A TQFT-based Platform for Efficient Computation of Knot Invariants

Abstract: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.

Geometric Topology (math.GT); Mathematical Software (cs.MS); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph); Quantum Physics (quant-ph)

arXiv:2607.23551 [math.GT]

(or arXiv:2607.23551v1 [math.GT] for this version)

https://doi.org/10.48550/arXiv.2607.23551 arXiv-issued DOI via DataCite (pending registration)