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: Brill–Noether number | Statement: [Brill–Noether theory, centralInvariant, Brill–Noether number]

Target entity: Brill–Noether number
Context triple: [Brill–Noether theory, centralInvariant, Brill–Noether number]

• A. Brill–Noether theory chosen
  Brill–Noether theory is a branch of algebraic geometry that studies linear series on algebraic curves, particularly the existence and dimension of spaces of special divisors and maps to projective spaces.
• B. Grothendieck–Ogg–Shafarevich formula
  The Grothendieck–Ogg–Shafarevich formula is a result in arithmetic geometry that relates the Euler characteristic of an ℓ-adic sheaf on a curve over a finite field to local invariants such as conductors and ramification data.
• C. Riemann–Roch theorem
  The Riemann–Roch theorem is a fundamental result in algebraic geometry and complex analysis that relates the dimension of spaces of meromorphic sections of a line bundle on a curve to topological data such as genus and degree.
• D. Plücker formulas
  Plücker formulas are classical algebraic geometry relations that connect the degree and singularities of plane algebraic curves with the invariants of their dual curves.
• E. Hodge–Riemann bilinear relations
  The Hodge–Riemann bilinear relations are fundamental positivity and orthogonality conditions on the intersection form in Hodge theory that underpin results such as the hard Lefschetz theorem and the Hodge index theorem.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target predicate: centralInvariant
Context triple: [Brill–Noether theory, centralInvariant, Brill–Noether number]

• A. invariantOf chosen
  Indicates that one element is an invariant (a property or quantity that remains unchanged) with respect to another element, system, or transformation.
• B. invariantUnder
  Indicates that a property, structure, or quantity remains unchanged when a specified transformation or operation is applied.
• C. centralIn
  Indicates that one entity occupies a central or most important position within another entity, context, or structure.
• D. centralArtifact
  Indicates that an artifact serves as the primary or focal object within a given context, structure, or collection.
• E. centralWork
  Indicates that a particular work is the primary, most important, or focal work associated with an entity or context.
• F. None of above.