeenth problem
  Hilbert’s seventeenth problem is a famous question in real algebraic geometry asking whether every nonnegative polynomial can be represented as a sum of squares of rational functions.
• E. Hilbert’s Nullstellensatz
  Hilbert’s Nullstellensatz is a foundational theorem in algebraic geometry that establishes a deep correspondence between ideals in polynomial rings and algebraic sets, linking algebra and geometry.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.