Constructs a non-disk simply connected domain with real-analytic Jordan boundary and tenfold symmetry, using certified numerical estimates.
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Constructs a non-disk simply connected domain with real-analytic Jordan boundary and tenfold symmetry, using certified numerical estimates.
Passage ID: schiffer-pompeiu:entry:computer:v1
Source item: computer
Source record: schiffer-pompeiu:source:computer:v1
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Problem publication v7
Source assessment
Proved
Analytic tenfold witness certified by the authors
The spectral frequency k lies between 31.967007261 and 31.967007293.
Source date Aug 3, 2026 · Observed Oct 13, 2026
Scope
An analytic tenfold counterexample
Source assessment
Disproved
Planar disk-rigidity conjecture refuted in the cited paper
Simply connected non-disk with real-analytic boundary; this is not a multiply connected annulus construction.
Source date Aug 3, 2026 · Observed Oct 13, 2026
Source assessment
Disproved
Planar disk-rigidity conjecture refuted in the cited paper
Simply connected non-disk with real-analytic boundary; this is not a multiply connected annulus construction.
Source date Aug 3, 2026 · Observed Oct 13, 2026
Definition
Overdetermined boundary conditions
History
Pompeiu asks whether domain averages determine a function
History
An analytic computer-assisted construction
Question
Schiffer and Pompeiu conjectures
Further reading
Read the mathematical argument; inspect its Claim for assessment and scope.
Recorded authorship
Matthew J. Colbrook · George Stepaniants
Matthew J. Colbrook, George Stepaniants
The paper credits GPT-5.5 Codex for debugging early computational code, checked line by line by the authors. The authors own the mathematical argument and certificate.
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A computer-assisted counterexample to the planar Pompeiu and Schiffer conjectures
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