{
  "as_of": "2026-09-07",
  "references": [
    {
      "title": "On the Mobius function in all short intervals",
      "authors": [
        "Kaisa Matomaki",
        "Joni Teravainen"
      ],
      "arxiv": "1911.09076",
      "journal": "JEMS 25 (2023), 1207-1225",
      "role": "Ramaré prime extraction calibration; normalized conclusion is qualitative o(1), not a fixed X-power theorem for the present core"
    },
    {
      "title": "Expansion, divisibility and parity",
      "authors": [
        "Harald Andres Helfgott",
        "Maksym Radziwill"
      ],
      "arxiv": "2103.06853",
      "role": "prime-divisibility graph controlled by harmonic prime mass; Liouville two-point consequence has logarithmic-scale gain"
    },
    {
      "title": "Averages of the Mobius function on shifted primes",
      "author": "Jared Duker Lichtman",
      "arxiv": "2009.08969",
      "journal": "Q. J. Math. 73 (2022), 729-757",
      "role": "quantitative averaged-shift cancellation with logarithmic rather than fixed-X-power savings"
    },
    {
      "title": "On the Hardy-Littlewood-Chowla conjecture on average",
      "authors": [
        "Jared Duker Lichtman",
        "Joni Teravainen"
      ],
      "arxiv": "2111.08912",
      "journal": "Forum Math. Sigma 10 (2022)",
      "role": "hybrid prime/multiplicative correlations on average; not a direct single-dyadic fixed-X-power theorem for the structured weighted affine core"
    },
    {
      "title": "Smooth numbers and the Dickman rho function",
      "author": "Ofir Gorodetsky",
      "journal": "J. Anal. Math. 151 (2023), 139-169",
      "role": "modern smooth-number calibration; Paper 45 uses an elementary fixed-K prime-product lower bound instead"
    }
  ]
}