{
  "as_of": "2026-09-07",
  "references": [
    {
      "title": "Higher uniformity of arithmetic functions in short intervals II. Almost all intervals",
      "authors": ["Kaisa Matomaki", "Maksym Radziwill", "Xuancheng Shao", "Terence Tao", "Joni Teravainen"],
      "venue": "Inventiones Mathematicae 244 (2026), 967-1091",
      "doi": "10.1007/s00222-026-01408-6",
      "role": "Lemma 3.5 and equations (3.9)-(3.13) calibrate the Type-II fixed-power mean-square target and T < X W^(3/10)/H reduction"
    },
    {
      "title": "The logarithmically averaged Chowla and Elliott conjectures for two-point correlations",
      "author": "Terence Tao",
      "arxiv": "1509.05422",
      "role": "Logarithmically averaged two-linear-form Liouville cancellation; does not give ordinary Cesaro two-point Chowla"
    },
    {
      "title": "Improved bounds for the two-point logarithmic Chowla conjecture",
      "author": "Cedric Pilatte",
      "arxiv": "2310.19357",
      "role": "Fixed power-logarithmic saving for logarithmically weighted shift-one Liouville correlation"
    },
    {
      "title": "Quantitative Logarithmic Chowla Correlations Uniformly over Growing Shifts",
      "author": "Jizhou Guo",
      "arxiv": "2608.23500",
      "date": "2026-08-24",
      "role": "Quantitative logarithmically weighted Liouville two-point correlation for polylogarithmically growing shifts; explicitly not ordinary Cesaro Chowla"
    }
  ]
}