{
  "id": "the-square-root-degree-bound",
  "title": "The square-root degree bound",
  "description": "OpenAI's theorem (2026) that the linear Fourier coefficients of a Boolean function can sum to more than any constant multiple of the square root of its degree; through observations of independent signs, a tagged report on Gaussian intervals, and amplification by independent copies.",
  "units": [
    {
      "id": "linear-fourier-coefficients-and-degree",
      "title": "Linear Fourier coefficients and degree",
      "reader": "linear-fourier-coefficients-and-degree.html",
      "source": "src/linear-fourier-coefficients-and-degree.md",
      "source_sha256": "a65ba4f4c9eb9b9cfe0651fdb0dd9bc7ac8d5f2f9e10d1da2b7203c13798840a",
      "status": "author_self_checked"
    },
    {
      "id": "asymptotically-normal-scores",
      "title": "Asymptotically normal scores",
      "reader": "asymptotically-normal-scores.html",
      "source": "src/asymptotically-normal-scores.md",
      "source_sha256": "a4509e4195d722799a7eb10caa950900b79453fadd55a3fa12112db2db24b1d7",
      "status": "author_self_checked"
    },
    {
      "id": "a-tagged-report",
      "title": "A tagged report",
      "reader": "a-tagged-report.html",
      "source": "src/a-tagged-report.md",
      "source_sha256": "ac871fb568589c051a48419d93f5d987fb91d2ddfb5c9b81b7ab533b3a1e8b93",
      "status": "author_self_checked"
    },
    {
      "id": "average-degree-costs",
      "title": "Average degree costs",
      "reader": "average-degree-costs.html",
      "source": "src/average-degree-costs.md",
      "source_sha256": "ee5cec179b6dbb5dac70576afed77b2ea2942ae1500e3a1de61406207d1d0829",
      "status": "author_self_checked"
    }
  ],
  "prerequisites": [
    "core course Measure and Integration (D10): Fremlin, Measure Theory, Vol. 2, 274I (central limit theorem for independent identically distributed variables, uniform convergence of distribution functions)"
  ],
  "status": "author_self_checked",
  "proof_providers": "providers.json",
  "provenance": "provenance.json",
  "licence": "CC0-1.0"
}