What was already known
Berezinskii–Kosterlitz–Thouless theory predicted the critical power and logarithmic correction; rigorous work had established the phase picture and correlation bounds without this leading equivalent for the ordinary cosine model.
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 the predicted critical logarithmic correction with a positive finite amplitude for the planar cosine XY model.
Limitations
The statement uses the manuscript’s free-box thermodynamic correlation and coordinate-axis separation; it does not identify a universal numerical amplitude. No completed proof check was documented in the available sources.
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; technical check remains undocumented.
Read this published revision