What was already known
Foulkes’ conjecture had been proved for smaller fixed symmetric-power indices, and stabilization arguments covered sufficiently large b in cases beyond those indices; the sixth-power full range remained open.
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 sixth-symmetric-power case for every permitted b and vector-space dimension.
Limitations
The selected claim is for a=6 and b≥6. The linked Lean scope covers the corresponding injection only for b≥30, not the critical range 6≤b<30.
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, prior-work, and Lean-scope mismatch review for non-notifying local inclusion.
Read this published revision