{
  "as_of": "2026-09-05",
  "references": [
    {
      "title": "An Elementary Proof of the Prime-Number Theorem",
      "author": "Atle Selberg",
      "venue": "Annals of Mathematics 50 (1949)",
      "role": "Prime-only symmetry formula"
    },
    {
      "title": "On the prime number lemma of Selberg",
      "author": "Filip Saidak",
      "venue": "Mathematica Scandinavica 103 (2008), 5-10",
      "doi": "10.7146/math.scand.a-15065",
      "role": "Refined Selberg residual tracks the PNT error"
    },
    {
      "title": "Asymptotic sieve for primes",
      "authors": [
        "John Friedlander",
        "Henryk Iwaniec"
      ],
      "venue": "Annals of Mathematics 148 (1998), 1041-1065",
      "doi": "10.2307/121035",
      "role": "Parity-breaking sieve via an added bilinear hypothesis"
    },
    {
      "title": "254A, Notes 4: Some sieve theory",
      "author": "Terence Tao",
      "year": 2015,
      "url": "https://terrytao.wordpress.com/2015/01/21/254a-notes-4-some-sieve-theory/",
      "role": "Parity-problem calibration for ordinary sieve information"
    }
  ]
}