GoKawiilLean proof verifies optimal packing of 11 unit squares
A formal verification project has completed a machine-checked proof in the Lean theorem prover establishing the optimal side length for packing 11 unit squares into a square container, with the exact value defined as the root of a polynomial equation. The verification run, tied to a specific pinned commit, accepted all 7,920 local Lean modules with zero admissions, using native numerical certificates for computationally expensive exact checks alongside standard Lean proofs for geometry and proof assembly.
GoKawiil's interpretation of the reporting above, not reported fact.
The result relies on both Lean's kernel and its native compiler rather than kernel-only verification, a distinction the project explicitly flags for anyone assessing the strength of the optimality claim. Formal, machine-checked proofs of geometric packing problems are rare and could serve as a template for verifying other long-standing optimal packing conjectures with similarly high confidence.
- The proof establishes the exact optimal side length for packing 11 unit squares, given by a closed-form expression involving a root of an 8th-degree polynomial.
- Verification combined native_decide for numerical certificates with standard Lean proofs for geometric and structural arguments, meaning trust extends to Lean's native compiler, not just its kernel.
- All 7,920 local proof modules passed with zero admissions, and the exact source hashes for approved numerical declarations are published for independent audit.
Source: github.com, 2026-10-07
Published there as: “AI-assisted proof of optimal packing for 11 squares”
Read the original report → The summary and analysis above are GoKawiil's own, written from reporting by the source above. Facts and quotes belong to the original publisher.