AI-assisted proof of optimal packing for 11 squares
What happened
A formal proof of the optimal packing of 11 squares has been completed and verified using the Lean theorem prover. The proof, stored in the ElevenSquare repository, passes verification with native numerical certificates and was run through the EvolvingPrograms verification system, checking all 7,920 local Lean modules with zero admissions. The build uses Lean 4.34.1 and a specific Mathlib revision, and the verification can be reproduced with provided scripts on Linux or macOS. The result trusts both Lean's kernel and its native compiler, and the optimal packing achieves an approximate density of 3.8770835900228141773.
Why it matters
This shows that complex geometric optimization problems can now be formally verified, increasing confidence in such results for scientific and engineering work. Ordinary readers can trust that the claimed optimal packing is mathematically sound.
Reality check
An automated, sceptical read of the sourceIncremental. The work extends existing formal verification techniques to a specific geometry problem but does not introduce fundamentally new methods.
Is this a big deal?
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