{
  "id": "kim26-dgs-arbitrary-one",
  "categoryId": "dgs-arbitrary-width",
  "paperId": "kim-2026-one-dgs",
  "year": 2026,
  "date": "2026-08-04",
  "datePrecision": "day",
  "time": {
    "coefficient": 0.5,
    "expression": "2^{n/2+o(n)} expected bit operations"
  },
  "space": {
    "coefficient": 0.5,
    "expression": "2^{n/2+o(n)} bits on every execution"
  },
  "tags": [
    "classical",
    "provable",
    "worst case",
    "DGS",
    "arbitrary width",
    "centered",
    "single sample"
  ],
  "review": {
    "status": "source-checked"
  },
  "certificate": {
    "status": "not-provided",
    "lean": null
  },
  "notes": "One centered sample, rather than the older 2^{n/2}-output arbitrary-width batch. Polynomial dependence on basis and squared-width encoding lengths is explicit in the theorem.",
  "extra": {
    "width": "Any rational s^2 > 0 on a rank-n lattice with rational basis",
    "output": "One sample from D_{L,s}",
    "error": "exp(-Omega(n^3)) statistical distance",
    "model": "Randomized classical; expected time and bounded space per execution",
    "reference": "Kim26"
  },
  "evidence": {
    "url": "https://arxiv.org/abs/2608.03220v1",
    "locator": "Theorem 4.3, printed p. 10; Theorem 1.1",
    "sourceVersion": "arXiv:2608.03220v1, 4 August 2026"
  }
}