Eleven-square packing in Lean The complete optimality proof passed verification with native numerical certificates. The completed Evolving Programs 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. The optimal side length is T = (6u+4)/(1+2u-u^2), where u is the unique root in (9/25,37/100) of a polynomial.
The construction attains approximately 3.8770835900228141773. The model allows arbitrary orientations, legal boundary contact, and disjoint open interiors. The public statements in Eleven Square/Optimality.lean and the complete T03 source tree are unchanged.
Entry points include Eleven Square/Foundations.lean, Eleven Square/Interop/Wand125/Connections, and Eleven Square/Optimality.lean. Reproduce verification with Lean 4.34.1 and Mathlib revision d13f23b723b8a846827a245b89c10fc7d3f11612. On Linux: bash scripts/run_verification.sh --bootstrap --jobs 2.
On macOS, install elan first. The command checks every local module and performs final source, receipt, dependency, and axiom audit. Credits to Evolving Programs, @ctjlewis, and every project contributor.
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