Data deposit · Software · version 17 of 2026-11-07, first deposited 2026-10-29

knot-identification-pipeline: knot type of closed space curves from their geometry

Werner Alois Stanggassinger — in collaboration with Claude Code (Anthropic)

Permanent archive (all files, all versions): doi:10.5281/zenodo.23766950 (Zenodo, CERN).

Source code: github.com/WernerAloisStanggassinger/knot-identification-pipeline (GitHub).

Abstract

Identifies the knot type of a closed space curve given as a Fourier series, without consulting knot tables during identification: GPU camera-flight crossing scanner, crossing tracker, diagram resolution, simplification (Regina, spherogram), invariants (SnapPy, SageMath, KnotJob, Bar-Natan–van der Veen Theta), and only afterwards a comparison with KnotInfo, Fremlin and the SnapPy census. Built for the stainless-steel knot sculptures of Werner Alois Stanggassinger (sculptor). Werner Alois Stanggassinger in collaboration with Claude Code (Anthropic): the choice of problem, the direction of the work and the computing hardware are due to the author; the code was written by Claude Code, which orchestrates the computations, working with the author. Every Python module of the pipeline that has an authors' copy was checked against it by comparing abstract syntax trees after the documented changes (translated comments, messages and names; paths moved into one configuration file); the later program changes, including those made only in this release, are listed in the README; the equivalence gates are included. The corpus layer reads both the authors' records (German file and field names) and the English output of the released pipeline; the research tools in research/ list their changes in their own READMEs. Since v1.10.0 the release also holds the knot machines that built the machine knots of the corpus, the comparisons with Burton's census and Maguire's data, the identity checks, the corpus data (CC BY 4.0), the machine curves they read (CC BY-NC 4.0), nine sculpture centrelines (all rights reserved, download and computation for study allowed) and the producer scripts of six Zenodo deposits. Website: https://knot-structures.stainlesssteel4u.de/

Keywords: knot theory · knot identification · space curves · Fourier knots · knot invariants · GPU · SnapPy · Regina · SageMath

Cite

@misc{stanggassinger2026knot,
  author    = {Stanggassinger, Werner Alois},
  title     = {knot-identification-pipeline: knot type of closed space curves from their geometry},
  year      = {2026},
  publisher = {Zenodo},
  doi       = {10.5281/zenodo.23766950},
  url       = {https://knot-structures.stainlesssteel4u.de/preprints/knot-identification-pipeline-knot-type-closed-space/}
}

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