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: Minkowski sum | Statement: [Hermann Minkowski, knownFor, Minkowski sum]

Target entity: Minkowski sum
Context triple: [Hermann Minkowski, knownFor, Minkowski sum]

• A. Minkowski sum chosen
  The Minkowski sum is a fundamental operation in geometry and convex analysis that combines two sets by adding every vector in one set to every vector in the other, widely used in areas such as optimization, robotics, and computational geometry.
• B. Minkowski functional
  The Minkowski functional is a mathematical tool in functional analysis that assigns a nonnegative real number to each vector in a vector space based on its position relative to a given convex, balanced, absorbing set, generalizing the notion of a norm.
• C. Carathéodory’s theorem in convex geometry
  Carathéodory’s theorem in convex geometry is a fundamental result stating that any point in the convex hull of a set in ℝⁿ can be expressed as a convex combination of at most n+1 points from that set.
• D. Minkowski inequality
  The Minkowski inequality is a fundamental result in functional analysis and measure theory that generalizes the triangle inequality to L^p spaces, providing a key tool for studying norms and integrable functions.
• E. Steinmetz solid
  The Steinmetz solid is a three-dimensional geometric shape formed by the intersection of two or more cylinders at right angles, often studied in calculus and solid geometry for its interesting volume and symmetry properties.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.