一个基于拓扑量子场论的纽结不变量高效计算平台
A TQFT-based Platform for Efficient Computation of Knot Invariants
AI总结：
该平台统一费曼带状图构建、高阶陈 - 西蒙斯纽结不变量评估及类似FRD纽结识别，能将FRD构建为张量网络，评估相关不变量并识别纽结，是首个结合多种功能于统一工作流程的平台。
AI中文摘要：
我们展示了一个交互式网络平台，它统一了费曼带状图（FRD）的构建、高阶陈 - 西蒙斯纽结不变量的评估以及在更高交叉数下类似FRD纽结的识别。这些树状结构的图自然地表示了树形纽结，我们在文中一直将其称为类似FRD的纽结。在单一视觉环境中，用户可以将FRD构建为张量网络，评估其相关的陈 - 西蒙斯不变量，并使用所得不变量数据来区分和识别相应的纽结。据我们所知，这是首个在统一工作流程中结合图形构建、张量网络评估、不变量计算和纽结识别的平台。
英文摘要：
We present an interactive web platform that unifies the construction Feynman ribbon diagrams (FRDs), the evaluation of higher-rank Chern--Simons knot invariants, and the identification of FRD-like knots at higher crossing numbers. These tree-structured diagrams naturally represent arborescent knots, which we refer to throughout as FRD-like knots. Within a single visual environment, users can construct an FRD as a tensor network, evaluate its associated Chern--Simons invariants, and use the resulting invariant data to distinguish and identify the corresponding knot. To our knowledge, this is the first platform to combine diagrammatic construction, tensor-network evaluation, invariant computation, and knot identification within a unified workflow.
