{ "personId": "john-nash", "uid": "SL-0100", "name": "约翰·纳什", "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5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": "NASH-MENTAL-HEALTH-BIOGRAPHY-AND-POPULAR-REPRESENTATION", "title": "健康经历、传记与大众再现", "reason": "个人经历和他人创作的传记/影视不作为Nash数学成果。" }, { "id": "NASH-PARALLEL-CONTROL-COMPUTER-MEMORANDUM", "title": "并行计算控制备忘录", "reason": "The Essential John Nash称其想法不成熟且不具体，现无实现或独立交付，不按前瞻概念设M。" } ], "items": [ { "id": "OUT-SL0100-1950-1951-NONCOOPERATIVE-EQUILIBRIUM", "title": "有限非合作博弈的混合策略均衡存在框架", "year": "1950–1951", "summary": "将稳定最佳回应概念扩展到一般n人非合作博弈，并证明有限情形至少存在混合策略均衡。", "mReason": "Nobel事实页与1951原论文记录支持Nash equilibrium的核心对象和存在结果。按概念通用性、形式化和广泛方法影响取M6.8，不把均衡当现实行为必然预测。", "aReason": "Nash .43；博弈论前史 .22；不动点/凸分析前史 .17；机构 .05；未解析 .13。", "sources": [ { "label": "原作与学术资料：www.nobelprize.org", "url": "https://www.nobelprize.org/laureate/712" }, { "label": "原作与学术资料：www.jstor.org", "url": "https://www.jstor.org/stable/i307252" }, { "label": "原作与学术资料：jmvidal.cse.sc.edu", "url": "https://jmvidal.cse.sc.edu/lib/nash51a.html" } ], "missing": "1950短文与1951论文的具体工具来源、交流和证明差异未逐段闭合。；后继均衡选择、精炼与算法不在本点。", "status": "缺证暂估", "overlapNote": "1950–1951对有限n人非合作博弈的策略、最佳回应与混合策略均衡存在框架；不领取所有博弈论、均衡选择、算法、实验或经济应用。", "M": "6.8", "budget": [ { "actor": "约翰·纳什", "actorId": "SL-0100", "type": "PERSON", "share": "0.43" }, { "actor": "冯·诺依曼、摩根斯特恩等博弈论前驱", "actorId": "JOHN-NASH::VON-NEUMANN-MORGENSTERN-GAME-THEORY-PREDECESSORS", "type": "PREDECESSOR_POOL", "share": "0.22" }, { "actor": "不动点与凸分析前驱", "actorId": "JOHN-NASH::FIXED-POINT-AND-CONVEX-ANALYSIS-PREDECESSORS", "type": "PREDECESSOR_POOL", "share": "0.17" }, { "actor": "普林斯顿数学与出版机构", "actorId": "JOHN-NASH::PRINCETON-MATHEMATICS-AND-PUBLICATION-INSTITUTIONS", "type": "INSTITUTION", "share": "0.05" }, { "actor": "未分配的纳什均衡贡献", "actorId": 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"1954 C1与1956光滑黎曼流形等距嵌入存在结果及其构造性方法；不领取一般流形理论、后继Günther证明或所有几何/PDE应用。", "M": "6.8", "budget": [ { "actor": "约翰·纳什", "actorId": "SL-0100", "type": "PERSON", "share": "0.43" }, { "actor": "黎曼、惠特尼、雅内与嘉当等嵌入理论前驱", "actorId": "JOHN-NASH::RIEMANN-WHITNEY-JANET-CARTAN-EMBEDDING-PREDECESSORS", "type": "PREDECESSOR_POOL", "share": "0.3" }, { "actor": "纳什嵌入研究与编辑合作者", "actorId": "JOHN-NASH::NASH-EMBEDDING-RESEARCH-AND-EDITORIAL-COLLABORATORS", "type": "TEAM", "share": "0.07" }, { "actor": "麻省理工学院与数学出版机构", "actorId": "JOHN-NASH::MIT-AND-MATHEMATICS-PUBLICATION-INSTITUTIONS", "type": "INSTITUTION", "share": "0.05" }, { "actor": "未分配的纳什嵌入贡献", "actorId": "JOHN-NASH::UNRESOLVED-NASH-EMBEDDING-ATTRIBUTION", "type": "UNALLOCATED", "share": "0.15" } ], "share": "0.43", "exactLight": "1079.681165549119447766563789153710779488162783336464434332352020990544596521131362635155933817452692", "light": "1079.681166", "standaloneScore": "6.07", "lightSharePercent": "28.1207" }, { "id": "OUT-SL0100-1958-PARABOLIC-ELLIPTIC-PDE-CONTINUITY", "title": "粗糙系数抛物与椭圆方程解的连续性方法", "year": "1958", "summary": "给出弱条件下解连续性/正则性的独立方法，为后来统一称谓中的Nash路线提供可复用估计思想。", "mReason": "1958原论文记录和Abel评论把该PDE工作列为主要贡献；现代文献明确De Giorgi与Nash为并行基础、Moser后继。按定理深度和方法持续性取M6.4，不把联合领域名称当Nash单人所有。", "aReason": "Nash .39；PDE前史 .29；讨论发表团队 .07；机构 .05；未解析 .20。De Giorgi为独立并行，不硬配本点预算。", "sources": [ { "label": "原作与学术资料：www.mathnet.ru", "url": "https://www.mathnet.ru/eng/mat/v4/i1/p31" }, { "label": "原作与学术资料：abelprize.no", "url": "https://abelprize.no/sites/default/files/2021-09/The%20Abel%20Prize%202013-2017_Full.pdf" }, { "label": "原作与学术资料：arxiv.org", "url": "https://arxiv.org/abs/1808.00194" } ], "missing": "1958原文的完整假设、证明步骤与前史尚未逐段核读。；与De Giorgi并行结果的时间和信息独立性仍需专门史料。", "status": "缺证暂估", "overlapNote": "1958对具有粗糙系数的一类抛物和椭圆方程解连续性的正则性结果与证明方法；不领取De Giorgi独立结果、Moser后继证明或全部De Giorgi–Nash–Moser理论。", "M": "6.4", "budget": [ { "actor": "约翰·纳什", "actorId": "SL-0100", "type": "PERSON", "share": "0.39" }, { "actor": "椭圆抛物偏微分方程与正则性前驱", "actorId": "JOHN-NASH::ELLIPTIC-PARABOLIC-PDE-AND-REGULARITY-PREDECESSORS", "type": "PREDECESSOR_POOL", "share": "0.29" }, { "actor": "纳什 偏微分方程讨论与出版合作者", "actorId": "JOHN-NASH::NASH-PDE-DISCUSSION-AND-PUBLICATION-COLLABORATORS", "type": "TEAM", "share": "0.07" }, { "actor": "《美国数学杂志》与麻省理工学院", "actorId": "JOHN-NASH::AMERICAN-JOURNAL-OF-MATHEMATICS-AND-MIT", "type": "INSTITUTION", "share": "0.05" }, { "actor": "未分配的纳什 偏微分方程贡献", "actorId": "JOHN-NASH::UNRESOLVED-NASH-PDE-ATTRIBUTION", "type": "UNALLOCATED", "share": "0.2" } ], "share": "0.39", "exactLight": "617.7183450598342592288195356226877351750824321917652366433557568034961768306970522429790622999833072", "light": "617.718345", "standaloneScore": "5.58", "lightSharePercent": "16.0887" }, { "id": "OUT-SL0100-1952-REAL-ALGEBRAIC-MANIFOLDS", "title": "光滑紧流形的实代数模型与Nash函数框架", "year": "1952", "summary": "证明任一闭光滑流形可与实代数集的非奇异连通分支微分同胚，并组织出后来称为Nash函数、Nash流形的代数—微分桥梁。", "mReason": "Annals原刊目录、The Essential John Nash的原论文导言和IAS数学评论均支持1952结果及其后续形成独立研究传统。它解决的是拓扑/代数实现问题，与等距嵌入的度量保持问题终态不同；按一般定理范围与方法传承取M6.3，不按后来“Nash–Tognoli”名称把Tognoli成果回灌。", "aReason": "Nash .42；Whitney/实代数/微分拓扑前史 .30；讨论编辑 .05；机构 .05；未解析 .18。Tognoli是后继改进，不列本点预算。", "sources": [ { "label": "原作与学术资料：www.jstor.org", "url": "https://www.jstor.org/stable/i307259" }, { "label": "原作与学术资料：www.jstor.org", "url": "https://www.jstor.org/stable/j.ctt1c3gwz0" }, { "label": "原作与学术资料：www.math.ias.edu", "url": "https://www.math.ias.edu/delellis/sites/math.ias.edu.delellis/files/Nash_Abel_75.pdf" } ], "missing": "1952原文的全部技术引理、Whitney近似输入和同时代交流未逐段闭合。；Nash函数唯一性等同篇附加结果未分拆敏感性。", "status": "缺证暂估", "overlapNote": "1952《Real Algebraic Manifolds》中把闭光滑流形表示为非奇异实代数集连通分支的结果，以及由此形成的Nash函数/流形框架；不领取Tognoli 1973把“连通分支”加强为整个非奇异实代数集的结果，也不重复1954–56等距嵌入的度量保持价值。", "M": "6.3", "budget": [ { "actor": "约翰·纳什", "actorId": "SL-0100", "type": "PERSON", "share": "0.42" }, { "actor": "惠特尼及实代数几何、微分拓扑前驱", "actorId": "JOHN-NASH::WHITNEY-REAL-ALGEBRAIC-GEOMETRY-AND-DIFFERENTIAL-TOPOLOGY-PREDECESSORS", "type": "PREDECESSOR_POOL", "share": "0.3" }, { "actor": "纳什实代数研究的讨论与编辑合作者", "actorId": "JOHN-NASH::NASH-REAL-ALGEBRAIC-DISCUSSION-AND-EDITORIAL-COLLABORATORS", "type": "TEAM", "share": "0.05" }, { "actor": "《数学年刊》与普林斯顿机构", "actorId": "JOHN-NASH::ANNALS-OF-MATHEMATICS-AND-PRINCETON-INSTITUTIONS", "type": "INSTITUTION", "share": "0.05" }, { "actor": "实代数流形成果的未分配贡献", "actorId": "JOHN-NASH::UNRESOLVED-NASH-REAL-ALGEBRAIC-ATTRIBUTION", "type": "UNALLOCATED", "share": "0.18" } ], "share": "0.42", "exactLight": "592.8457687415568069053553028507011905116807830425327745830267950529438506704015053464236652652725459", "light": "592.845769", "standaloneScore": "5.55", "lightSharePercent": "15.4409" }, { "id": "OUT-SL0100-1950-TWO-PERSON-BARGAINING-SOLUTION", "title": "双人合作谈判的公理解与效用边界", "year": "1950", "summary": "用可比较的可行效用集合和若干公理约束刻画谈判解，使公平/效率主张成为显式可争论的模型。", "mReason": "1950原文明确双人合作互利范围并致谢von Neumann、Morgenstern审读；学术导言指出无关替代独立性长期有争议。按独立公理方法和持续分析用途取M6.0。", "aReason": "Nash .47；von Neumann .04；Morgenstern .04；前史 .25；机构 .05；未解析 .15。", "sources": [ { "label": "原作与学术资料：www.haverford.edu", "url": "https://www.haverford.edu/sites/default/files/Nash1950.pdf" }, { "label": "原作与学术资料：www.jstor.org", "url": "https://www.jstor.org/stable/1907266" }, { "label": "原作与学术资料：www.jstor.org", "url": "https://www.jstor.org/stable/j.ctt1c3gwz0" } ], "missing": "各公理的直接思想前史与审读建议内容未闭合。；经验适用性及权力不对称边界未系统评价。", "status": "缺证暂估", "overlapNote": "1950《The Bargaining Problem》对两人可合作互利情形的公理模型与唯一解刻画；不把工会、垄断、外交或现实政策结果计作已交付，也不与非合作均衡合并。", "M": "6.0", "budget": [ { "actor": "约翰·纳什", "actorId": "SL-0100", "type": "PERSON", "share": "0.47" }, { "actor": "约翰·冯·诺伊曼", "actorId": "SL-0018", "type": "PERSON", "share": "0.04" }, { "actor": "奥斯卡·摩根斯特恩", "actorId": "EXT-NAME:OSKAR-MORGENSTERN", "type": "PERSON", "share": "0.04" }, { "actor": "效用合作博弈与谈判前驱", "actorId": 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