{
  "as_of": "2026-09-06",
  "references": [
    {
      "title": "Primes in short intervals",
      "authors": [
        "Hugh L. Montgomery",
        "K. Soundararajan"
      ],
      "venue": "Communications in Mathematical Physics 252 (2004), 589-617",
      "doi": "10.1007/s00220-004-1222-4",
      "role": "Gaussian moment / variance prediction and conditional higher-moment calibration"
    },
    {
      "title": "Prime numbers in logarithmic intervals",
      "authors": [
        "D. Bazzanella",
        "A. Languasco",
        "A. Zaccagnini"
      ],
      "venue": "Transactions of the American Mathematical Society 362 (2010), 2667-2684",
      "doi": "10.1090/S0002-9947-09-05009-0",
      "role": "Unconditional Gallagher/Klimov-type moment upper bounds; raw fixed fourth moment has H^4 leading scale for polynomial H"
    },
    {
      "title": "Higher moments of primes in short intervals I",
      "author": "Tsz Ho Chan",
      "arxiv": "math/0409530",
      "role": "Higher centered moment strength calibration under RH / deep prime-correlation information"
    },
    {
      "title": "Higher uniformity of arithmetic functions in short intervals II. Almost all intervals",
      "authors": [
        "Kaisa Matomäki",
        "Maksym Radziwiłł",
        "Xuancheng Shao",
        "Terence Tao",
        "Joni Teräväinen"
      ],
      "venue": "Inventiones Mathematicae 244 (2026), 967-1091",
      "doi": "10.1007/s00222-026-01408-6",
      "role": "Current short-interval higher-uniformity calibration; arbitrary logarithmic precision rather than fixed H-exponent gain"
    }
  ]
}