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: Wigner–Dyson statistics | Statement: [Gaussian orthogonal ensemble, eigenvalueStatistics, Wigner–Dyson statistics]

Target entity: Wigner–Dyson statistics
Context triple: [Gaussian orthogonal ensemble, eigenvalueStatistics, Wigner–Dyson statistics]

• A. Wigner surmise
  The Wigner surmise is an approximate formula in random matrix theory that describes the statistical distribution of spacings between neighboring energy levels in complex quantum systems.
• B. Gaussian unitary ensemble
  The Gaussian unitary ensemble is a fundamental random matrix ensemble of complex Hermitian matrices with statistically independent, Gaussian-distributed entries, central to quantum chaos and random matrix theory.
• C. Wigner matrices
  Wigner matrices are large random symmetric (or Hermitian) matrices with independent, identically distributed entries (up to symmetry) that serve as a fundamental model in random matrix theory for studying eigenvalue statistics and universal spectral behavior.
• D. Gaussian symplectic ensemble
  The Gaussian symplectic ensemble is a random matrix ensemble of self-dual quaternionic Hermitian matrices used in random matrix theory to model systems with time-reversal symmetry and strong spin–orbit coupling.
• E. Wigner semicircle law
  The Wigner semicircle law is a fundamental result in random matrix theory that describes how the eigenvalues of large random symmetric (or Hermitian) matrices are distributed according to a characteristic semicircular density.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Wigner–Dyson statistics
Target entity description: Wigner–Dyson statistics describe the characteristic level-spacing distributions of eigenvalues in random matrix ensembles, capturing universal spectral correlations in complex quantum and chaotic systems.

• A. Wigner surmise chosen
  The Wigner surmise is an approximate formula in random matrix theory that describes the statistical distribution of spacings between neighboring energy levels in complex quantum systems.
• B. Gaussian unitary ensemble
  The Gaussian unitary ensemble is a fundamental random matrix ensemble of complex Hermitian matrices with statistically independent, Gaussian-distributed entries, central to quantum chaos and random matrix theory.
• C. Wigner matrices
  Wigner matrices are large random symmetric (or Hermitian) matrices with independent, identically distributed entries (up to symmetry) that serve as a fundamental model in random matrix theory for studying eigenvalue statistics and universal spectral behavior.
• D. Gaussian symplectic ensemble
  The Gaussian symplectic ensemble is a random matrix ensemble of self-dual quaternionic Hermitian matrices used in random matrix theory to model systems with time-reversal symmetry and strong spin–orbit coupling.
• E. Wigner semicircle law
  The Wigner semicircle law is a fundamental result in random matrix theory that describes how the eigenvalues of large random symmetric (or Hermitian) matrices are distributed according to a characteristic semicircular density.
• F. None of above.

Target predicate: eigenvalueStatistics
Context triple: [Gaussian orthogonal ensemble, eigenvalueStatistics, Wigner–Dyson statistics]

• A. eigenvaluesCorrespondTo
  Indicates that the eigenvalues are associated in a defined way with another mathematical object or set, such as arising from or matching the spectrum of that object.
• B. areEigenfunctionsOf
  Indicates that certain functions serve as eigenfunctions corresponding to a specified operator or transformation.
• C. eigenvectorsCorrespondTo
  Indicates that one set of eigenvectors is associated with, or corresponds in a defined way to, another set of eigenvectors (typically via a shared transformation, matrix, or mapping).
• D. CPEigenstate
  Indicates that a quantum state is an eigenstate of the combined charge-conjugation and parity (CP) symmetry operator, remaining unchanged up to a phase under the CP transformation.
• E. hasCPApproximateEigenvalue
  Indicates that one entity is an approximate eigenvalue of a completely positive (CP) map or operator associated with another entity.
• F. None of above. chosen