[
  {
    "id": "llmp90-general",
    "categoryId": "ifp-general-heuristic",
    "paperId": "llmp90",
    "date": "1990-12-31",
    "datePrecision": "year",
    "time": {
      "coefficient": 2.080083823051904,
      "expression": "L_N[1/3, 3^{2/3}]"
    },
    "space": {
      "coefficient": null,
      "expression": "Not extracted from the source"
    },
    "tags": [],
    "review": {
      "status": "source-checked"
    },
    "certificate": {
      "status": "not-provided",
      "lean": null
    },
    "notes": "The 1990 work-in-progress paper describes the proposed generalization to arbitrary integers with this heuristic constant. It is an early general-purpose bound, not the special-form 1.526 bound.",
    "extra": {
      "coefficientExact": "3^{2/3}"
    },
    "evidence": {
      "url": "https://wstein.org/129/references/Lenstra-Lenstra-Manasse-Pollard-The%20number%20field%20sieve.pdf",
      "locator": "Introduction, second page; generalized algorithm discussion",
      "sourceVersion": "Version available at the cited URL; bibliographic metadata and stated bound checked on 2026-11-08"
    }
  },
  {
    "id": "blp93-general",
    "categoryId": "ifp-general-heuristic",
    "paperId": "blp93",
    "date": "1993-12-31",
    "datePrecision": "year",
    "time": {
      "coefficient": 1.9229994270765445,
      "expression": "L_N[1/3, (64/9)^{1/3}]"
    },
    "space": {
      "coefficient": null,
      "expression": "Not extracted from the source"
    },
    "tags": [],
    "review": {
      "status": "source-checked"
    },
    "certificate": {
      "status": "not-provided",
      "lean": null
    },
    "notes": "The general number field sieve has this predicted expected running time under smoothness and related heuristic assumptions. It is not a rigorous worst-case theorem.",
    "extra": {
      "coefficientExact": "(64/9)^{1/3}"
    },
    "evidence": {
      "url": "https://www.cs.umd.edu/~gasarch/TOPICS/factoring/1993_Book_TheDevelopmentOfTheNumberField.pdf",
      "locator": "Abstract; general NFS complexity analysis",
      "sourceVersion": "Version available at the cited URL; bibliographic metadata and stated bound checked on 2026-11-08"
    }
  },
  {
    "id": "coppersmith93-general",
    "categoryId": "ifp-general-heuristic",
    "paperId": "coppersmith93",
    "date": "1993-03-31",
    "datePrecision": "month",
    "time": {
      "coefficient": 1.9018836118648392,
      "expression": "L_N[1/3, (92+26 sqrt(13))^{1/3}/3]"
    },
    "space": {
      "coefficient": null,
      "expression": "Not extracted from the source"
    },
    "tags": [
      "multiple number fields",
      "theoretical asymptotics"
    ],
    "review": {
      "status": "source-checked"
    },
    "certificate": {
      "status": "not-provided",
      "lean": null
    },
    "notes": "Heuristic many-polynomial/many-number-field variant; includes the first sieve/precomputation in the single-factorization cost. This theoretical asymptotic improvement is distinct from practical two-polynomial GNFS and from the separate factorization-factory regime.",
    "extra": {
      "coefficientExact": "(92+26 sqrt(13))^{1/3}/3"
    },
    "evidence": {
      "url": "https://link.springer.com/content/pdf/10.1007/BF00198464.pdf",
      "locator": "Section 3, Parameters and Running Time, pp. 176–177",
      "sourceVersion": "Version available at the cited URL; bibliographic metadata and stated bound checked on 2026-11-08"
    }
  }
]