[
  {
    "id": "ghh26-dgs-smoothing-batch",
    "categoryId": "dgs-smoothing-reduced-batch",
    "paperId": "paper-fd038bb9c63f",
    "year": 2026,
    "date": "2026-11-03",
    "datePrecision": "day",
    "time": {
      "coefficient": 0.2924812503605781,
      "expression": "(3/2)^{n/2+o(n)} total batch time"
    },
    "space": {
      "coefficient": 0.20751874963942188,
      "expression": "(4/3)^{n/2+o(n)} including outputs"
    },
    "tags": [
      "classical",
      "provable",
      "worst case",
      "DGS",
      "shifted",
      "above smoothing",
      "batch"
    ],
    "review": {
      "status": "source-checked"
    },
    "certificate": {
      "status": "not-provided",
      "lean": null
    },
    "notes": "The batch is smaller than the 2^{n/2} outputs in ADRS15; its total cost is kept in a separate category.",
    "extra": {
      "width": "s >= (3/2) eta_{1/2}(L)",
      "output": "floor((4/3)^{n/2}) samples on L+a",
      "error": "Joint TV from independent target samples <= exp(-Omega(n/log^2(n+2)))",
      "model": "Randomized word RAM; total batch cost and output storage included"
    },
    "evidence": {
      "url": "https://arxiv.org/abs/2611.04336v1",
      "locator": "Theorem 1.2 and following paragraph, printed p. 6",
      "sourceVersion": "arXiv:2611.04336v1, 3 November 2026; first ePrint release 30 October not inspected separately"
    }
  }
]