What was already known
Rota’s flat-count unimodality conjecture stood since 1970. Larson had refuted stronger log-concavity, but that alone did not give nonunimodality.
AI involvement
ChatGPT supplied a q-lift seed example. Divoux, Lowen and Wang recognized its stronger consequence and supplied the final adaptation and proof.
The original paper explicitly identifies the model-supplied q-lift nonconvex example that initiated the retained counterexample mechanism, while crediting the final adaptation and proof to human authors.
Importance
The final counterexample resolves the flat-count unimodality conjecture.
Limitations
Divoux, Lowen and Wang develop the adaptation, count the flats and explain the mechanism. The model transcript is unavailable, and no completed separate proof check of the final construction is documented.
Technical verification
The authors give a proof but do not document a separate completed human or machine check of the final construction; Reported is the evidence default.
Human understanding
The human authors explain the flat-count formulas for q-lifts and how a strong log-concavity failure becomes a local valley in the flat-count sequence.
Correction and publication history
If correct, the final counterexample resolves the flat-count unimodality conjecture.
Read this published revision