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"仅计有限条件下的一般阶数构造；二阶超几何显式解归于已有成果，不纳入后继一般存在理论。", "sources": [ { "label": "1876年论文集，第357—362页", "url": "https://www.e-rara.ch/zut/download/ftpack/plain/5507588" } ], "aReason": "黎曼手稿以有限奇点、常数单值变换、有限阶增长和行列式论证导出线性关系及两个推论，承担主要构造份额；不计未完成的一般存在理论。", "M": "4.8", "status": "已纳入研究估分", "budget": [ { "actor": "伯恩哈德·黎曼", "actorId": "SL-0072", "type": "PERSON", "share": "0.85" }, { "actor": "Weber", "actorId": "EXT-LITERAL:Weber", "type": "PERSON", "share": "0.15" } ], "share": "0.85", "exactLight": "212.6603466783143094422277257629428285034740385665104114377905157772006760565027112185773357546127415", "light": "212.660347", "standaloneScore": "4.66", "lightSharePercent": "2.8673" }, { "id": "OUT-SL0072-1866-THETA-VANISHING-INCREMENT", "title": "theta 函数消失条件的后期修补", "year": "1866", "summary": "处理既有theta反演理论中的恒零例外，给出消失条件及导数条件相关推论的后期增量。", "mReason": "4.3反映消失与导数条件对既有框架的实质修补；它不是整个现代奇点理论，也不重复1857主价值，故低于5档中部。", "overlapNote": "仅计恒零例外和消失条件的新增研究，不重复1857年反演主成果。", "sources": [ { "label": "《论theta函数的消失》", "url": "https://www.maths.tcd.ie/pub/HistMath/People/Riemann/Theta/" } ], "aReason": "黎曼处理1857年框架中的恒零例外并给出消失及导数条件推论，直接承担主要增量；早期框架不重复归功。", "M": "4.3", "status": "已纳入研究估分", "budget": [ { "actor": "伯恩哈德·黎曼", "actorId": "SL-0072", "type": "PERSON", "share": "0.92" }, { "actor": "未分配", "actorId": "OUT-SL0072-1866-THETA-VANISHING-INCREMENT::EP-SL0072-1866-THETA-VANISHING-INCREMENT::UNALLOCATED", "type": "UNALLOCATED", "share": "0.08" } ], "share": "0.92", "exactLight": "129.0334541052933957983159234815821655406538858093167030039011074877877006230403297425499457247739862", "light": "129.033454", "standaloneScore": "4.23", "lightSharePercent": "1.7397" }, { "id": "OUT-SL0072-1860-SELF-GRAVITATING-FLUID-ELLIPSOID", "title": "自引力流体椭球的运动与受限稳定性", "year": "1860—1861", "summary": "在线性运动假设下，对均匀自引力流体椭球的转轴、内部相对运动、恒定形态和受限变分稳定性作系统分析。", "mReason": "4.4高于专业子领域一般结果，因为运动、形态和稳定性被连成系统方法；无条件非线性稳定性、精确全积分和后继成果排除，使其低于5档中部。", "overlapNote": "仅计线性运动条件下的椭球分析，不扩展到任意流体或无条件非线性稳定性。", "sources": [ { "label": "《均匀流体椭球运动研究》", "url": "https://www.maths.tcd.ie/pub/HistMath/People/Riemann/Ellipsd/" } ], "aReason": "黎曼在先行线性运动假设下完成主轴、相对运动、恒定形态和受限稳定性分析，承担主要份额；前驱假设与已知特例另计。", "M": "4.4", "status": "已纳入研究估分", "budget": [ { "actor": "伯恩哈德·黎曼", "actorId": "SL-0072", "type": "PERSON", "share": "0.78" }, { "actor": "彼得·古斯塔夫·勒热纳·狄利克雷", "actorId": "SL-3805", "type": "PERSON", "share": "0.15" }, { "actor": "Maclaurin", "actorId": "EXT-LITERAL:Maclaurin", "type": "PERSON", "share": "0.05" }, { "actor": "未分配", "actorId": "OUT-SL0072-1860-SELF-GRAVITATING-FLUID-ELLIPSOID::EP-SL0072-1860-1861-FLUID-ELLIPSOID::UNALLOCATED", "type": "UNALLOCATED", "share": "0.02" } ], "share": "0.78", "exactLight": "122.8416690119668518457639071245375470350164864383530473286711513606992353661394104485958124599966614", "light": "122.841669", "standaloneScore": "4.19", "lightSharePercent": "1.6563" }, { "id": "OUT-SL0072-ZETA-EXACT-DOUBLE-CONTOUR-REPRESENTATION", "title": "ζ函数的精确双轮廓积分表示", "year": "遗稿；1932整理刊出", "summary": "由Φ恒等式得到ζ函数的精确双斜轮廓积分表示，并在临界线上化为带Gamma因子的单积分实部。", "mReason": "精确双轮廓表示及其可用形式构成独立计算工具，采用M4.6；范围窄于整个ζ函数理论，不重复计入解析延拓和函数方程。", "overlapNote": "精确积分表示与有限和渐近计算分别按独立增量计分，共用恒等式不再另立一项。", "sources": [ { "label": "西格尔1932年论文英译，第3节（可修订译稿）", "url": "https://arxiv.org/abs/1810.05198" } ], "aReason": "精确积分表示的数学核心来自黎曼遗稿，采用55%的个人份额；西格尔为应用而作的实质重写及成文保留独立归功。", "M": "4.6", "status": "已纳入研究估分", "budget": [ { "actor": "伯恩哈德·黎曼", "actorId": "SL-0072", "type": "PERSON", "share": "0.55" }, { "actor": "CARL LUDWIG SIEGEL", "actorId": "EXT-NAME:CARL-LUDWIG-SIEGEL", "type": "PERSON", "share": "0.41" }, { "actor": "Bessel Hagen", "actorId": "EXT-LITERAL:Bessel-Hagen", "type": "PERSON", "share": "0.04" } ], "share": "0.55", "exactLight": "109.1894273232883780743850468206744556892450873472940354576452516852712000883926930461459043888644138", "light": "109.189427", "standaloneScore": "4.08", "lightSharePercent": "1.4722" }, { "id": "OUT-SL0072-1862-GENUS3-QUARTIC-BITANGENT-CONSTRUCTION", "title": "三亏格平面四次曲线的28条双切线构造", "year": "1862课程；1876刊出", "summary": "在非奇异非超椭圆三亏格平面四次曲线上，用theta奇特征、线性形式、配对零点和六对分组构造28条双切线的有限配置。", "mReason": "4.3高于普通特例，因为28对象、特征分组和代数关系构成完整有限配置；它是一般框架的专门应用，故不进入5档高部。", "overlapNote": "仅计四次曲线双切线的具体构造；一般theta框架、课程教学服务与现代推广不重复计入。", "sources": [ { "label": "1876年论文集，第456—472页", "url": "https://www.e-rara.ch/zut/download/ftpack/plain/5507588" } ], "aReason": "黎曼在课程中完成三亏格四次曲线的theta特征、双切线配对及分组构造；罗赫的听课记录及后续编辑出版分别保留归功。", "M": "4.3", "status": "已纳入研究估分", "budget": [ { "actor": "伯恩哈德·黎曼", "actorId": "SL-0072", "type": "PERSON", "share": "0.68" }, { "actor": "GUSTAV ROCH", "actorId": "EXT-NAME:GUSTAV-ROCH", "type": "PERSON", "share": "0.17" }, { "actor": "HEINRICH MARTIN WEBER", "actorId": "EXT-NAME:HEINRICH-MARTIN-WEBER", "type": "PERSON", "share": "0.12" }, { "actor": "未分配", "actorId": "OUT-SL0072-1862-GENUS3-QUARTIC-BITANGENT-CONSTRUCTION::EP-SL0072-1862-GENUS3-LECTURE-CONSTRUCTION-BY-1876::UNALLOCATED", "type": "UNALLOCATED", "share": "0.03" } ], "share": "0.68", "exactLight": 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"standaloneScore": "3.85", "lightSharePercent": "1.1245" }, { "id": "OUT-SL0072-1847-FINITE-ORIGIN-FRACTIONAL-CALCULUS", "title": "有限起点的分数阶积分与受限微分构造", "year": "1847；1876刊出", "summary": "有限起点的分数阶积分核、由普通微分延伸的受限构造，以及普通幂函数计算。", "mReason": "有限起点核和阶数运算组成可复用方法族，深度超过孤式；未证广泛采用不能预支国际平台价值。专业方法中心4.0。", "overlapNote": "相关分数阶公式合为一个方法族；不计首创整个分数阶微积分或现代应用。", "sources": [ { "label": "Dugowson：分数阶运算史及黎曼手稿译文", "url": "https://www.numdam.org/item/10.24033/rhm.61.pdf" } ], "aReason": "黎曼手稿给出有限起点积分核、受限微分扩展和幂函数计算，因此承担主要构造份额；先行思想与身后整理出版分别保留归功。", "M": "4.0", "status": "已纳入研究估分", "budget": [ { "actor": "伯恩哈德·黎曼", "actorId": "SL-0072", "type": "PERSON", "share": "0.72" }, { "actor": "Lagrange", "actorId": "EXT-LITERAL:Lagrange", "type": "PERSON", "share": "0.1" }, { "actor": "Weber", "actorId": "EXT-LITERAL:Weber", "type": "PERSON", "share": "0.11" }, { "actor": "Dedekind", "actorId": "EXT-LITERAL:Dedekind", "type": "PERSON", "share": "0.07" } ], "share": "0.72", "exactLight": "71.28", "light": "71.280000", "standaloneScore": "3.72", "lightSharePercent": "0.9611" }, { "id": "OUT-SL0072-1860-MINIMAL-CIRCULAR-SURFACES", "title": "平行圆截面极小曲面的一参数族", "year": "1860年前后；身后刊出", "summary": "平行平面圆截面的极小曲面条件构造，包含catenoid和一个一参数新族，至1868年前整理公开。", "mReason": "4.0处于领域重要结果门槛，因为交付不只是单例而是受条件控制的一参数新族；覆盖限于平行圆截面，故不越过5。", "overlapNote": "与三直线边界构造区分；既有复函数工具、非平行圆截面延伸和后世分类不重复计入。", "sources": [ { "label": "《给定边界下的最小面积曲面》", "url": "https://www.maths.tcd.ie/pub/HistMath/People/Riemann/Minimal/" } ], "aReason": "核心圆截面极小曲面构造来自黎曼原稿；身后整理与补成分别归功于实际参与者，不将后世分类结果回填到原稿。", "M": "4", "status": "已纳入研究估分", "budget": [ { "actor": "伯恩哈德·黎曼", "actorId": "SL-0072", "type": "PERSON", "share": "0.66" }, { "actor": "K.Hattendorff", "actorId": "EXT-LITERAL:K.Hattendorff", "type": "PERSON", "share": "0.18" }, { "actor": "M.H.Weber", "actorId": "EXT-LITERAL:M.H.Weber", "type": "PERSON", "share": "0.16" } ], "share": "0.66", "exactLight": "65.34", "light": "65.340000", "standaloneScore": "3.64", "lightSharePercent": "0.8810" }, { "id": "OUT-SL0072-1861-HEAT-COORDINATE-FLATNESS", "title": "热传导坐标变换判据", "year": "1861", "mReason": "3.4反映六条件及其独立性关系构成可复用判据，并有独立历史作用确认；范围不扩到一般维数或全部热问题，使其远离5档。", "sources": [ { "label": "黎曼1861年热传导论文：文集第二版391–404页", "url": "https://www.maths.tcd.ie/pub/HistMath/People/Riemann/Paris/" } ], "aReason": "黎曼完成三维热方程常系数变换的充分条件与具体判据，承担主要份额；不重复计入早期几何框架。", "M": "3.4", "status": "已纳入研究估分", "budget": [ { "actor": "伯恩哈德·黎曼", "actorId": "SL-0072", "type": "PERSON", "share": "0.78" }, { "actor": "卡尔·弗里德里希·高斯", "actorId": "SL-0012", "type": "PERSON", "share": "0.09" }, { "actor": "Heinrich Weber", "actorId": "EXT-LITERAL:Heinrich Weber", "type": "PERSON", "share": "0.13" } ], "share": "0.78", "exactLight": "38.31260422292723823012122657702576990871681520695990258651640155934287794372879373886210208475508150", "light": "38.312604", "standaloneScore": "3.19", "lightSharePercent": "0.5166" }, { "id": "OUT-SL0072-CIRCULAR-DOMAIN-POTENTIAL-CONFORMAL-CONSTRUCTION", "title": "圆界区域的势问题与条件保角构造", "year": "1876刊出", "summary": "把平行圆柱的势或稳态温度问题化为平面边界问题，并以镜像加倍、圆反射、Möbius变换和二阶方程解比构造条件圆界映射。", "mReason": "条件化约、圆反射与解比构造形成完整的专门方法，采用M3.5；全局常数的确定及任意圆界配置尚未闭合，限制了适用范围。", "overlapNote": "仅计圆界势问题的特定构造，一般复函数、加倍及微分方程工具不重复计入。", "sources": [ { "label": "1876年论文集，第413—416页", "url": "https://www.e-rara.ch/zut/download/ftpack/plain/5507588" } ], "aReason": "黎曼留下公式、条件化约与解比构造的数学核心；韦伯使这些材料成为可理解的公开文本，其实质编辑工作另行归功。", "M": "3.5", "status": "已纳入研究估分", "budget": [ { "actor": "伯恩哈德·黎曼", "actorId": "SL-0072", "type": "PERSON", "share": "0.66" }, { "actor": "HEINRICH MARTIN WEBER", "actorId": "EXT-NAME:HEINRICH-MARTIN-WEBER", "type": "PERSON", "share": "0.27" }, { "actor": "未分配", "actorId": "OUT-SL0072-CIRCULAR-DOMAIN-POTENTIAL-CONFORMAL-CONSTRUCTION::EP-SL0072-WEBER-CIRCULAR-DOMAIN-REDACTION-BY-1876::UNALLOCATED", "type": "UNALLOCATED", "share": "0.07" } ], "share": "0.66", "exactLight": "36.45452746256303930606676862524776127690456884451364982939150196656831553044214802778662697873054019", "light": "36.454527", "standaloneScore": "3.15", "lightSharePercent": "0.4915" }, { "id": "OUT-SL0072-1852-RATIONAL-BOUNDARY-MODULAR-LIMITS", "title": "模函数有理边界的径向极限", "year": "1852；1876刊出", "summary": "椭圆模函数在周期比径向趋近有理实边界时，对边界级数积分与逼近所得的具体极限关系。", "mReason": "有理边界关系与径向逼近组成可复用的有限方法，采用M3.4；现代严密补证与更广泛的模函数理论未纳入。", "overlapNote": "仅计有理边界的特定方法，不重复一般theta反演、消失条件或后人的严密补证。", "sources": [ { "label": "1876年论文集，第427—437页", "url": "https://www.e-rara.ch/zut/download/ftpack/plain/5507588" } ], "aReason": "黎曼在1852年片段中完成边界级数积分与径向逼近的具体运算。归功包含原稿方法，未将后人的严密补证算给他；辨读、校正与刊出另行分配。", "M": "3.4", "status": "已纳入研究估分", "budget": [ { "actor": "伯恩哈德·黎曼", "actorId": "SL-0072", "type": "PERSON", "share": "0.66" }, { "actor": "卡尔·雅可比", "actorId": "SL-3804", "type": "PERSON", "share": "0.1" }, { "actor": "HEINRICH MARTIN WEBER", "actorId": "EXT-NAME:HEINRICH-MARTIN-WEBER", "type": "PERSON", "share": "0.09" }, { "actor": "RICHARD DEDEKIND", "actorId": "EXT-NAME:RICHARD-DEDEKIND", "type": "PERSON", "share": "0.15" } ], "share": "0.66", 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"status": "已纳入研究估分", "budget": [ { "actor": "伯恩哈德·黎曼", "actorId": "SL-0072", "type": "PERSON", "share": "0.85" }, { "actor": "彼得·古斯塔夫·勒热纳·狄利克雷", "actorId": "SL-3805", "type": "PERSON", "share": "0.15" } ], "share": "0.85", "exactLight": "8.687156861566689202523831045062198762139622312564700180783132809445878072832907025509740490892119080", "light": "8.687157", "standaloneScore": "1.97", "lightSharePercent": "0.1171" }, { "id": "OUT-SL0072-1854-POTENTIAL-ELECTRICITY-RETENTION", "title": "势函数与电学中的残余电模型", "year": "1854", "mReason": "1.6反映方程与现象比较形成可复用模型；只做定性比对且缺装置参数，使中心低于2档中部。", "sources": [ { "label": "黎曼1854年电学论文：三一学院文本版本", "url": "https://www.maths.tcd.ie/pub/HistMath/People/Riemann/Spann/" } ], "aReason": "黎曼组织电荷松弛方程并作定性比较，构成主要交付；采用的电学关系、观测与纠错分别保留份额。", "M": "1.6", "status": "已纳入研究估分", "budget": [ { "actor": "伯恩哈德·黎曼", "actorId": "SL-0072", "type": "PERSON", "share": "0.62" }, { "actor": "Ohm", "actorId": "EXT-LITERAL:Ohm", "type": "PERSON", "share": "0.09" }, { "actor": "Kohlrausch", 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"status": "已纳入研究估分", "budget": [ { "actor": "伯恩哈德·黎曼", "actorId": "SL-0072", "type": "PERSON", "share": "0.52" }, { "actor": "WILHELM EDUARD WEBER", "actorId": "EXT-NAME:WILHELM-EDUARD-WEBER", "type": "PERSON", "share": "0.32" }, { "actor": "Hankel", "actorId": "EXT-LITERAL:Hankel", "type": "PERSON", "share": "0.06" }, { "actor": "未分配", "actorId": "OUT-SL0072-1861-HANKEL-REVIEW-SUPPORT::EP-SL0072-1861-HANKEL-PRIZE-REVIEW::UNALLOCATED", "type": "UNALLOCATED", "share": "0.1" } ], "share": "0.52", "exactLight": "0.2316286807878823062043704038343834672226705128340550765605093909856046445701867533809614331149619969", "light": "0.231629", "standaloneScore": "0.18", "lightSharePercent": "0.0031" } ], "exclusions": [], "provisionalCount": 0, "provenance": { "releaseId": "research-200-20260914", "baselineLedgerSha256": "8bdd406b3e20ae22357644499e622922c670ff11010df0478c70c23b38902108", "c24DeltaSha256": "b0b96144d1d3397e54a61c3d706ff2da5920fe7617e3bef50407149cb97d9d62", "generatorSha256": "25de659e9852503508e7c27d8a31773b8da5d6310531b1e3699d18cc94319929" }, "priorScopeNote": "32项已列贡献的研究估分。账本覆盖有限的主要成果，尚未穷尽生涯。M与归功份额是可修订的评估判断；未覆盖经历和负面影响不按零处理。", "rank": 2 }