What was already known
Finite sums and finite products each had classical monochromatic-set theorems separately. Hindman’s simultaneous finite conjecture remained open; the analogous infinite simultaneous statement is false.
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
Resolves Hindman’s finite sums-and-products conjecture.
Limitations
The chosen set is finite for each requested k. The result does not assert one infinite set with all finite sums and products monochromatic. 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