What was already known
Ohsawa–Takegoshi gave one inclusion, and Fubini gave equality outside a Lebesgue-null set. Xia had proved a projective-fibration version; Boucksom asked for a pluripolar exceptional set locally.
AI involvement
Xia supplied the original jet-bundle strategy. Rethlas, running GPT-5.6 Sol, first worked out difficult proof details; Xia simplified and largely rewrote them.
Rethlas first supplied substantive proof details needed to complete Xia’s pre-existing strategy; independent AI leadership of the theorem is not established.
Importance
Settles Boucksom’s local analytic Bertini question under the stated setting.
Limitations
Xia says the proof strategy predates the AI work and he largely rewrote the details first developed by Rethlas. The surviving AI lemmas are not individually identified, and no completed final-proof check is documented.
Technical verification
The manuscript gives a complete proof and Xia rewrote it, but availability and rewriting do not document a completed rigorous check of the final claim.
Human understanding
Xia explains the central proof mechanism and rewrote the AI draft; no central reasoning gap is reported.
Correction and publication history
Settles Boucksom’s local analytic Bertini question under the stated setting.
Read this published revision