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: SO(2) | Statement: [SO(3), maximalTorus, SO(2)]

Target entity: SO(2)
Context triple: [SO(3), maximalTorus, SO(2)]

• A. rotation group SO(3)
  The rotation group SO(3) is the group of all rotations in three-dimensional space, represented by 3×3 orthogonal matrices with determinant 1, and plays a central role in classical mechanics, quantum mechanics, and geometry.
• B. rotation group SU(2)
  The rotation group SU(2) is the Lie group of 2×2 unitary matrices with determinant 1 that serves as the double cover of the three-dimensional rotation group SO(3) and underlies the quantum theory of angular momentum and spin.
• C. special orthogonal group SO(n) chosen
  The special orthogonal group SO(n) is the group of all n×n real rotation matrices with determinant 1, representing orientation-preserving isometries of n-dimensional Euclidean space that fix the origin.
• D. Spin(2,d)
  Spin(2,d) is the double-covering spin group of SO(2,d), serving as the relevant symmetry group for spinor fields in (d+1)-dimensional anti-de Sitter space.
• E. SL(2,R)
  SL(2,R) is the Lie group of 2×2 real matrices with determinant 1, fundamental in representation theory, geometry, and the study of symmetries in mathematics and physics.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target predicate: maximalTorus
Context triple: [SO(3), maximalTorus, SO(2)]

• A. hasMaximalTorusDimension
  Indicates that the associated group or algebraic structure has a maximal torus whose dimension equals the specified value or satisfies a given dimensional property.
• B. hasMaximalCompactSubgroupOf
  Indicates that one mathematical group is the maximal compact subgroup contained within another group.
• C. isMaximalSymmetryGroupOf
  Indicates that a group represents the largest possible symmetry group for a given object or structure, such that no strictly larger symmetry group of that object exists containing it.
• D. isMaximallySymmetric
  Indicates that the subject exhibits the highest possible degree of symmetry allowed by the relevant structure, constraints, or context.
• E. maximalIdealsCorrespondTo
  Indicates that there is a correspondence or bijective relationship between maximal ideals in one structure and certain objects or properties in another structure.
• F. None of above. chosen