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: local normal form theorem | Statement: [Darboux theorem, type, local normal form theorem]

Target entity: local normal form theorem
Context triple: [Darboux theorem, type, local normal form theorem]

• A. Kleene’s normal form theorem
  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.
• B. Noether normalization lemma
  The Noether normalization lemma is a fundamental result in commutative algebra and algebraic geometry that shows any finitely generated algebra over a field can be made integral over a polynomial subring, providing a way to relate complicated varieties to affine space.
• C. Łoś–Tarski preservation theorem
  The Łoś–Tarski preservation theorem is a fundamental result in model theory that characterizes when a first-order sentence is preserved under substructures in terms of its equivalence to a universal sentence.
• D. 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.
• E. Artin approximation theorem
  The Artin approximation theorem is a fundamental result in algebraic geometry and commutative algebra that allows formal power series solutions of polynomial equations to be approximated by convergent or algebraic solutions.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: local normal form theorem
Target entity description: A local normal form theorem is a result in differential geometry that guarantees any geometric structure can be expressed in a particularly simple, standardized form in a neighborhood of each point.

• A. Kleene’s normal form theorem
  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.
• B. Noether normalization lemma
  The Noether normalization lemma is a fundamental result in commutative algebra and algebraic geometry that shows any finitely generated algebra over a field can be made integral over a polynomial subring, providing a way to relate complicated varieties to affine space.
• C. Łoś–Tarski preservation theorem
  The Łoś–Tarski preservation theorem is a fundamental result in model theory that characterizes when a first-order sentence is preserved under substructures in terms of its equivalence to a universal sentence.
• D. 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.
• E. Artin approximation theorem
  The Artin approximation theorem is a fundamental result in algebraic geometry and commutative algebra that allows formal power series solutions of polynomial equations to be approximated by convergent or algebraic solutions.
• F. None of above. chosen