{
  "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"
  }
}