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: Helmholtz decomposition | Statement: [Clebsch representation, relatedTo, Helmholtz decomposition]

Target entity: Helmholtz decomposition
Context triple: [Clebsch representation, relatedTo, Helmholtz decomposition]

• A. Helmholtz equation
  The Helmholtz equation is a fundamental partial differential equation that describes time-harmonic wave propagation in fields such as acoustics, electromagnetism, and optics.
• B. Hodge decomposition chosen
  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.
• C. Taylor–Proudman theorem
  The Taylor–Proudman theorem is a fundamental result in geophysical fluid dynamics stating that in a rapidly rotating, inviscid, incompressible fluid, steady flows tend to be uniform along the axis of rotation, leading to columnar motion.
• D. Biot–Savart law
  The Biot–Savart law is a fundamental equation in electromagnetism that gives the magnetic field produced by a steady electric current by integrating contributions from each current element in space.
• E. Hilbert transform
  The Hilbert transform is an integral transform that produces the harmonic conjugate of a real-valued function, playing a central role in signal processing, harmonic analysis, and the theory of analytic signals.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.