AI-assisted proof of optimal packing for 11 squares
This article details an AI-assisted mathematical proof verifying the optimal packing configuration for 11 squares, utilizing Lean modules and native numerical certificates. The proof passed rigorous verification, ensuring its accuracy and completeness with zero admissions.
Why it matters
This represents a significant advancement in automated theorem proving and the application of AI to complex mathematical problems, potentially accelerating discovery in fields requiring rigorous verification and computational geometry.
The complete optimality proof passed verification with native numerical certificates. The completed EvolvingPrograms verification run accepted all 7,920 local Lean modules , and its final audit reports zero admissions . This repository imports those exact proof sources and pinned build configuration from commit 1bf942a7af1ea330e95489d8997deebd4227ca71 . See the verification report for evidence and scope.
Selected expensive, exact numerical certificate checks use native_decide . Geometry, checker soundness, and proof assembly retain ordinary Lean proofs. Consequently the final theorem trusts Lean's kernel and native compiler ; this is not a kernel-only verification claim. The approved numerical declarations and their exact source hashes are recorded in verification/native-certificates.json .
where u is the unique root in (9/25,37/100) of
[ 5u^8-10u^7-2u^6+14u^5+12u^4-6u^3+2u^2+2u-1=0. ]
Get smarter about the news
Sign up free for a feed built around what you actually care about, Dive Deeper research on any story, and the full text of every article.
Create free accountAlready have an account? Sign in