[
  {
    "id": "ch12-deterministic",
    "categoryId": "ifp-deterministic",
    "paperId": "ch12",
    "date": "2012-01-10",
    "datePrecision": "day",
    "time": {
      "coefficient": 0.25,
      "expression": "O(M_int(N^{1/4} log N) / sqrt(log log N))"
    },
    "space": {
      "coefficient": null,
      "expression": "Not extracted from the source"
    },
    "tags": [],
    "review": {
      "status": "source-checked"
    },
    "certificate": {
      "status": "not-provided",
      "lean": null
    },
    "notes": "The exact improvement is a sqrt(log log N) factor over the Bostan–Gaudry–Schost bound. The normalized exponent is still 1/4. M_int(k) denotes k-bit integer multiplication cost.",
    "extra": {
      "coefficientExact": "1/4"
    },
    "evidence": {
      "url": "https://arxiv.org/abs/1201.2116",
      "locator": "Abstract",
      "sourceVersion": "Version available at the cited URL; bibliographic metadata and stated bound checked on 2026-11-08"
    }
  },
  {
    "id": "hittmeir20-deterministic",
    "categoryId": "ifp-deterministic",
    "paperId": "hittmeir20",
    "date": "2020-06-30",
    "datePrecision": "day",
    "time": {
      "coefficient": 0.2222222222222222,
      "expression": "N^{2/9+o(1)} bit operations"
    },
    "space": {
      "coefficient": null,
      "expression": "Not extracted from the source"
    },
    "tags": [],
    "review": {
      "status": "source-checked"
    },
    "certificate": {
      "status": "not-provided",
      "lean": null
    },
    "notes": "Unconditional deterministic improvement using a time-space tradeoff for a generalization of Lehman’s method.",
    "extra": {
      "coefficientExact": "2/9"
    },
    "evidence": {
      "url": "https://arxiv.org/abs/2006.16729",
      "locator": "Abstract",
      "sourceVersion": "Version available at the cited URL; bibliographic metadata and stated bound checked on 2026-11-08"
    }
  },
  {
    "id": "harvey20-deterministic",
    "categoryId": "ifp-deterministic",
    "paperId": "harvey20",
    "date": "2020-10-12",
    "datePrecision": "day",
    "time": {
      "coefficient": 0.2,
      "expression": "N^{1/5+o(1)} bit operations"
    },
    "space": {
      "coefficient": null,
      "expression": "Not extracted from the source"
    },
    "tags": [],
    "review": {
      "status": "source-checked"
    },
    "certificate": {
      "status": "not-provided",
      "lean": null
    },
    "notes": "Unconditional deterministic complete factorization. This exponent is in N, so it is exponential in the input bitlength.",
    "extra": {
      "coefficientExact": "1/5"
    },
    "evidence": {
      "url": "https://arxiv.org/abs/2010.05450",
      "locator": "Abstract",
      "sourceVersion": "Version available at the cited URL; bibliographic metadata and stated bound checked on 2026-11-08"
    }
  },
  {
    "id": "hh21-deterministic",
    "categoryId": "ifp-deterministic",
    "paperId": "hh21",
    "date": "2021-05-24",
    "datePrecision": "day",
    "time": {
      "coefficient": 0.2,
      "expression": "O(N^{1/5} (log N)^{16/5} / (log log N)^{3/5}) bit operations"
    },
    "space": {
      "coefficient": null,
      "expression": "Not extracted from the source"
    },
    "tags": [],
    "review": {
      "status": "source-checked"
    },
    "certificate": {
      "status": "not-provided",
      "lean": null
    },
    "notes": "Same leading exponent 1/5; improves the logarithmic factors. This should appear as a tied leading exponent rather than an artificial exponent improvement.",
    "extra": {
      "coefficientExact": "1/5"
    },
    "evidence": {
      "url": "https://arxiv.org/abs/2105.11105",
      "locator": "Abstract",
      "sourceVersion": "Version available at the cited URL; bibliographic metadata and stated bound checked on 2026-11-08"
    }
  }
]