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: Liouville theorem | Statement: [Poisson bracket, appearsIn, Liouville theorem]

Target entity: Liouville theorem
Context triple: [Poisson bracket, appearsIn, Liouville theorem]

• A. Liouville's theorem
  Liouville's theorem is a fundamental result in complex analysis stating that any bounded entire function must be constant.
• B. Picard theorem
  Picard theorem is a fundamental result in complex analysis stating that entire non-constant functions take on all possible complex values, with at most one exception.
• C. Montel theorem
  Montel's theorem is a fundamental result in complex analysis stating that a family of holomorphic functions that is uniformly bounded on every compact subset of a domain is a normal family, meaning every sequence in it has a subsequence that converges uniformly on compact sets.
• D. 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.
• E. 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.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Liouville theorem
Target entity description: Liouville's theorem is a fundamental result in Hamiltonian mechanics stating that the phase-space volume occupied by an ensemble of systems is conserved over time under Hamiltonian evolution.

• A. Liouville's theorem
  Liouville's theorem is a fundamental result in complex analysis stating that any bounded entire function must be constant.
• B. Picard theorem
  Picard theorem is a fundamental result in complex analysis stating that entire non-constant functions take on all possible complex values, with at most one exception.
• C. Montel theorem
  Montel's theorem is a fundamental result in complex analysis stating that a family of holomorphic functions that is uniformly bounded on every compact subset of a domain is a normal family, meaning every sequence in it has a subsequence that converges uniformly on compact sets.
• D. 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.
• E. 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.
• F. None of above. chosen