Arc Geometry III: Spectral Stability and Resonant Bifurcation from the q-Fold Circle

Arc Geometry III – Public Benchmark Edition This record contains the public benchmark release of Arc Geometry III: Spectral Stability and Resonant Bifurcation from the q-Fold Circle. The work is part of the Arc Geometry research program: Arc Geometry I – Differential and Topological Structure of Arc Heliceshttps://doi.org/10.5281/zenodo.18869377 Arc Geometry II – Variational Structures and Energies of Arc Heliceshttps://doi.org/10.5281/zenodo.18905574 The present paper develops the spectral stability theory and resonant bifurcation structure for q-fold circles under the Arc energy functional. Contents of this record Main article arc_geometry_iii_draft.pdf LaTeX source arc_geometry_iii_draft.tex Verification module arc_geometry_iii_verify.pyarc_geometry_iii_verify_output.txt Reproducibility and documentation README_public_benchmark.mdmanifest.txtchecksums.txt Verification module The symbolic verification script arc_geometry_iii_verify.py reproduces the quartic reduction calculations presented in Section 5 and Appendix A of the article. The file arc_geometry_iii_verify_output.txt contains reference output from a verified execution. These materials are provided to support independent verification of the derivations. Publication philosophy This work is released as a public benchmark preprint. The objective is not merely journal submission but the establishment of a transparent and reproducible mathematical framework for Arc theory. The article follows journal-level formatting standards while providing additional verification material and reproducibility modules beyond typical journal publications.