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: Fermat quintic surface (n = 5) | Statement: [Fermat surface, hasSpecialCase, Fermat quintic surface (n = 5)]

Target entity: Fermat quintic surface (n = 5)
Context triple: [Fermat surface, hasSpecialCase, Fermat quintic surface (n = 5)]

• A. Fermat surface chosen
  A Fermat surface is an algebraic surface in projective space defined by a homogeneous equation where each variable appears with the same exponent, generalizing the notion of Fermat curves to higher dimensions.
• B. Fermat curve
  A Fermat curve is an algebraic curve defined by an equation of the form \(x^n + y^n = 1\), studied in number theory and algebraic geometry for its rich arithmetic and geometric properties.
• C. Cayley surface
  The Cayley surface is a classical cubic ruled surface in projective three-dimensional space, studied in algebraic geometry and named after the mathematician Arthur Cayley.
• D. Whitney umbrella surface
  The Whitney umbrella surface is a classic example in singularity theory and differential topology, illustrating a self-intersecting surface with a pinch point singularity in three-dimensional space.
• E. Clebsch diagonal surfaces
  Clebsch diagonal surfaces are classical 19th-century algebraic surfaces in projective three-space, famous as the first explicit smooth cubic surface with all 27 lines defined over the real numbers.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.