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: Dehn algorithm | Statement: [Dehn function, relatedConcept, Dehn algorithm]

Target entity: Dehn algorithm
Context triple: [Dehn function, relatedConcept, Dehn algorithm]

• A. Dehn algorithm chosen
  The Dehn algorithm is a decision procedure in combinatorial group theory that solves the word problem for certain groups by systematically reducing words using defining relations.
• B. Dehn’s decision problems in group theory
  Dehn’s decision problems in group theory are foundational early 20th-century problems that introduced algorithmic questions about the solvability of word, conjugacy, and isomorphism problems in finitely presented groups, helping launch the field of algorithmic group theory.
• C. Dehn function
  The Dehn function is a mathematical tool in geometric group theory that measures the complexity of filling loops with discs in a space or group, quantifying the difficulty of solving the word problem.
• D. Dehn complex
  The Dehn complex is a topological construction introduced by Max Dehn in the study of group presentations and decision problems, encoding relations of a group as a 2-dimensional cell complex.
• E. Dehn lemma
  The Dehn lemma is a fundamental result in 3-manifold topology that gives conditions under which a loop on the boundary of a 3-manifold bounds an embedded disk in the manifold.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.