What was already known
Kollár and Kovács asked whether first structure-sheaf cohomology can vary under these fiber conditions.
AI involvement
Jihao Liu first asked ChatGPT 5.5 Pro for general ideas and then used Rethlas, which the paper says supplied the right example. The retained counterexample is therefore model-origin work, though the initial idea and final proof steps are not individually allocated.
The paper expressly credits Rethlas with the decisive example and generative AI with the main result, under Liu's question and presentation.
Importance
Constructs a family answering that question over a smooth affine curve.
Limitations
The projective-base variant is not established. Assistance checking an earlier blueprint does not document a completed check of this final construction.
Technical verification
Reported is the default when evidence for a higher level is insufficient. The stated human assistance concerns an earlier blueprint, with no scope tying it to the final construction and proof. No completed final-version check is documented; Reported is the evidence default.
Human understanding
Few is the default when evidence for a higher level is insufficient. The paper presents the construction and cohomology calculation, but credits generative AI with the main result and does not identify a human explanation or completed review of its central mechanism. Few is the evidence default, not a positive claim of incomprehension.
Correction and publication history
Constructs a family answering that question over a smooth affine curve.
Read this published revision