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: weak form of Hensel’s lemma | Statement: [Hensel’s lemma, hasVariant, weak form of Hensel’s lemma]

Target entity: weak form of Hensel’s lemma
Context triple: [Hensel’s lemma, hasVariant, weak form of 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. Henselization
  Henselization is a construction in commutative algebra that minimally modifies a local ring to satisfy Hensel’s lemma, making it “Henselian” while preserving much of its original structure.
• C. Hasse–Arf theorem
  The Hasse–Arf theorem is a fundamental result in algebraic number theory that precisely characterizes the jumps in the ramification filtration of abelian extensions of local fields, showing they occur at integer values.
• D. Hensel
  Hensel is a German surname most notably associated with mathematician Kurt Hensel, known for introducing p-adic numbers.
• E. Kummer's lemma
  Kummer's lemma is a result in algebraic number theory that provides conditions on ideal factorization in cyclotomic fields, particularly relating to divisibility properties of class numbers and units.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.