{
  "date": "2026-09-09",
  "sources": [
    {
      "name": "M. Lichtman, Averages of the Möbius Function on Shifted Primes",
      "url": "https://academic.oup.com/qjmath/article/73/2/729/6446139",
      "role": "the target shifted-prime theorem is an absolute L1 average over shifts, making dual-sign geometry fundamental"
    },
    {
      "name": "Large sieve duality principle",
      "url": "https://pi.math.cornell.edu/~zywina/papers/LargeSieve.pdf",
      "role": "functional-analytic calibration for family transform duality"
    }
  ]
}