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: Hodge star operator | Statement: [Hodge Laplacian, dependsOn, Hodge star operator]

Target entity: Hodge star operator
Context triple: [Hodge Laplacian, dependsOn, Hodge star operator]

• A. Hodge star operator chosen
  The Hodge star operator is a linear map on differential forms in oriented Riemannian manifolds that sends a k-form to an (n−k)-form in a way that encodes the metric and orientation, enabling duality operations such as defining codifferentials and expressing vector calculus identities.
• B. Hodge Laplacian
  The Hodge Laplacian is a differential operator on differential forms of a Riemannian manifold that combines the exterior derivative and its adjoint to study harmonic forms and de Rham cohomology.
• C. Lefschetz operator
  The Lefschetz operator is a linear operator in Kähler geometry that acts on differential forms by wedging with the Kähler form, playing a central role in the Hard Lefschetz theorem and Hodge theory.
• D. Fubini–Study form
  The Fubini–Study form is the canonical Kähler form on complex projective space, encoding its standard Hermitian and symplectic geometry.
• E. Hodge decomposition
  Hodge decomposition is a fundamental result in differential geometry and Hodge theory that expresses differential forms on a Riemannian manifold uniquely as sums of exact, co-exact, and harmonic components.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.