{
  "id": "sensitivity-and-block-sensitivity",
  "title": "Sensitivity and block sensitivity",
  "description": "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.",
  "units": [
    {
      "id": "sensitivity-block-sensitivity-and-composition",
      "title": "Sensitivity, block sensitivity and composition",
      "reader": "sensitivity-block-sensitivity-and-composition.html",
      "source": "src/sensitivity-block-sensitivity-and-composition.md",
      "source_sha256": "71a47de3b846e7a521ca92fa9a2f6b0596a7af9a84d95f672c1c60aa5c7f7da2",
      "status": "author_self_checked"
    },
    {
      "id": "nested-predicates-on-a-labelled-tournament",
      "title": "Nested predicates on a labelled tournament",
      "reader": "nested-predicates-on-a-labelled-tournament.html",
      "source": "src/nested-predicates-on-a-labelled-tournament.md",
      "source_sha256": "9926ca5f5a9816000a85a80446e6c160f14abad6a71ab273106a56988607373a",
      "status": "author_self_checked"
    },
    {
      "id": "sensitivity-recurrences-and-a-superquadratic-separation",
      "title": "Sensitivity recurrences and a superquadratic separation",
      "reader": "sensitivity-recurrences-and-a-superquadratic-separation.html",
      "source": "src/sensitivity-recurrences-and-a-superquadratic-separation.md",
      "source_sha256": "6969827c05844370e28c7ff2f09b2563ee3b85b8cea6bd2358d24f86ffe26a12",
      "status": "author_self_checked"
    }
  ],
  "prerequisites": [
    "core course Probability (finite probability: independence and the union bound)"
  ],
  "status": "author_self_checked",
  "proof_providers": "providers.json",
  "provenance": "provenance.json",
  "licence": "CC0-1.0"
}