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OpenAI reports: The Hilbert–Smith conjecture

OpenAI claims Lie-group structure for any locally compact second-countable Hausdorff group with a faithful jointly continuous action on a connected finite-dimensional manifold under the stated topological conventions.

Sources for this record

What was already known

Low-dimensional and stronger-regularity cases do not settle every jointly continuous action on topological manifolds.

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

Second-countable Hausdorff groups and connected second-countable Hausdorff manifolds without boundary are the scope. Faithful does not mean free; arbitrary stabilizers are allowed. 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