What made useful knowledge cumulative was not discovery alone but the institutions that transmitted it. We provide the first exhaustive structural measurement of the network through which upper-tail human capital passed from master to student across a millennium. Using 470,000 mentor-student records from Wikidata (which integrates the Mathematics Genealogy Project and MacTutor Archive), and all 64 historical Fields Medalists as a fixed, ex ante tracer set, backward traversal yields a directed acyclic graph of 25.5 million paths reaching 57 generations. We document two institutional transitions. First, a 17th-century watershed concentrates lineage traffic on Leibniz: 47 of 64 lineages pass through him with a 10:1 downstream-to-upstream ratio, and seven independent attributes -- learned-society membership (a 46-fold rise per scholar), field, language, employer, institutional diversification, student production, and diffusion entropy -- re-organize coherently across the same window. This is the network signature of Mokyr's Republic of Letters, and it reframes the Newton-Leibniz priority dispute as a distinction between the possession and the transmission of upper-tail human capital: it is transmission that generates the spillovers on which growth depends. Second, 84% of lineages converge upstream on five 12th-13th-century Islamic and Byzantine scholars before terminating at an 11th-century boundary -- the ``Monastery Wall'' -- at which personal academic mentorship first becomes record-generating in Europe. Our claims are descriptive-structural, not causal. Because exhaustive traversal at this scale defeats standard tools, we also contribute a deterministic, algebraic graph-traversal instrument whose measurement bias we characterize in closed form, and report one emergent property of independent methodological interest.

翻译：使有用知识得以累积的不仅是发现本身，更是传递这些知识的制度。我们首次对上层人力资本跨越千年从导师传递至学生的网络进行了详尽的结构性测量。利用维基数据（整合了数学谱系计划与MacTutor档案）中的47万条导师-学生记录，并以全部64位历史上的菲尔兹奖得主作为固定的、事前设定的追踪种子集，通过反向遍历生成一个有向无环图，包含2550万条路径，跨越57代人。我们记录了两项制度性转变。首先，17世纪的一个分水岭将谱系流量集中于莱布尼茨：64条谱系中有47条经由他传递，下游/上游比为10:1，并且七个独立属性——学会会员身份（每位学者增长46倍）、领域、语言、雇主、机构多样化、学生产出及扩散熵——在同一时间窗口内发生协同重组。这是莫基尔"文人共和国"的网络特征，并将牛顿-莱布尼茨优先权争议重新诠释为上层人力资本的拥有与传递之间的区别：正是传递产生了增长所依赖的知识溢出。其次，84%的谱系在上游汇聚于五位12至13世纪的伊斯兰与拜占庭学者，最终止步于11世纪的一个边界——"修道院之墙"——在欧洲，个人学术指导关系正是在此之后才开始产生可记录的证据。我们的主张是描述性-结构性的，而非因果性的。由于在此规模上进行详尽遍历超出了标准工具的能力，我们还贡献了一种确定性的代数图遍历工具，其测量偏差我们以闭式表达进行了刻画，并报告了一项具有独立方法论意义的涌现特性。