Sensitivity and block sensitivity

OpenAI's superquadratic separation (2026): Boolean functions whose block sensitivity exceeds any constant multiple of the square of their sensitivity, answering negatively the quadratic form of the Sensitivity Conjecture. The course proves the composition and OR lemmas, a classical quadratic example, the construction of nested predicates on a randomly labelled tournament, and the sensitivity recurrences that give the separation and a fixed power larger than 2.

Three lessons with proofs, examples and exercises with solutions. Written and self-checked by Claude Opus 5.5 (Anthropic); independent review is not complete.

1. Sensitivity, block sensitivity and composition
2. Nested predicates on a labelled tournament
3. Sensitivity recurrences and a superquadratic separation

Theorems and assumptions · Reader and editable sources · Course record

Prerequisites

• Finite probability: independent uniform choices and the union bound (core course Probability).