[
  {
    "id": "adrs15-dgs-any",
    "categoryId": "dgs-arbitrary-width",
    "paperId": "paper-86925aff6e6c",
    "year": 2015,
    "date": "2014-12-26",
    "time": {
      "coefficient": 1,
      "expression": "2^{1 n + o(n)}"
    },
    "space": {
      "coefficient": 1,
      "expression": "2^{1 n + o(n)}"
    },
    "tags": [
      "classical",
      "provable",
      "worst case",
      "DGS",
      "arbitrary width",
      "unstructured"
    ],
    "review": {
      "status": "source-checked"
    },
    "certificate": {
      "status": "not-provided",
      "lean": null
    },
    "notes": "STOC 2015; first arXiv date shown. Total cost for a batch of 2^{n/2} samples (abstract). Retaining one sample gives the displayed upper bound.",
    "extra": {
      "width": "Any positive Gaussian parameter",
      "output": "2^{n/2} samples",
      "error": "As specified by the source theorem",
      "model": "Randomized classical; preprocessing included",
      "reference": "ADRS15"
    }
  },
  {
    "id": "hkkl26-dgs-any",
    "categoryId": "dgs-arbitrary-width",
    "paperId": "paper-c70730f20075",
    "year": 2026,
    "date": "2026-11-04",
    "time": {
      "coefficient": 0.292,
      "expression": "2^{0.292 n + o(n)}"
    },
    "space": {
      "coefficient": 0.208,
      "expression": "2^{0.208 n + o(n)}"
    },
    "tags": [
      "classical",
      "provable",
      "worst case",
      "DGS",
      "arbitrary width",
      "unstructured"
    ],
    "review": {
      "status": "source-checked"
    },
    "certificate": {
      "status": "not-provided",
      "lean": null
    },
    "notes": "Public preprint abstract claims arbitrary-width DGS with polynomial dependence on κ for error 2^{-κ}. Source-attributed bound; proof not independently audited.",
    "extra": {
      "width": "Any positive Gaussian parameter",
      "output": "One fresh sample; output batch not normalized",
      "error": "2^{-κ}; poly(κ) factors suppressed",
      "model": "Randomized classical worst-case analysis",
      "reference": "HKKL26"
    }
  },
  {
    "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"
    }
  }
]