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: König's theorem | Statement: [Julius König, notableWork, König's theorem]

Target entity: König's theorem
Context triple: [Julius König, notableWork, König's theorem]

• A. Kesten’s theorem
  Kesten’s theorem is a fundamental result in probability theory that characterizes when a random walk on a group is transient or recurrent, with deep implications for random walks on groups and percolation theory.
• B. Szekeres–Lindström theorem
  The Szekeres–Lindström theorem is a result in combinatorics that characterizes the maximum size of intersecting families of subsets, serving as a precursor to and special case of the Erdős–Ko–Rado theorem.
• C. Kuhn’s theorem
  Kuhn’s theorem is a fundamental result in game theory that shows any finite extensive-form game with perfect recall has an equivalent normal-form (strategic-form) representation, ensuring the existence of mixed-strategy equilibria.
• D. Robbins theorem
  Robbins theorem is a result in graph theory that characterizes when a connected graph can be oriented to become strongly connected, providing a key condition for the existence of strongly connected orientations.
• E. Bose–Nair theorem
  The Bose–Nair theorem is a result in combinatorial design theory that provides conditions for the existence and construction of certain balanced incomplete block designs, contributing to the foundations of modern combinatorics and coding theory.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: König's theorem
Target entity description: König's theorem is a fundamental result in graph theory that relates the size of a maximum matching to the size of a minimum vertex cover in bipartite graphs.

• A. Kesten’s theorem
  Kesten’s theorem is a fundamental result in probability theory that characterizes when a random walk on a group is transient or recurrent, with deep implications for random walks on groups and percolation theory.
• B. Szekeres–Lindström theorem
  The Szekeres–Lindström theorem is a result in combinatorics that characterizes the maximum size of intersecting families of subsets, serving as a precursor to and special case of the Erdős–Ko–Rado theorem.
• C. Kuhn’s theorem
  Kuhn’s theorem is a fundamental result in game theory that shows any finite extensive-form game with perfect recall has an equivalent normal-form (strategic-form) representation, ensuring the existence of mixed-strategy equilibria.
• D. Robbins theorem
  Robbins theorem is a result in graph theory that characterizes when a connected graph can be oriented to become strongly connected, providing a key condition for the existence of strongly connected orientations.
• E. Bose–Nair theorem
  The Bose–Nair theorem is a result in combinatorial design theory that provides conditions for the existence and construction of certain balanced incomplete block designs, contributing to the foundations of modern combinatorics and coding theory.
• F. None of above. chosen