What was already known
Neukirch and Uchida reconstructed fields from Galois-group isomorphisms. Uchida proved the open-homomorphism assertion when the source number field is Q, uniqueness in general, and existence under an additional local decomposition-group condition (manuscript introduction, pp. 1–2).
AI involvement
OpenAI credits itself as manuscript author and states that its internal frontier model produced the results in this release. Individual human input is not detailed enough to establish task-only autonomy.
OpenAI is named as author on the manuscript, and its release attributes the results to an internal frontier model. The individual human input is not detailed enough to establish autonomy.
Importance
Proves Uchida’s full open-homomorphism conjecture for these global Galois groups.
Limitations
The theorem assumes number fields and solvably closed Galois extensions; it does not apply to arbitrary profinite groups or arbitrary field extensions.
Technical verification
Reported is the default when evidence for a higher level is insufficient. The OpenAI-authored manuscript reports and argues the result, but the reviewed sources do not document a completed check of the full assessed claim.
Human understanding
Few is the default when evidence for a higher level is insufficient. No named person is documented as explaining the central argument for this assessed contribution.
Correction and publication history
Primary manuscript, attribution, and prior-work review for non-notifying local inclusion.
Read this published revision