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: Steiner’s theorem in projective geometry | Statement: [Jakob Steiner, notableWork, Steiner’s theorem in projective geometry]

Target entity: Steiner’s theorem in projective geometry
Context triple: [Jakob Steiner, notableWork, Steiner’s theorem in projective geometry]

• A. 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.
• B. Traité des propriétés projectives des figures
  Traité des propriétés projectives des figures is a foundational 19th-century mathematical treatise that systematically develops projective geometry and helped establish it as an independent discipline.
• C. On the Principles of Geometry
  "On the Principles of Geometry" is Nikolai Lobachevsky’s foundational work that introduced non-Euclidean (hyperbolic) geometry, challenging the universality of Euclid’s parallel postulate.
• D. Cremona group of the projective plane
  The Cremona group of the projective plane is the group of all birational self-maps of the complex projective plane, serving as a fundamental object in algebraic geometry and the study of plane transformations.
• E. 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.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Steiner’s theorem in projective geometry
Target entity description: Steiner’s theorem in projective geometry is a classical result that characterizes the locus and incidence properties of points or conics associated with a complete quadrilateral (or related projective configurations), illustrating fundamental principles of projective transformations and duality.

• A. 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.
• B. Traité des propriétés projectives des figures
  Traité des propriétés projectives des figures is a foundational 19th-century mathematical treatise that systematically develops projective geometry and helped establish it as an independent discipline.
• C. On the Principles of Geometry
  "On the Principles of Geometry" is Nikolai Lobachevsky’s foundational work that introduced non-Euclidean (hyperbolic) geometry, challenging the universality of Euclid’s parallel postulate.
• D. Cremona group of the projective plane
  The Cremona group of the projective plane is the group of all birational self-maps of the complex projective plane, serving as a fundamental object in algebraic geometry and the study of plane transformations.
• E. 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.
• F. None of above. chosen