What was already known
Nazarov–Petermichl–Treil–Volberg introduced convex-body domination and conjectured the general implication from scalar sparse domination. Earlier work proved an implication only under a stronger generic estimate arising in typical sparse-domination proofs.
AI involvement
Aapo Laukkarinen and Emiel Lorist co-developed an initial commutator approach with ChatGPT 5.6, then suggested Rademacher randomization. ChatGPT helped find a rough dyadic proof; the authors developed, verified and explained the complete theorem.
The model co-developed a rough central dyadic proof, while humans supplied the Rademacher pivot and completed the final theorem.
Importance
The final theorem proves the conjectured implication from scalar sparse bounds to convex-body sparse bounds.
Limitations
The human authors supplied the Rademacher pivot and completed the non-dyadic theorem. The rough model-generated dyadic proof is unavailable for direct comparison with the final proof.
Technical verification
The authors explicitly state that they fully developed and verified the final proof; the reported check covers the dyadic AI-associated step and its final use.
Human understanding
The authors explain and complete the randomization and stopping-time mechanism.
Correction and publication history
The final theorem proves the conjectured implication from scalar sparse bounds to convex-body sparse bounds.
Read this published revision