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: maximum modulus principle | Statement: [Lindelöf theorem in complex analysis, refines, maximum modulus principle]

Target entity: maximum modulus principle
Context triple: [Lindelöf theorem in complex analysis, refines, maximum modulus principle]

• A. Schwarz lemma
  Schwarz lemma is a fundamental result in complex analysis that constrains holomorphic self-maps of the unit disk, particularly bounding their magnitude and derivative at the origin.
• B. Borel–Carathéodory theorem
  The Borel–Carathéodory theorem is a result in complex analysis that provides bounds on the modulus of a holomorphic function inside a disk in terms of the maximum of its real part on a larger concentric disk.
• C. Schwarz–Pick theorem
  The Schwarz–Pick theorem is a fundamental result in complex analysis that characterizes holomorphic self-maps of the unit disk by showing they are distance-decreasing with respect to the hyperbolic (Poincaré) metric.
• D. Casorati–Weierstrass theorem
  The Casorati–Weierstrass theorem is a fundamental result in complex analysis stating that near an essential singularity, a complex function attains values arbitrarily close to every complex number.
• E. Rouché's theorem
  Rouché's theorem is a result in complex analysis that provides conditions under which two holomorphic functions have the same number of zeros inside a given contour.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: maximum modulus principle
Target entity description: The maximum modulus principle is a fundamental result in complex analysis stating that a non-constant holomorphic function on a connected open set cannot attain its maximum modulus in the interior, only on the boundary.

• A. Schwarz lemma
  Schwarz lemma is a fundamental result in complex analysis that constrains holomorphic self-maps of the unit disk, particularly bounding their magnitude and derivative at the origin.
• B. Borel–Carathéodory theorem
  The Borel–Carathéodory theorem is a result in complex analysis that provides bounds on the modulus of a holomorphic function inside a disk in terms of the maximum of its real part on a larger concentric disk.
• C. Schwarz–Pick theorem
  The Schwarz–Pick theorem is a fundamental result in complex analysis that characterizes holomorphic self-maps of the unit disk by showing they are distance-decreasing with respect to the hyperbolic (Poincaré) metric.
• D. Casorati–Weierstrass theorem
  The Casorati–Weierstrass theorem is a fundamental result in complex analysis stating that near an essential singularity, a complex function attains values arbitrarily close to every complex number.
• E. Rouché's theorem
  Rouché's theorem is a result in complex analysis that provides conditions under which two holomorphic functions have the same number of zeros inside a given contour.
• F. None of above. chosen