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: Lieb–Oxford inequality | Statement: [Elliott H. Lieb, notableWork, Lieb–Oxford inequality]

Target entity: Lieb–Oxford inequality
Context triple: [Elliott H. Lieb, notableWork, Lieb–Oxford inequality]

• A. Hohenberg–Kohn theorem
  The Hohenberg–Kohn theorem is a foundational result in quantum mechanics that establishes the ground-state electron density as the central quantity determining all properties of a many-electron system, forming the basis of density functional theory.
• B. Kohn–Sham equations
  The Kohn–Sham equations are a set of self-consistent single-particle equations in density functional theory that map an interacting many-electron system onto a fictitious non-interacting system with the same electron density.
• C. Bogoliubov inequality
  The Bogoliubov inequality is a fundamental result in statistical mechanics and quantum field theory that provides bounds on correlation functions and plays a key role in the rigorous analysis of phase transitions.
• D. Herzberg–Teller approximation
  The Herzberg–Teller approximation is a refinement in molecular spectroscopy that accounts for vibronic coupling by allowing electronic transition dipole moments to depend on nuclear coordinates, explaining intensity in otherwise forbidden transitions.
• E. Gagliardo–Nirenberg interpolation inequalities
  The Gagliardo–Nirenberg interpolation inequalities are fundamental results in functional analysis and partial differential equations that bound intermediate norms of functions by combinations of lower and higher order norms, playing a key role in regularity theory and nonlinear analysis.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Lieb–Oxford inequality
Target entity description: The Lieb–Oxford inequality is a fundamental result in mathematical physics and density functional theory that provides a rigorous lower bound on the indirect part of the Coulomb interaction energy of many-electron systems.

• A. Hohenberg–Kohn theorem
  The Hohenberg–Kohn theorem is a foundational result in quantum mechanics that establishes the ground-state electron density as the central quantity determining all properties of a many-electron system, forming the basis of density functional theory.
• B. Kohn–Sham equations
  The Kohn–Sham equations are a set of self-consistent single-particle equations in density functional theory that map an interacting many-electron system onto a fictitious non-interacting system with the same electron density.
• C. Bogoliubov inequality
  The Bogoliubov inequality is a fundamental result in statistical mechanics and quantum field theory that provides bounds on correlation functions and plays a key role in the rigorous analysis of phase transitions.
• D. Herzberg–Teller approximation
  The Herzberg–Teller approximation is a refinement in molecular spectroscopy that accounts for vibronic coupling by allowing electronic transition dipole moments to depend on nuclear coordinates, explaining intensity in otherwise forbidden transitions.
• E. Gagliardo–Nirenberg interpolation inequalities
  The Gagliardo–Nirenberg interpolation inequalities are fundamental results in functional analysis and partial differential equations that bound intermediate norms of functions by combinations of lower and higher order norms, playing a key role in regularity theory and nonlinear analysis.
• F. None of above. chosen