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: Leech lattice | Statement: [Co2, actsFaithfullyOn, Leech lattice]

Target entity: Leech lattice
Context triple: [Co2, actsFaithfullyOn, Leech lattice]

• A. Leech lattice chosen
  The Leech lattice is a highly symmetric 24-dimensional lattice in Euclidean space, notable for its dense sphere packing and deep connections to sporadic simple groups and modular forms.
• B. E8 lattice
  The E8 lattice is an eight-dimensional, highly symmetric even unimodular lattice that plays a central role in Lie theory, sphere packing, and string theory.
• C. Klein quartic
  The Klein quartic is a highly symmetric algebraic curve of genus 3 that plays a central role in complex geometry, group theory, and the study of Riemann surfaces.
• D. Conway’s topograph
  Conway’s topograph is a geometric visualization tool introduced by mathematician John H. Conway to study binary quadratic forms and their arithmetic properties using a planar graph of curves and regions.
• E. Conway–Norton collaboration
  The Conway–Norton collaboration was a joint mathematical effort, led by John Conway and Simon Norton, that played a key role in developing the theory of monstrous moonshine and the construction of the Monster group.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target predicate: actsFaithfullyOn
Context triple: [Co2, actsFaithfullyOn, Leech lattice]

• A. actsOn chosen
  Indicates that one entity performs an action that affects, targets, or is directed toward another entity.
• B. servesFaithfulOf
  Indicates that one entity performs services or acts in a ministering or supportive role for those who are faithful to another entity.
• C. invariantUnder
  Indicates that a property, structure, or quantity remains unchanged when a specified transformation or operation is applied.
• D. actsOnBehalfOf
  Indicates that one entity performs actions or makes decisions as a representative or proxy for another entity.
• E. conjugacyProperty
  Indicates that two elements or structures are related by conjugation, sharing the same form up to an inner automorphism or similarity transformation.
• F. None of above.