{
  "as_of": "2026-09-07",
  "references": [
    {
      "title": "Introduction to Analytic Number Theory, Theorems 5.18-5.21",
      "author": "A. J. Hildebrand",
      "year": 2013,
      "role": "Explicit formula for integrated Chebyshev psi_1; absolute convergence of zero series; isolated off-line zero produces x^(1+beta) log-periodic oscillation"
    }
  ]
}