{
  "personId": "david-hilbert",
  "uid": "SL-0091",
  "name": "大卫·希尔伯特",
  "version": "V2研究贡献账",
  "updatedAt": "2026-09-15",
  "formula": {
    "q": "Q = 10^(M/2) − 1",
    "light": "Lᵢ = aᵢ × Qᵢ",
    "total": "L = Σ Lᵢ",
    "score": "S = 2 × log₁₀(1 + L)"
  },
  "scopeNote": "本轮当前已列9项有限研究账；M与归功份额为可修订判断。未覆盖内容和未核清的负面作用不按零处理，具体缺口见逐项说明。",
  "exclusions": [
    {
      "id": "HILBERT-GR-FINAL-THEORY",
      "title": "广义相对论最终理论的单人归属",
      "reason": "1915年 Hilbert 的变分工作与 Einstein 的最终场方程发表时间相邻，优先权史复杂；本页只计 Hilbert 可定位的作用量与协变性方法，不将完整理论或最终方程单独归于他。",
      "sources": [
        {
          "label": "Physics Today：Hilbert 与 Einstein 的历史综述",
          "url": "https://doi.org/10.1063/PT.3.2979"
        }
      ]
    },
    {
      "id": "HILBERT-PROOF-PROGRAM-COMPLETION",
      "title": "基础纲领的完整一致性证明",
      "reason": "基础纲领提出有限主义一致性证明计划，但其形式化与目标仍有未解决问题；不将后来证明论成果或计划完成归入希尔伯特。",
      "sources": [
        {
          "label": "斯坦福哲学百科：Hilbert 纲领",
          "url": "https://plato.stanford.edu/archives/fall2015/entries/hilbert-program/"
        }
      ]
    }
  ],
  "items": [
    {
      "id": "OUT-SL0091-1880S-1890S-INVARIANT-THEORY-METHOD",
      "title": "代数不变量理论的有限生成方法",
      "year": "1880",
      "summary": "在 Gordan 主导的不变量理论研究网络中提出新的解决与组织路径。",
      "M": "5.8",
      "budget": [
        {
          "actor": "大卫·希尔伯特",
          "actorId": "SL-0091",
          "type": "PERSON",
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        },
        {
          "actor": "Paul Gordan（不变量理论前辈）",
          "actorId": "EXT-NAME:PAUL-GORDAN",
          "type": "PERSON",
          "share": "0.15"
        },
        {
          "actor": "Felix Klein 与不变量理论网络",
          "actorId": "HILBERT::FELIX-KLEIN-AND-INVARIANT-NETWORK",
          "type": "PREDECESSOR_AND_COLLABORATOR_POOL",
          "share": "0.15"
        },
        {
          "actor": "不变量理论前史",
          "actorId": "HILBERT::INVARIANT-THEORY-PREHISTORY",
          "type": "PREDECESSOR_POOL",
          "share": "0.15"
        },
        {
          "actor": "未分配的背景贡献",
          "actorId": "HILBERT::UNKNOWN-CONTRIBUTORS",
          "type": "UNALLOCATED",
          "share": "0.05"
        }
      ],
      "mReason": "把逐例构造问题改造成一般有限生成存在方法，改变了代数研究的可处理边界；按Noether理想/环M6.5以下的直接前驱通用方法取M5.8。来源完整度只影响区间，不压低文明价值。",
      "aReason": "Hilbert 0.50；Gordan 0.15；Klein及网络0.15；理论前史0.15；未知0.05。",
      "overlapNote": "1880至1890年代在Gordan等人的不变量问题基线上形成的有限生成证明与方法转向；不领取全部交换代数、代数几何或后世同名对象。",
      "status": "缺证暂估",
      "missing": "逐一定理和构造性边界仍需技术原文校准。",
      "sources": [
        {
          "label": "MacTutor：David Hilbert",
          "url": "https://mathshistory.st-andrews.ac.uk/Biographies/Hilbert/"
        }
      ],
      "share": "0.5",
      "exactLight": "396.6641173621407510329591414181939662944803158777421660461619646584778485957437687485476259235951390",
      "light": "396.664117",
      "standaloneScore": "5.20",
      "lightSharePercent": "20.2133"
    },
    {
      "id": "OUT-SL0091-1899-1900-AXIOMATIC-GEOMETRY",
      "title": "几何公理化、独立性与一致性分析",
      "year": "1899",
      "summary": "以显式公理、独立性与一致性分析重组欧氏几何基础。",
      "M": "5.8",
      "budget": [
        {
          "actor": "大卫·希尔伯特",
          "actorId": "SL-0091",
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        },
        {
          "actor": "Euclid、Pasch、Peano 与公理化前史",
          "actorId": "HILBERT::EUCLID-PASCH-PEANO-AXIOMATIC-PREHISTORY",
          "type": "PREDECESSOR_POOL",
          "share": "0.27"
        },
        {
          "actor": "哥廷根研究网络",
          "actorId": "HILBERT::GOTTINGEN-NETWORK",
          "type": "COLLABORATOR_POOL",
          "share": "0.1"
        },
        {
          "actor": "编辑、译者与采用者",
          "actorId": "HILBERT::EDITORS-TRANSLATORS-ADOPTERS",
          "type": "SERVICE_POOL",
          "share": "0.1"
        },
        {
          "actor": "未分配的背景贡献",
          "actorId": "HILBERT::UNKNOWN-CONTRIBUTORS",
          "type": "UNALLOCATED",
          "share": "0.05"
        }
      ],
      "mReason": "把公理选择和逻辑关系变成可检验数学对象，形成跨几何复用的方法终态，取M5.8；奠基效应已进入M。",
      "aReason": "Hilbert 0.48；公理化前史0.27；哥廷根网络0.10；传播采用0.10；未知0.05。",
      "overlapNote": "1899年前后以显式公理、独立性与一致性分析重组欧氏及解析几何；一般形式化理念与后期基础纲领只消费一次。",
      "status": "缺证暂估",
      "missing": "各版公理修订和具体独立性证明仍需校准。",
      "sources": [
        {
          "label": "斯坦福哲学百科：Hilbert 纲领",
          "url": "https://plato.stanford.edu/archives/fall2015/entries/hilbert-program/"
        }
      ],
      "share": "0.48",
      "exactLight": "380.7975526676551209916407757614662076427011032426324794043154860721387346519140179986057208866513335",
      "light": "380.797553",
      "standaloneScore": "5.16",
      "lightSharePercent": "19.4048"
    },
    {
      "id": "OUT-SL0091-1897-ZAHLBERICHT-NUMBER-FIELDS",
      "title": "Zahlbericht数域框架与具名新证明",
      "year": "1897",
      "summary": "《Zahlbericht》组织一般数域的整数、理想、判别式、单位和素数分解，并包含 Kronecker–Weber 定理的完整证明和对 Satz 90 的更易理解的代数证明；命题前史不归于他。",
      "M": "5.9",
      "budget": [
        {
          "actor": "大卫·希尔伯特",
          "actorId": "SL-0091",
          "type": "PERSON",
          "share": "0.38"
        },
        {
          "actor": "Kummer、Dedekind、Kronecker（数论前史）",
          "actorId": "HILBERT::KUMMER-DEDEKIND-KRONECKER",
          "type": "PREDECESSOR_POOL",
          "share": "0.3"
        },
        {
          "actor": "代数数论研究网络",
          "actorId": "HILBERT::ALGEBRAIC-NUMBER-THEORY-RESEARCH-NETWORK",
          "type": "COLLABORATOR_AND_PARALLEL_POOL",
          "share": "0.12"
        },
        {
          "actor": "编辑、译者与采用者",
          "actorId": "HILBERT::EDITORS-TRANSLATORS-AND-ADOPTERS",
          "type": "SERVICE_POOL",
          "share": "0.12"
        },
        {
          "actor": "未分配的背景贡献",
          "actorId": "HILBERT::UNKNOWN-CONTRIBUTORS",
          "type": "UNALLOCATED",
          "share": "0.08"
        }
      ],
      "mReason": "将分散结果组织为可工作的数域理论框架，并含可辨认的新证明和证明简化，产生跨问题复用的研究基础，取M5.9。资料未逐页覆盖全书只扩大置信区间，不把该成果降为一般书目。",
      "aReason": "Hilbert 0.38；Kummer、Dedekind、Kronecker前史0.30；研究网络0.12；编辑传播采用0.12；未知0.08。",
      "overlapNote": "1897 Zahlbericht对一般数域的整数、理想、判别式、单位、理想类及Galois扩张素数分解的统一框架，连同Kronecker–Weber完整证明和Satz 90的简洁代数证明。综合、证明和教材式可及性合为一项；Satz 90命题来源和后续类域论排除。",
      "status": "缺证暂估",
      "missing": "全书逐项原创、综合与后世术语边界尚未分解。",
      "sources": [
        {
          "label": "Landmark Writings：Zahlbericht",
          "url": "https://www.sciencedirect.com/science/chapter/edited-volume/abs/pii/B9780444508713501352"
        },
        {
          "label": "德国数学会：Zahlbericht 120周年",
          "url": "https://www.mathematik.de/dmv-blog/4055-120-jahre-zahlbericht"
        }
      ],
      "share": "0.38",
      "exactLight": "338.2953564908233013821812988097528463146324175134183805802185281256381860249225127247455734794499299",
      "light": "338.295356",
      "standaloneScore": "5.06",
      "lightSharePercent": "17.2389"
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    {
      "id": "OUT-SL0091-1904-1910-INTEGRAL-EQUATIONS-FRAMEWORK",
      "title": "线性积分方程的一般分析框架",
      "year": "1904",
      "summary": "围绕线性积分方程发表系列研究，形成一般分析框架；Erhard Schmidt、Riesz 与后续函数分析研究者承担独立发展。",
      "M": "5.8",
      "budget": [
        {
          "actor": "大卫·希尔伯特",
          "actorId": "SL-0091",
          "type": "PERSON",
          "share": "0.4"
        },
        {
          "actor": "Erhard Schmidt（积分方程合作者）",
          "actorId": "EXT-NAME:ERHARD-SCHMIDT",
          "type": "PERSON",
          "share": "0.15"
        },
        {
          "actor": "尚待分解的技术输入（不自动归给并行或后继人物）",
          "actorId": "HILBERT::HILBERT-INTEGRAL-EQUATIONS-AND-HILBERT-SPACE-UNRESOLVED-TECHNICAL-INPUTS",
          "type": "UNALLOCATED",
          "share": "0.13"
        },
        {
          "actor": "积分方程前史",
          "actorId": "HILBERT::INTEGRAL-EQUATION-PREHISTORY",
          "type": "PREDECESSOR_POOL",
          "share": "0.17"
        },
        {
          "actor": "哥廷根助手与编辑人员",
          "actorId": "HILBERT::GOTTINGEN-ASSISTANTS-AND-EDITORS",
          "type": "TEAM",
          "share": "0.1"
        },
        {
          "actor": "未分配的背景贡献",
          "actorId": "HILBERT::UNKNOWN-CONTRIBUTORS",
          "type": "UNALLOCATED",
          "share": "0.05"
        }
      ],
      "mReason": "形成跨问题可用的一般分析与谱框架，作为Neumann算子M6的直接分析基线取M5.8；后续抽象化不回灌。",
      "aReason": "Hilbert 0.40；Schmidt 0.15；Riesz等0.13；前史0.17；助手编辑0.10；未知0.05。 原列并行或后继研究者的混合份额保留为未解析输入，未证明直接传递前不归于这些具名人物。",
      "overlapNote": "1904至1910年线性积分方程系列论文和一般理论；抽象Hilbert空间、后续谱理论及量子应用排除。",
      "status": "缺证暂估",
      "missing": "收敛、谱与空间概念的精确优先权待校准。；并行及后继工作的具体输入关系尚未解析；预算不把独立发展自动视为同一成果。",
      "sources": [
        {
          "label": "MacTutor：Hilbert 著作资料",
          "url": "https://mathshistory.st-andrews.ac.uk/Extras/Hilbert_books/"
        }
      ],
      "share": "0.4",
      "exactLight": "317.3312938897126008263673131345551730355842527021937328369295717267822788765950149988381007388761112",
      "light": "317.331294",
      "standaloneScore": "5.01",
      "lightSharePercent": "16.1706"
    },
    {
      "id": "OUT-SL0023-1918-INVARIANT-VARIATIONAL-THEOREM-FAMILY",
      "title": "变分问题中的对称性与守恒关系（两条定理合族）",
      "year": "1918",
      "summary": "在《不变变分问题》中提出两条相互关联的定理及逆命题，建立连续对称性与守恒律的系统联系。此处作为一个定理家族呈现，不把能量、动量等后来的应用重复计入。",
      "M": "7.0",
      "budget": [
        {
          "actor": "埃米·诺特",
          "actorId": "SL-0023",
          "type": "SUBJECT",
          "share": "0.65"
        },
        {
          "actor": "大卫·希尔伯特",
          "actorId": "SL-0091",
          "type": "PREDECESSOR",
          "share": "0.10"
        },
        {
          "actor": "Felix Klein（哥廷根协作方）",
          "actorId": "EXT-NAME:FELIX-KLEIN",
          "type": "PREDECESSOR",
          "share": "0.05"
        },
        {
          "actor": "变分不变量、相对论与守恒律前史",
          "actorId": "NOETHER-1918::VARIATIONAL-INVARIANT-RELATIVITY-FOUNDATIONS",
          "type": "PREDECESSOR_POOL",
          "share": "0.15"
        },
        {
          "actor": "未分配的背景贡献",
          "actorId": "NOETHER-1918::UNKNOWN",
          "type": "UNALLOCATED",
          "share": "0.05"
        }
      ],
      "mReason": "M7.0与Maxwell电磁场—光统一同档：两者都把广泛物理现象压入可复用的数学结构。Noether方法跨经典场论、相对论和后续物理形式，但当前未把后世全部应用收入，因此不因应用数量继续上调。它高于Maxwell输运M6和ACE M5的有界方法锚。",
      "aReason": "Noether以定理、逆命题和一般证明的核心作者责任获0.65；Hilbert的问题与相对论背景0.10，Klein的问题组织0.05；变分、不变量和群论前史0.15；未知0.05。问题提出与前史在a中可见，但不从M重复扣减。",
      "overlapNote": "把1918《Invariante Variationsprobleme》中两条相互关联定理及其逆命题视为一个方法族：连续变换群在变分问题中的守恒律与恒等关系；区分由独立参数描述的连续对称及依赖任意函数的局部对称。不按两条定理名称、能量、动量、规范或后世每类应用分别累加M。排除Hilbert和Klein的问题背景、Weyl后续发展、量子场论与规范理论的独立增量。",
      "status": "缺证暂估",
      "missing": "本次修订未取得可逐页解析的1918原文。；Hilbert、Klein与Noether具体问题往来的份额仍是规范暂估。 高档M的跨代直接使用证据须与思想同样展示来源定位，不能由熟悉的科学史结论免验；具名前驱再次归功同样接受消费审查。",
      "sources": [
        {
          "label": "EuDML：1918年原作书目信息",
          "url": "https://eudml.org/doc/59024"
        },
        {
          "label": "UCLA：Noether 定理历史说明",
          "url": "https://cwp.library.ucla.edu/articles/noether.asg/noether.html"
        }
      ],
      "share": "0.10",
      "exactLight": "316.1277660168379331998893544432718533719555139325216826857504852792594438639238221344248108379300295",
      "light": "316.127766",
      "standaloneScore": "5.00",
      "lightSharePercent": "16.1093"
    },
    {
      "id": "OUT-SL0091-1917-1930S-FOUNDATIONAL-PROGRAM",
      "title": "数学基础纲领与有限主义证明论计划",
      "year": "1917",
      "summary": "与 Paul Bernays 等人推动数学公理化、有限主义与一致性证明的研究纲领。",
      "M": "4.9",
      "budget": [
        {
          "actor": "大卫·希尔伯特",
          "actorId": "SL-0091",
          "type": "PERSON",
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        },
        {
          "actor": "Paul Bernays（证明论合作者）",
          "actorId": "EXT-NAME:PAUL-BERNAYS",
          "type": "PERSON",
          "share": "0.25"
        },
        {
          "actor": "Russell、Whitehead、Poincaré 与逻辑前史/批评",
          "actorId": "HILBERT::RUSSELL-WHITEHEAD-POINCARE-LOGIC-PREHISTORY",
          "type": "PREDECESSOR_AND_CRITIC_POOL",
          "share": "0.2"
        },
        {
          "actor": "哥廷根逻辑团队",
          "actorId": "HILBERT::GOTTINGEN-LOGIC-TEAM",
          "type": "TEAM",
          "share": "0.1"
        },
        {
          "actor": "后继证明论研究者",
          "actorId": "HILBERT::LATER-PROOF-THEORY-ADOPTERS",
          "type": "SUCCESSOR_POOL",
          "share": "0.05"
        },
        {
          "actor": "未分配的背景贡献",
          "actorId": "HILBERT::UNKNOWN-CONTRIBUTORS",
          "type": "UNALLOCATED",
          "share": "0.05"
        }
      ],
      "mReason": "形成持续研究议程和可复用证明论工具，但全数学一致性目标未完成，按有实际工具产出且目标受限的研究纲领取M4.9。",
      "aReason": "Hilbert 0.35；Bernays 0.25；逻辑前史与批评0.20；团队0.10；采用和未知各0.05。",
      "overlapNote": "1917年后形式化数学并以有限方法证明一致性的计划及与Bernays共同的证明论工作；未完成目标进入边界，Gödel与Gentzen成果排除。",
      "status": "缺证暂估",
      "missing": "仍成立的具体证明论工具范围待技术核读。",
      "sources": [
        {
          "label": "斯坦福哲学百科：Hilbert 纲领",
          "url": "https://plato.stanford.edu/archives/fall2015/entries/hilbert-program/"
        }
      ],
      "share": "0.35",
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      "light": "98.293403",
      "standaloneScore": "3.99",
      "lightSharePercent": "5.0089"
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    {
      "id": "OUT-SL0091-1915-VARIATIONAL-GR-FORMULATION",
      "title": "引力—电磁作用量与广义协变性推导",
      "year": "1915",
      "summary": "以引力—电磁作用量给出变分表述，并从坐标不变性组织恒等结构。场方程整体、物理解释及预言由相对论理论程序消费，不在此重复。",
      "M": "4.9",
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        {
          "actor": "阿尔伯特·爱因斯坦",
          "actorId": "SL-0001",
          "type": "PERSON",
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        },
        {
          "actor": "广义相对论数学物理前史",
          "actorId": "HILBERT::GENERAL-RELATIVITY-MATHEMATICAL-PHYSICS-PREHISTORY",
          "type": "PREDECESSOR_POOL",
          "share": "0.18"
        },
        {
          "actor": "哥廷根物理与数学网络",
          "actorId": "HILBERT::GOTTINGEN-PHYSICS-MATHEMATICS-NETWORK",
          "type": "COLLABORATOR_POOL",
          "share": "0.1"
        },
        {
          "actor": "当时发表与早期传播支持",
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          "actor": "未分配贡献与时间线未决部分",
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          "share": "0.07"
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      ],
      "mReason": "作用量与不变性恒等结构具有独立数学物理方法价值；排除场方程整体后，残余范围采用M4.9。此次修正来自成果边界缩窄，不因人名或资料未读调分。",
      "aReason": "Hilbert 0.28；Einstein 0.32；数学物理与GR前史0.18；哥廷根网络0.10；当时发表与早期传播支持0.05；校样与时间线未解析0.07。",
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      "status": "缺证暂估",
      "missing": "Hilbert校样、正式版及具体场方程出现时间尚未以档案原件收口。；能量方程意义在当时并不清楚。；不把后世历史研究作者计作1915年成果创造者。",
      "sources": [
        {
          "label": "Noether 定理与广义相对论能量研究",
          "url": "https://philsci-archive.pitt.edu/18871/1/Noether%27s%20Theorems%20and%20Energy%20in%20GR.pdf"
        },
        {
          "label": "Physics Today：Hilbert 与 Einstein 的历史综述",
          "url": "https://doi.org/10.1063/PT.3.2979"
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      "year": "1900",
      "summary": "提出二十三问题并在哥廷根组织教学和研究议程；问题的后续解决属于不同数学家的工作。",
      "M": "3.9",
      "budget": [
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          "actor": "Felix Klein（哥廷根协作方）",
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      "aReason": "Hilbert 0.38；Klein 0.17；团队0.20；参与者0.15；前史和未知各0.05。",
      "overlapNote": "1900问题清单及与Klein共同参与的教学研究组织；不领取问题解答、学生未来研究或机构全部声望。",
      "status": "缺证暂估",
      "missing": "具体课程、行政措施与学习效果待校准。",
      "sources": [
        {
          "label": "AMS Notices：Hilbert 问题",
          "url": "https://www.ams.org/journals/notices/200008/200008FullIssue.pdf"
        }
      ],
      "share": "0.38",
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    {
      "id": "OUT-SL0023-1916-1935-ALGEBRA-TEACHING-SERVICE",
      "title": "Göttingen 与 Bryn Mawr 的抽象代数教学和学派服务",
      "year": "1916",
      "summary": "在 Göttingen、Bryn Mawr 与 Princeton 通过课程、研讨班和每周讲座传播抽象代数的概念与方法；相关教材由 van der Waerden 撰写，并吸收 Artin 与诺特的讲课。",
      "M": "3.5",
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          "actor": "埃米·诺特",
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          "actor": "大卫·希尔伯特",
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          "actorId": "INSTITUTION:PRINCETON-UNIVERSITY",
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          "actor": "Artin 与抽象代数讲课输入",
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          "actor": "未分配的教学背景贡献",
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      "aReason": "Noether作为主要教师0.65；Hilbert早期课程承载0.05；Göttingen 0.05、Bryn Mawr 0.10、Princeton 0.05；Artin及代数讲授输入0.05；未知0.05。学生作为受益者不因未来成果获得或转回本点份额。",
      "overlapNote": "只计1916–1935年可证的课程协助、Göttingen理想理论教学、1933年家中学生聚会、Bryn Mawr三名学生和一名教员研讨班，以及1934年Princeton每周讲授。排除学生与同事未来研究成果、van der Waerden独著教材的完整价值、全部流亡学术史和抽象代数的本体定理。",
      "status": "缺证暂估",
      "missing": "缺完整班级名册、课时和学生学习效果。；1935同事悼文本次修订只核到元数据。",
      "sources": [
        {
          "label": "MacTutor：Emmy Noether",
          "url": "https://mathshistory.st-andrews.ac.uk/Biographies/Noether_Emmy/"
        },
        {
          "label": "MacTutor：van der Waerden 书评资料",
          "url": "https://mathshistory.st-andrews.ac.uk/Extras/Van_der_Waerden_reviews/"
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  "displayScore": "6.59",
  "provisionalCount": 9,
  "provenance": {
    "releaseId": "research-200-20260914",
    "baselineLedgerSha256": "8bdd406b3e20ae22357644499e622922c670ff11010df0478c70c23b38902108",
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  "rank": 33
}