{
  "as_of": "2026-09-07",
  "references": [
    {
      "title": "New large value estimates for Dirichlet polynomials",
      "authors": [
        "Larry Guth",
        "James Maynard"
      ],
      "venue": "Annals of Mathematics 203 (2026), 623-675",
      "role": "Zero density A0=30/13 and all-interval short-prime asymptotic scale 17/30"
    },
    {
      "title": "On the number of exceptional intervals to the prime number theorem in short intervals",
      "authors": [
        "Ayla Gafni",
        "Terence Tao"
      ],
      "venue": "Essential Number Theory 5 (2026), 221-241",
      "role": "Exceptional-set exponent framework; fixed relative threshold delta; almost-all scale 2/15 via modern zero density"
    },
    {
      "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",
      "role": "Prime residual arbitrary fixed log-power almost-all short-interval precision"
    },
    {
      "title": "A new zero-density estimate for zeta(s) and the error term in the Prime Number Theorem",
      "author": "Chiara Bellotti",
      "year": 2025,
      "role": "Current PNT remainder remains Vinogradov-Korobov subpower class"
    },
    {
      "title": "On a variant of the prime number theorem",
      "author": "Wei Zhang",
      "year": 2023,
      "role": "Fixed-power quotient-transform von-Mangoldt theorem used as observability false-positive test"
    }
  ]
}