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: s-m-n theorem | Statement: [Kleene numbering, relatedTo, s-m-n theorem]

Target entity: s-m-n theorem
Context triple: [Kleene numbering, relatedTo, s-m-n theorem]

• A. Kleene’s recursion theorem
  Kleene’s recursion theorem is a fundamental result in computability theory that guarantees the existence of self-referential programs, allowing a program to effectively obtain and use its own description.
• B. Kleene’s normal form theorem chosen
  Kleene’s normal form theorem is a fundamental result in computability theory that characterizes all partial recursive (effectively computable) functions using a universal primitive recursive function and the μ-operator.
• C. Gödel numbering
  Gödel numbering is a method in mathematical logic that encodes symbols, formulas, and proofs as unique natural numbers, enabling arithmetic to represent and reason about syntactic statements.
• D. Kleene numbering
  Kleene numbering is a method in computability theory for effectively assigning natural numbers to partial recursive functions, refining Gödel numbering to study algorithmic properties of functions.
• E. Davis–Putnam–Robinson–Matiyasevich theorem
  The Davis–Putnam–Robinson–Matiyasevich theorem is a landmark result in mathematical logic and number theory that shows every recursively enumerable set is Diophantine, implying the unsolvability of Hilbert’s tenth problem.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.