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OpenAI reports: Koebe’s circle-domain conjecture

OpenAI claims a conformal circle-domain model for an arbitrary planar domain, allowing uncountably many complementary components.

Sources for this record

What was already known

Finite and countably connected uniformization results leave the unrestricted complement problem separate.

What changed and why it matters

Advances the stated target relative to the recorded baseline.

The AI contribution

OpenAI attributes the manuscript to its internal model; individual human contributions remain unspecified.

Limitations

No uniqueness up to Möbius transformations is claimed. The companion removability-to-rigidity result is a separate statement; a family artifact link does not establish checking of this manuscript. Preprint. AIProofWatch read the source statement and context; it has not refereed the proof, compiled a formal development, or established community acceptance.

Verification evidence

Evidence labels show what supports the claim. Importance rates its impact if correct.

Author claim

The original source reports this scoped result; AIProofWatch reviewed its statement, not the full proof.

Accessible artifact / proof

A research manuscript or proof artifact is publicly accessible; availability is not independent checking.

Correction and publication history