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: [Hodge decomposition, generalizationOf, Helmholtz decomposition]

Target entity: Helmholtz decomposition
Context triple: [Hodge decomposition, generalizationOf, 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
  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. Prandtl–Batchelor theorem
  The Prandtl–Batchelor theorem is a result in fluid dynamics that characterizes the uniform vorticity distribution in regions of closed streamlines at high Reynolds numbers.
• D. Hicks potential flow solutions
  Hicks potential flow solutions are a set of analytical solutions in fluid dynamics that describe idealized, inviscid, incompressible flow patterns around bodies, developed by mathematician William Mitchinson Hicks.
• E. 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.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Helmholtz decomposition
Target entity description: Helmholtz decomposition is a fundamental result in vector calculus stating that any sufficiently smooth vector field can be uniquely decomposed into an irrotational (gradient) part and a solenoidal (divergence-free) part under suitable conditions.

• 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. Prandtl–Batchelor theorem
  The Prandtl–Batchelor theorem is a result in fluid dynamics that characterizes the uniform vorticity distribution in regions of closed streamlines at high Reynolds numbers.
• D. Hicks potential flow solutions
  Hicks potential flow solutions are a set of analytical solutions in fluid dynamics that describe idealized, inviscid, incompressible flow patterns around bodies, developed by mathematician William Mitchinson Hicks.
• E. 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.
• F. None of above.