AI-assisted proof of optimal packing for 11 squares

Researchers have completed an AI-assisted formal proof that demonstrates the optimal packing configuration for 11 squares, with the proof verified in the Lean theorem prover. The optimal side length is approximately 3.877, derived from a specific polynomial equation, and the proof allows for arbitrary orientations and legal boundary contact while maintaining disjoint interiors. The verification process involved 7,920 local Lean modules and native numerical certificates, with the complete proof now publicly available in a repository.