Priority and significance assessment

Henry Zweiman. September 15, 2026. Developed as Q57.

Contribution and internal decision

Provisionally admit this as one substantial research preprint under the revised program standard, conditional on completing the public artifact transaction. The proposed theorem gives global sharp quadratic stability for planar physical torsion with any finite number of Lipschitz holes. It controls the outer domain and hole union by disks with one common center, with a constant depending only on their area ratio. Separate individual asymmetries have a universal constant when the hole area is at most two-thirds of the outer area. A smooth second-harmonic perturbation proves exponent optimality. These conclusions and the transport proposition form one paper.

The problem is explicit and current: Amato-Barbato's final article, Section 7, page 30, asks for the optimal exponents in its two stability theorems. The principal proposed advances are quantitative accounting for the positive-measure plateaus and fixed-center propagation through the whole prescribed range of areas. The argument applies without diameter, component-count or boundary-regularity constants. Its intermediate mass-window estimate is a possible reusable tool for elliptic problems with constrained flat regions.

This is a significance judgment, not an acceptance or citation prediction. The result is planar and linear, and uses strong recent external geometric input. Editors could regard the adaptation of recent transport methods as narrower than the intended Advances in Mathematics/Transactions of the AMS standard. Internal admission is revisable. No independent expert has reviewed the argument.

Main source and essential dependencies

The final Amato-Barbato PDF was read at the variational definition, main statements, relevant rearrangement material and final open questions. Its normalization agrees with this manuscript. Its first theorem has the area ratio 2/3; the preliminary 3/4 lead was corrected. The displayed annular index abbreviates its center convention. Our definition expressly requires a common center and implies the weaker two-center comparison too.

Hensel-Laux, arXiv:2606.17172v1, Theorem 1 and Lemma 3, supplies the global relative-energy estimate. Its introduction, main statements and Section 4.6 global argument were inspected. The confined, barycenter-normalized Theorem 2 alone would not suffice. The manuscript smooths the calibration by pointwise domination, then proves its own center-transfer estimate. No numerical or effective value of the global constant is claimed.

Guerra-Machado-Ramos, arXiv:2609.07772v1, supplies the recent level-set velocity and deficit viewpoint. Its introduction, Section 2, Section 3 through Proposition 3.6, and targeted closing-section passages were compared. This precedent is credited in the abstract and proof. The present extension handles hole atoms and uses a compact smooth field with one fixed center. The all-Dirichlet sharp theorem itself is established prior work, including Brasco-De Philippis-Velichkov.

Other comparisons and access limits

Cito's primary author text, introduction, main statements and final questions, treats a Sobolev exterior trace functional with perimeter-volume constraints and a convex outer domain. Its arXiv history lists v2, February 12, 2026. The final article is Nonlinear Analysis 269 (2026), 114086, DOI 10.1016/j.na.2026.114086, also identified in Amato-Barbato's final references. The publisher body could not be retrieved; it is not described as read.

Barbato-Salerno's Robin comparison preprint v2, introduction and Section 5, establishes qualitative comparison and optimization. The final DOI 10.1016/j.jmaa.2026.130847 was identified in the final Amato-Barbato references; its publisher body was unavailable. Neither this comparison source nor Cito is a proof dependency. Their inspected functionals and statements do not supply the present sharp physical-torsion estimate, but unread final changes remain a bounded priority limitation.

Further checks cover Barbato-Salerno's local Dirichlet stability preprint, Cavallina's finite-conductivity two-phase formulation, the final-author Brasco-De Philippis-Velichkov text, and Brasco's moment/duality discussion. Classical moment identities and qualitative annular optimality are not claimed as new. The Pólya-Weinstein historical reference is attributed through Amato-Barbato; the qualitative bound is independently derived in the manuscript.

Current discovery and limits

Six complete arXiv API feeds, including exact annular terminology, the primary authors, recent sharp torsion, moment terminology and calibration/physical-torsion successors, were retrieved. Raw XML and entry summaries are retained locally. The calibration query was noisy; unrelated uses of torsion were excluded by their titles and abstracts. Current histories still list Amato-Barbato v2, Hensel-Laux v1 and Guerra-Machado-Ramos v1. Targeted web searches added no matching resolution. Feed completeness means completeness of the returned query results, not exhaustive historical coverage.

The originating assistant performed both proof and literature audits. No independent human review, absolute priority certification, journal acceptance or future citation count is claimed. This is an AI-assisted, unreviewed research preprint containing a complete proposed hand proof. Artifact verification is separate from mathematical review.