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: Kadison–Singer problem | Statement: [Bourgain–Tzafriri restricted invertibility principle, relatedTo, Kadison–Singer problem]

Target entity: Kadison–Singer problem
Context triple: [Bourgain–Tzafriri restricted invertibility principle, relatedTo, Kadison–Singer problem]

• A. Connes embedding problem
  The Connes embedding problem is a central open question in operator algebras and quantum theory that asks whether every separable II₁ factor can be approximated in a specific way by finite-dimensional matrix algebras.
• B. Grothendieck inequality
  The Grothendieck inequality is a fundamental result in functional analysis and theoretical computer science that bounds certain bilinear forms and has deep implications for Banach space theory, operator theory, and approximation algorithms.
• C. Erdős discrepancy problem
  The Erdős discrepancy problem is a famous question in combinatorial number theory that asks whether every infinite ±1 sequence has arbitrarily large discrepancy along some homogeneous arithmetic progression.
• D. Bourgain–Tzafriri restricted invertibility principle
  The Bourgain–Tzafriri restricted invertibility principle is a fundamental result in functional analysis and operator theory that guarantees the existence of large, well-invertible submatrices within certain classes of linear operators.
• E. Bose–Nair theorem
  The Bose–Nair theorem is a result in combinatorial design theory that provides conditions for the existence and construction of certain balanced incomplete block designs, contributing to the foundations of modern combinatorics and coding theory.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Kadison–Singer problem
Target entity description: The Kadison–Singer problem is a famous question in functional analysis and operator algebras, originally posed in 1959, concerning the unique extension of pure states on a diagonal subalgebra of bounded operators on a Hilbert space, and has deep connections to frame theory, signal processing, and discrepancy theory.

• A. Connes embedding problem
  The Connes embedding problem is a central open question in operator algebras and quantum theory that asks whether every separable II₁ factor can be approximated in a specific way by finite-dimensional matrix algebras.
• B. Grothendieck inequality
  The Grothendieck inequality is a fundamental result in functional analysis and theoretical computer science that bounds certain bilinear forms and has deep implications for Banach space theory, operator theory, and approximation algorithms.
• C. Erdős discrepancy problem
  The Erdős discrepancy problem is a famous question in combinatorial number theory that asks whether every infinite ±1 sequence has arbitrarily large discrepancy along some homogeneous arithmetic progression.
• D. Bourgain–Tzafriri restricted invertibility principle
  The Bourgain–Tzafriri restricted invertibility principle is a fundamental result in functional analysis and operator theory that guarantees the existence of large, well-invertible submatrices within certain classes of linear operators.
• E. Bose–Nair theorem
  The Bose–Nair theorem is a result in combinatorial design theory that provides conditions for the existence and construction of certain balanced incomplete block designs, contributing to the foundations of modern combinatorics and coding theory.
• F. None of above. chosen