{
  "as_of": "2026-09-05",
  "references": [
    {
      "title": "Correlations of the von Mangoldt and higher divisor functions I. Long shift ranges",
      "authors": [
        "Kaisa Matomäki",
        "Maksym Radziwiłł",
        "Terence Tao"
      ],
      "venue": "Proceedings of the London Mathematical Society 118 (2019), 284-350",
      "doi": "10.1112/plms.12181",
      "role": "Averaged Hardy-Littlewood prime-pair asymptotic with arbitrary logarithmic savings and H>=X^(8/33+epsilon)"
    },
    {
      "title": "Higher uniformity of arithmetic functions in short intervals II. Almost all intervals",
      "authors": [
        "Kaisa Matomäki",
        "Maksym Radziwiłł",
        "Xuancheng Shao",
        "Terence Tao",
        "Joni Teräväinen"
      ],
      "arxiv": "2411.05770",
      "role": "Current higher-uniformity / short-average Hardy-Littlewood calibration with log-power precision for von Mangoldt"
    },
    {
      "title": "Simple Barban-Davenport-Halberstam type asymptotics for general sequences",
      "author": "Adam J. Harper",
      "venue": "Journal of the London Mathematical Society",
      "year": 2025,
      "doi": "10.1112/jlms.70293",
      "role": "Current AP-variance calibration"
    },
    {
      "title": "On the connection between zero-free regions and the error term in the prime number theorem",
      "author": "Frederik Broucke",
      "venue": "Analysis Mathematica",
      "year": 2026,
      "doi": "10.1007/s10476-026-00176-y",
      "role": "Current zero-free-region / PNT-remainder calibration"
    }
  ]
}