Sharp stability of the annulus for physical torsion

Henry Zweiman. September 15, 2026.

This preprint gives sharp quadratic stability for planar physical torsion with finitely many Lipschitz holes. The deficit controls the outer domain and hole union by two disks with a common center. It also gives a universal individual-asymmetry constant when the hole area is at most two-thirds of the outer area. The proof combines an exact plateau deficit with fixed-center level-set transport and the global calibration theorem of Hensel and Laux, crediting the transport viewpoint of Guerra, Machado and Ramos.

• Full Markdown manuscript
• Typeset PDF and LaTeX source
• Priority and significance assessment
• Internal proof review
• Source audit, download provenance, and search summary
• Artifact checks, MathJax checks, and hashes

The exponent is optimal. Best constants, limiting area ratios, nonlinear loads and higher-dimensional counterparts remain outside the theorem. All conclusions form one paper.

Prepared with OpenAI Codex. This is an internally audited, unreviewed preprint; no independent human verification, absolute priority certification or journal acceptance is claimed. No finite computation is used as proof.

Rebuild

Run python3 build.py with Pandoc and Tectonic on PATH. The Markdown is authoritative. Third-party source texts are not redistributed.