A Certified Robustness Threshold for Constructible Cubic Angle Approximation
Year: 2026
Type: preprint
Abstract: Exact angle trisection by straightedge and compass is impossible in general. This research establishes exact deterministic robustness thresholds for the publicly documented Baker D4 approximate angle-trisection construction. Necessary-and-sufficient chord-error and multistage measurement-error bounds are derived, together with convexity-based certification of a unique minimum admissible input angle. The analysis extends to random-effects calibration, statistical tolerance certification, readout-transfer safeguards, and continuous-angle Lipschitz envelopes. Four frozen numerical benchmark versions investigate Gaussian, heavy-tailed, and counterexample error distributions, demonstrating both the applicability and limitations of statistical certification. The archival package contains the complete manuscript, LaTeX source, Python scripts, generated tables, numerical results, and a SHA-256 manifest. The construction is approximate rather than an exact solution to classical angle trisection. Physical instrument calibration and independent full Monte Carlo replication remain outstanding. Copyright and licensing Copyright © 2026 C. Wayne Baker. Manuscript, PDF and explanatory documentation: Creative Commons Attribution 4.0 International (CC BY 4.0). Python source code: MIT License. Numerical datasets and generated tables: CC BY 4.0. The licenses apply to the respective materials as identified above. The author retains copyright. Reproducibility The release ZIP contains the verified manuscript, source code, benchmark outputs and SHA-256 manifest. The archival files are preserved unchanged.
Author: Baker, C. Wayne
Language: English
Topic: Mathematics and Applications
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225315171