What was already known
Han and Jiang asked whether klt type is open in flat families. Singh’s earlier construction and F-regularity results supply essential inputs but did not answer this question.
AI involvement
ChatGPT Pro 5.5 suggested the counterexample direction. Rethlas found and proved the explicit example. Jihao Liu selected the family and wrote its proof.
The explicit counterexample and its proof are assigned to Rethlas, with the broad idea credited to ChatGPT, while the human author supplies the presentation and prior inputs.
Importance
The example settles a specific openness question in birational geometry.
Limitations
The special- and general-fiber arguments use Singh’s earlier results. The source labels the paper human verified but does not specify a completed step-by-step check of this argument.
Technical verification
The arXiv record labels the paper human verified, but does not identify the checked steps or method for the final counterexample. Reported remains the evidence default for this exact claim.
Human understanding
Liu explains how the substituted Singh family separates the klt-type special fiber from neighboring fibers in a detailed human-authored proof.
Correction and publication history
The example settles a specific openness question in birational geometry.
Read this published revision