What was already known
Džamonja and Shelah asked whether the known implication from SOP₃ to SOP₂ reverses. Earlier work had resolved related dividing lines but not this implication.
AI involvement
Artem Chernikov credits ChatGPT 5.6 with finding the proof. Chernikov simplified it and explains the two-case construction; the model interaction does not establish autonomy.
The author directly credits the model with finding the central proof and credits himself with its later simplification.
Importance
Answers a longstanding classification-theory question if the proof holds.
Limitations
No completed check of the new implication is documented. Nick Ramsey’s correction of an older lemma used in the proof is separately credited.
Technical verification
The manuscript contains a proof and acknowledges comments, but no named completed proof check or machine verification of the SOP_2⇒SOP_3 argument was documented. This is a default for missing check evidence, not a failed check.
Human understanding
Chernikov simplified the model-found proof and gives an explicit two-case explanation constructing the SOP_3 witness from a treetop SOP_2 witness.
Correction and publication history
The AI-found implication SOP₂⇒SOP₃ is assessed with its equality consequence; the older lemma repair is credited separately.
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