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: Icosian game of William Rowan Hamilton | Statement: [Hamiltonian cycle, historicalOrigin, Icosian game of William Rowan Hamilton]

Target entity: Icosian game of William Rowan Hamilton
Context triple: [Hamiltonian cycle, historicalOrigin, Icosian game of William Rowan Hamilton]

• A. Seven Bridges of Königsberg problem
  The Seven Bridges of Königsberg problem is a historic puzzle in graph theory that asks whether one can walk through the city of Königsberg crossing each of its seven bridges exactly once, leading Euler to found the field of topology.
• B. Conway’s soldiers
  Conway’s soldiers is a mathematical puzzle and thought experiment in combinatorial game theory that explores how far checkers-like pieces can advance on an infinite grid under specific movement rules.
• C. Kayles
  Kayles is a classic impartial combinatorial game in which players alternately remove one or two adjacent pins from a row, with the goal of making the last move.
• D. Mathematical Recreations and Essays
  Mathematical Recreations and Essays is a classic book of popular mathematics that explores a wide range of mathematical puzzles, curiosities, and historical topics in an accessible style.
• E. Conway’s Game of Sprouts
  Conway’s Game of Sprouts is a pencil-and-paper topological game in which players alternately connect dots with lines under simple rules, leading to rich combinatorial and mathematical analysis.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Icosian game of William Rowan Hamilton
Target entity description: The Icosian game of William Rowan Hamilton is a 19th-century mathematical puzzle based on finding a Hamiltonian cycle on the vertices of a dodecahedron, which helped introduce and popularize the concept of Hamiltonian paths in graph theory.

• A. Seven Bridges of Königsberg problem
  The Seven Bridges of Königsberg problem is a historic puzzle in graph theory that asks whether one can walk through the city of Königsberg crossing each of its seven bridges exactly once, leading Euler to found the field of topology.
• B. Conway’s soldiers
  Conway’s soldiers is a mathematical puzzle and thought experiment in combinatorial game theory that explores how far checkers-like pieces can advance on an infinite grid under specific movement rules.
• C. Kayles
  Kayles is a classic impartial combinatorial game in which players alternately remove one or two adjacent pins from a row, with the goal of making the last move.
• D. Mathematical Recreations and Essays
  Mathematical Recreations and Essays is a classic book of popular mathematics that explores a wide range of mathematical puzzles, curiosities, and historical topics in an accessible style.
• E. Conway’s Game of Sprouts
  Conway’s Game of Sprouts is a pencil-and-paper topological game in which players alternately connect dots with lines under simple rules, leading to rich combinatorial and mathematical analysis.
• F. None of above. chosen