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: Taylor–Wiles method | Statement: [Richard Taylor, knownFor, Taylor–Wiles method]

Target entity: Taylor–Wiles method
Context triple: [Richard Taylor, knownFor, Taylor–Wiles method]

• A. Serre’s conjecture on Galois representations
  Serre’s conjecture on Galois representations is a landmark statement in number theory that predicts which two-dimensional mod p Galois representations of the absolute Galois group of the rationals arise from modular forms.
• B. Ribet's theorem
  Ribet's theorem is a result in number theory that linked certain modular forms to Galois representations and played a crucial role in the proof of Fermat's Last Theorem.
• C. 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.
• D. Mazur's deformation theory of Galois representations
  Mazur's deformation theory of Galois representations is a foundational framework in number theory that systematically studies how p-adic Galois representations can be deformed, with deep applications to modular forms and the proof of Fermat’s Last Theorem.
• E. Bloch–Kato conjecture
  The Bloch–Kato conjecture is a deep statement in arithmetic geometry and K-theory that predicts an exact correspondence between Galois cohomology and Milnor K-theory, linking algebraic K-groups to field arithmetic.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Taylor–Wiles method
Target entity description: The Taylor–Wiles method is a powerful technique in number theory and arithmetic geometry used to prove modularity lifting theorems, notably enabling the proof of Fermat’s Last Theorem.

• A. Serre’s conjecture on Galois representations
  Serre’s conjecture on Galois representations is a landmark statement in number theory that predicts which two-dimensional mod p Galois representations of the absolute Galois group of the rationals arise from modular forms.
• B. Ribet's theorem
  Ribet's theorem is a result in number theory that linked certain modular forms to Galois representations and played a crucial role in the proof of Fermat's Last Theorem.
• C. 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.
• D. Mazur's deformation theory of Galois representations
  Mazur's deformation theory of Galois representations is a foundational framework in number theory that systematically studies how p-adic Galois representations can be deformed, with deep applications to modular forms and the proof of Fermat’s Last Theorem.
• E. Bloch–Kato conjecture
  The Bloch–Kato conjecture is a deep statement in arithmetic geometry and K-theory that predicts an exact correspondence between Galois cohomology and Milnor K-theory, linking algebraic K-groups to field arithmetic.
• F. None of above. chosen