An Exact Computer-Assisted Improvement of the Lower Bound for Packing Eleven Unit Squares

We give an exact computer-assisted certificate implying s(11) > 3875000000/999999999 = 3.875000003875000003875... for packing eleven independently rotatable unit squares into a square. The certificate is obtained by reweighting thirteen threshold-charge orbits in the public s(11) > 31/8 certificate and then applying the common exact rational scaling factor 999999999/1000000000 to the parent and strict-core side parameters. The accompanying reproducibility package contains the frozen source and improved certificates, exact replay receipts, two separately implemented exact verifiers, integrity hashes, source attribution, and the preprint in PDF, DOCX, and LaTeX formats. The exact improvement over 31/8 is 31/7999999992 > 0. During final packaging, a fresh primary exact replay covered all 12,028 angular rows, with histogram {1000047559: 12028} and zero bad rows. An earlier complete independent-verifier replay is also preserved in the archive. A dated public literature and registry check on 29 September 2026 located no registered strict lower bound at this value or a larger value. The record states this dated search result without making a separate priority claim.