[
  {
    "id": "dg13-general",
    "categoryId": "ssip-classical-heuristic",
    "paperId": "dg13",
    "date": "2013-10-29",
    "datePrecision": "day",
    "time": {
      "coefficient": 0.5,
      "expression": "O~(p^{1/2})"
    },
    "space": {
      "coefficient": null,
      "expression": "Not stated in the checked source"
    },
    "tags": [],
    "review": {
      "status": "source-checked"
    },
    "certificate": {
      "status": "not-provided",
      "lean": null
    },
    "notes": "The F_p-subfield strategy gives a low-storage general isogeny-search method. The source uses random-walk heuristics; its F_p connectivity argument uses GRH. The p^{1/4} subroutine does not make the general algorithm p^{1/4}.",
    "extra": {
      "output": "A composition of isogenies; not necessarily a fixed-degree short path"
    },
    "evidence": {
      "url": "https://arxiv.org/pdf/1310.7789",
      "locator": "Section 4: The General Isogeny Problem",
      "sourceVersion": "Checked 2026-11-08; see linked source version/date"
    }
  },
  {
    "id": "wesolowski26-general",
    "categoryId": "ssip-classical-heuristic",
    "paperId": "wesolowski26-isogeny",
    "date": "2026-07-23",
    "datePrecision": "day",
    "time": {
      "coefficient": 0.3333333333333333,
      "expression": "p^{1/3+o(1)}"
    },
    "space": {
      "coefficient": null,
      "expression": "p^{1/3+o(1)}"
    },
    "tags": [],
    "review": {
      "status": "source-checked"
    },
    "certificate": {
      "status": "not-provided",
      "lean": null
    },
    "notes": "The time and memory bound assumes smoothness of certain random integers. The source notes a superpolynomial overhead hidden in o(1) and substantial memory requirements; concrete impact is not established.",
    "extra": {
      "assumption": "Smoothness heuristic",
      "source-chronology": "Received 20 July; approved 23 July 2026"
    },
    "evidence": {
      "url": "https://eprint.iacr.org/2026/1486",
      "locator": "Abstract; approved 2026-07-23",
      "sourceVersion": "Checked 2026-11-08; see linked source version/date"
    }
  }
]