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 arcgeometryᵢiidraft. pdf LaTeX source arcgeometryᵢiidraft. tex Verification module arcgeometryᵢiiᵥerify. pyarcgeometryᵢiiᵥerifyₒutput. txt Reproducibility and documentation READMEₚublicbenchmark. mdmanifest. txtchecksums. txt Verification module The symbolic verification script arcgeometryᵢiiᵥerify. py reproduces the quartic reduction calculations presented in Section 5 and Appendix A of the article. The file arcgeometryᵢiiᵥerifyₒutput. 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.