What was already known
Real-rootedness and log-concavity had been conjectured for these polynomials. Nonunimodality is stronger evidence against those expectations than failure of real-rootedness alone.
AI involvement
Rethlas/GPT-5.6 Sol found the binary real-rootedness counterexample and useful degree approach; Ronnie Cheng and Shurui Liu developed and proved the all-fields nonunimodality extension.
The AI-origin projective-deletion construction and convolution/degree approach are central inputs to the human generalization; the headline stronger theorem remains separately human-credited.
Importance
The AI-found example and method informed a later human theorem refuting unimodality over all finite fields.
Limitations
The all-fields nonunimodality theorem is Cheng and Liu’s contribution. The earlier AI verification-agent acceptance is not a completed human or formal check of that theorem.
Technical verification
The paper supplies two proofs and reports acceptance by an AI verification agent of its earlier example, but no completed rigorous human or qualifying machine check of the assessed all-fields claim is documented.
Human understanding
The human authors isolate the degree criterion and explain both the combinatorial induction and geometric small-map mechanism.
Correction and publication history
The AI-found example and method informed a later human theorem refuting unimodality over all finite fields.
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