{
  "date": "2026-09-09",
  "sources": [
    {
      "name": "Vaughan identity — Encyclopedia of Mathematics",
      "url": "https://encyclopediaofmath.org/wiki/Vaughan_identity",
      "role": "exact three-piece Vaughan decomposition and Type-I/Type-II coefficient structure"
    },
    {
      "name": "Kevin Ford and James Maynard — On the theory of prime-producing sieves",
      "url": "https://www.ford126.web.illinois.edu/wwwpapers/prime-producing-sieves.pdf",
      "role": "calibration that exact Type-I/Type-II information can transfer to prime sums; Vaughan sufficiency gamma+nu>1"
    }
  ]
}