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: Lichnerowicz formula | Statement: [Dirac operator, squareGivenBy, Lichnerowicz formula]

Target entity: Lichnerowicz formula
Context triple: [Dirac operator, squareGivenBy, Lichnerowicz formula]

• A. Lichnerowicz formula chosen
  The Lichnerowicz formula is a fundamental identity in differential geometry and spin geometry that relates the square of the Dirac operator on a spin manifold to the spinor Laplacian plus a curvature term involving the scalar curvature.
• B. Bochner–Kodaira–Nakano identity
  The Bochner–Kodaira–Nakano identity is a fundamental formula in complex differential geometry relating the Laplacian on differential forms to curvature terms, with key applications to vanishing theorems and Hodge theory.
• C. Bochner technique in Riemannian geometry
  The Bochner technique in Riemannian geometry is a method that uses Bochner-type identities and curvature conditions to derive vanishing theorems and rigidity results for differential forms and harmonic maps on manifolds.
• D. Yamabe problem
  The Yamabe problem is a fundamental question in differential geometry concerning whether every compact Riemannian manifold admits a metric of constant scalar curvature within a given conformal class.
• E. Ricci curvature tensor
  The Ricci curvature tensor is a geometric object in differential geometry that measures how volumes in a curved space-time deviate from those in flat space, playing a central role in general relativity.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target predicate: squareGivenBy
Context triple: [Dirac operator, squareGivenBy, Lichnerowicz formula]

• A. squareUse
  Indicates that one entity uses or occupies another entity in a square or rectangular configuration, typically implying a grid-like or evenly spaced arrangement.
• B. squareName
  Indicates that an entity is identified by or associated with the name of a square (such as a public square or plaza).
• C. locationOnSquare
  Indicates that one entity is positioned on a specific square region or cell within a larger spatial grid or board.
• D. approximateSquare
  Indicates that one quantity is approximately equal to the square of another quantity, within some acceptable margin of error.
• E. squareProperty
  Indicates that one entity is the square (second power) of a numerical property or value associated with another entity.
• F. None of above. chosen