Gowers–Hatami stability theorem

Target entity: Gowers–Hatami stability theorem
Context triple: [Timothy Gowers, notableWork, Gowers–Hatami stability theorem]

• A. Szemerédi's theorem
  Szemerédi's theorem is a fundamental result in combinatorial number theory stating that any subset of the integers with positive upper density contains arbitrarily long arithmetic progressions.
• B. 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.
• C. Graham–Rothschild theorem
  The Graham–Rothschild theorem is a fundamental result in Ramsey theory that generalizes classical partition theorems to higher-dimensional combinatorial structures.
• 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. Håstad’s switching lemma
  Håstad’s switching lemma is a fundamental result in computational complexity theory that provides powerful bounds on the simplification of Boolean formulas under random restrictions, with major applications in circuit lower bounds.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Gowers–Hatami stability theorem
Target entity description: The Gowers–Hatami stability theorem is a result in functional analysis and group theory that characterizes when approximate representations of finite groups are close to genuine representations, providing a quantitative form of stability for such structures.

• A. Szemerédi's theorem
  Szemerédi's theorem is a fundamental result in combinatorial number theory stating that any subset of the integers with positive upper density contains arbitrarily long arithmetic progressions.
• B. 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.
• C. Graham–Rothschild theorem
  The Graham–Rothschild theorem is a fundamental result in Ramsey theory that generalizes classical partition theorems to higher-dimensional combinatorial structures.
• 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. Håstad’s switching lemma
  Håstad’s switching lemma is a fundamental result in computational complexity theory that provides powerful bounds on the simplification of Boolean formulas under random restrictions, with major applications in circuit lower bounds.
• F. None of above. chosen