What was already known
Friedgut, Kahn, Kalai and Keller formulated the flow conjecture in 2018. Chang, Liu and Liu had already proved the weaker Chvátal and Kleitman inequalities, whose result became an input here.
AI involvement
Peter Keevash credits GPT-6 Astra with finding the proof within his suggested approach. Keevash simplified and rewrote it; Chang, Liu and Liu retain credit for their earlier theorem.
The model found the missing proof within a human-suggested approach and using a separate human theorem; central AI work is documented, but the source does not support little human mathematical input.
Importance
Settles a structural strengthening of the intersecting-family inequalities.
Limitations
Keevash supplied the approach and used the separate Chang–Liu–Liu theorem. He rewrote and explained the model-found proof, but no completed independent or machine check is documented.
Technical verification
Keevash supplies a detailed rewritten proof but does not expressly report a completed independent check of the model-origin argument or a machine verification. Reported is the missing-check-evidence default.
Human understanding
Keevash explains the proof strategy, its dependence on the sharp correlation inequality, and the flow deduction in the human-rewritten manuscript.
Correction and publication history
Settles a structural strengthening of the intersecting-family inequalities.
Read this published revision