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: multivariate Hensel’s lemma | Statement: [Hensel’s lemma, hasVariant, multivariate Hensel’s lemma]

Target entity: multivariate Hensel’s lemma
Context triple: [Hensel’s lemma, hasVariant, multivariate Hensel’s lemma]

• A. Hensel’s lemma chosen
  Hensel’s lemma is a fundamental result in number theory and p-adic analysis that allows one to lift solutions of polynomial congruences modulo a prime power to higher powers, analogous to Newton’s method in the p-adic setting.
• B. 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.
• C. Hilbert’s irreducibility theorem
  Hilbert’s irreducibility theorem is a fundamental result in number theory and algebraic geometry that ensures many polynomial equations with parameterized coefficients retain irreducibility for infinitely many specializations of those parameters.
• D. Siegel’s lemma
  Siegel’s lemma is a result in number theory that guarantees the existence of small-height integer solutions to systems of linear equations with integer coefficients.
• 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.
• G. Unsure - the case is ambiguous/there is not enough information to decide.