What was already known
The planar Steklov analogue of Kac’s question remained open in this restrictive class; Sunada and orbifold methods supplied a general template.
AI involvement
Hu, Shi and Tang supplied the initial Sunada adaptation. Their disclosure credits ChatGPT with substantial development of the concrete counterexample, especially passage from orbifold quotients to weighted disks and Euclidean plane domains, and technical propositions. That retained construction is AI-centered within a human-led project.
The authors identify model development of the concrete counterexample, not just editing or routine calculations, while crediting their own overall strategy.
Importance
Answers the planar inverse-Steklov question even for strictly convex analytic domains.
Limitations
Hu, Shi and Tang supplied the Sunada strategy and checked, revised and rewrote the model-assisted construction. No separate external full-proof check is documented.
Technical verification
The authors explicitly say they checked the model-assisted construction and technical arguments before revising the final proof. This is a source-reported complete author check; no machine check is documented.
Formal checking
Author checking, revision and rewriting of the model-assisted arguments
- Checker
- Tao Hu, Jiachen Shi and Quanyu Tang
- Scope
- Theorem 1.1.2 construction, including weighted-disk transfer, Euclidean realization and supporting Propositions 2.3.1, 2.4.1 and 3.4.1
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
The authors identify the original strategy and explain the concrete mechanism and each realization step in the final paper.
Correction and publication history
Answers the planar inverse-Steklov question even for strictly convex analytic domains.
Read this published revision