{
  "date": "2026-09-09",
  "sources": [
    {
      "name": "P. X. Gallagher — On the distribution of primes in short intervals",
      "url": "https://doi.org/10.1112/S0025579300016442",
      "role": "classical Poisson/factorial-moment framework and unconditional sieve upper-tail bound in logarithmic intervals"
    },
    {
      "name": "Vivian Kuperberg — Sums of singular series with large sets and the tail of the distribution of primes",
      "url": "https://arxiv.org/abs/2210.09775",
      "role": "large-k singular-series and prime-tail analysis; unconditional Selberg-sieve moments r=o((log X)^(1/4)) with coarse overhead"
    },
    {
      "name": "Abhishek Jha — The Poisson Tail Conjecture for Primes in Short Intervals",
      "url": "https://arxiv.org/abs/2605.23014",
      "role": "2026 conditional Poisson-tail asymptotics for slowly growing lambda under strong Hardy-Littlewood"
    },
    {
      "name": "Kaisa Matomaki — Almost primes in almost all very short intervals",
      "url": "https://doi.org/10.1112/jlms.12592",
      "role": "lower-tail almost-prime control via weighted sieve and Kloosterman input; calibration of the extra difficulty of prime parity"
    }
  ]
}