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: modular group PSL(2,Z) | Statement: [Farey tessellation, isInvariantUnder, modular group PSL(2,Z)]

Target entity: modular group PSL(2,Z)
Context triple: [Farey tessellation, isInvariantUnder, modular group PSL(2,Z)]

• A. modular group PSL(2,Z) chosen
  The modular group PSL(2,ℤ) is a fundamental discrete group of 2×2 integer matrices modulo sign, acting by fractional linear transformations on the upper half-plane and playing a central role in number theory, geometry, and the theory of modular forms.
• B. PSL(2,ℤ/Nℤ)
  PSL(2,ℤ/Nℤ) is the projective special linear group of 2×2 matrices with entries in the ring of integers modulo N, modulo scalar matrices, forming a fundamental example of a finite (or, for composite N, generally non-simple) group in algebra and number theory.
• C. SL(2,ℤ)
  SL(2,ℤ) is the group of 2×2 integer matrices with determinant 1, fundamental in number theory, geometry, and the theory of modular forms.
• D. Fuchsian group
  A Fuchsian group is a discrete group of isometries of the hyperbolic plane, fundamental in the study of Riemann surfaces, modular forms, and hyperbolic geometry.
• E. PSL(2,7)
  PSL(2,7) is a finite simple group of order 168, notable as the full automorphism group of the Klein quartic and as a key example in the theory of projective linear groups over finite fields.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.