The Planar Berenstein Conjecture
Statement
The unrestricted planar Berenstein conjecture holds that overdetermined Dirichlet-Neumann data characterize the disc. Disproved: a bounded simply connected domain with real-analytic Jordan boundary that is not a disc, carrying a nonzero real eigenfunction with zero Dirichlet data and constant nonzero Neumann data.
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No person has examined this. Nothing here has been checked at all. say whether it holds →
computation · #1
Matthew J. Colbrook, Siavash Sadeghi and George Stepaniants, using ChatGPT 5.6That credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.
The authors declare the role and are careful about its limits: "We believe it is important to declare the use of AI in mathematical research, and in the present case its role is particularly noteworthy. ChatGPT 5.6 was given a substantial warm start consisting of an early draft and working code independently developed by MJC and GS" for the earlier Pompeiu-Schiffer paper, material that "already contained the central construction, conformal fixed-disc formulation, coefficient spaces, disk-polynomial algebra, tail strategy, and computational architecture on which the present paper rests. The system was used to explore the modification" to the Dirichlet endpoint.
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