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: Fano plane incidence structure | Statement: [PSL(2,7), isAutomorphismGroupOf, Fano plane incidence structure]

Target entity: Fano plane incidence structure
Context triple: [PSL(2,7), isAutomorphismGroupOf, Fano plane incidence structure]

• A. Fano plane chosen
  The Fano plane is the smallest finite projective plane, consisting of seven points and seven lines with rich symmetrical and combinatorial properties.
• B. Szekeres configuration
  The Szekeres configuration is a notable geometric arrangement in projective geometry consisting of points and lines with specific incidence properties, studied for its combinatorial and symmetry characteristics.
• C. Sylvester–Gallai theorem
  The Sylvester–Gallai theorem is a result in incidence geometry stating that for any finite set of points in the Euclidean plane not all on a single line, there exists a line that passes through exactly two of the points.
• D. Veblen axioms for projective geometry
  The Veblen axioms for projective geometry are a foundational set of incidence-based axioms introduced by Oswald Veblen to rigorously formalize the structure of projective spaces.
• E. The Real Projective Plane
  The Real Projective Plane is a classic mathematical monograph by H. S. M. Coxeter that systematically develops the geometry and topology of the real projective plane, emphasizing its axiomatic foundations and non-Euclidean properties.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target predicate: isAutomorphismGroupOf
Context triple: [PSL(2,7), isAutomorphismGroupOf, Fano plane incidence structure]

• A. automorphismGroupIsomorphicTo
  Indicates that the automorphism group of one structure is isomorphic, as a group, to the automorphism group of another structure.
• B. hasAutomorphism
  Indicates that there exists a structure-preserving bijection from an entity to itself that maintains all relevant relations and operations.
• C. isMaximalSymmetryGroupOf
  Indicates that a group represents the largest possible symmetry group for a given object or structure, such that no strictly larger symmetry group of that object exists containing it.
• D. automorphismGroupOrder
  Indicates the size of the group of all structure-preserving bijections (automorphisms) of an object under composition.
• E. hasOuterAutomorphismGroupOrder
  Indicates the relationship that specifies the order (size) of the outer automorphism group associated with a given mathematical structure.
• F. None of above. chosen