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: Mazur's torsion theorem | Statement: [Barry Mazur, knownFor, Mazur's torsion theorem]

Target entity: Mazur's torsion theorem
Context triple: [Barry Mazur, knownFor, Mazur's torsion theorem]

• A. Mazur control theorem
  The Mazur control theorem is a fundamental result in Iwasawa theory that relates Selmer groups over infinite p-adic extensions to those over finite layers, allowing arithmetic information to be “controlled” across the tower.
• B. Shafarevich group of a torus
  The Shafarevich group of a torus is an arithmetic invariant measuring the failure of local-global principles for principal homogeneous spaces under an algebraic torus over a global field.
• C. Mordell–Weil theorem
  The Mordell–Weil theorem is a fundamental result in number theory stating that the group of rational points on an abelian variety (in particular, an elliptic curve) over a number field is finitely generated.
• D. Fontaine–Mazur conjecture
  The Fontaine–Mazur conjecture is a central open problem in number theory that predicts which p-adic Galois representations of number fields arise from geometry or from automorphic forms.
• E. Faltings' theorem
  Faltings' theorem is a landmark result in arithmetic geometry that proves every algebraic curve of genus greater than one over a number field has only finitely many rational points.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Mazur's torsion theorem
Target entity description: Mazur's torsion theorem is a landmark result in number theory that classifies all possible torsion subgroups of elliptic curves over the rational numbers.

• A. Mazur control theorem
  The Mazur control theorem is a fundamental result in Iwasawa theory that relates Selmer groups over infinite p-adic extensions to those over finite layers, allowing arithmetic information to be “controlled” across the tower.
• B. Shafarevich group of a torus
  The Shafarevich group of a torus is an arithmetic invariant measuring the failure of local-global principles for principal homogeneous spaces under an algebraic torus over a global field.
• C. Mordell–Weil theorem
  The Mordell–Weil theorem is a fundamental result in number theory stating that the group of rational points on an abelian variety (in particular, an elliptic curve) over a number field is finitely generated.
• D. Fontaine–Mazur conjecture
  The Fontaine–Mazur conjecture is a central open problem in number theory that predicts which p-adic Galois representations of number fields arise from geometry or from automorphic forms.
• E. Faltings' theorem
  Faltings' theorem is a landmark result in arithmetic geometry that proves every algebraic curve of genus greater than one over a number field has only finitely many rational points.
• F. None of above. chosen