Certificates for a computer-assisted proof of g5 <= 4.15 for complete pivoting

Certificate files for the computer-assisted proof that no real 5×5 matrix, with any legal complete-pivoting sequence, has fifth pivot p₅ ≥ K for K = 9/2 and K = 2175795/2¹⁹ = 4.1499996…, hence g₅ ≤ 4.15, where g₅ is the largest growth factor of Gaussian elimination with complete pivoting on real 5×5 matrices. The previous best upper bound was g₅ ≤ 4.84 (Chen, Edelman, Urschel, 2026). The paper, node logs, generator code and the exact checker checker.py (Python ≥ 3.9, standard library only, exact rational arithmetic) are at https://github.com/SupersonicMan12/g5-upper-bound. Files certificates_K4p5.jsonl.xz: certificates for K = 9/2 (7,543 nodes, 102,899 certificates; 154 MB decompressed) certificates_K4p15.jsonl.xz.part00 … part49: certificates for K = 2175795/2¹⁹ (225,465 nodes, 3,478,969 certificates; 6.18 GB decompressed), split into 50 chunks with split -d -a 2 -n 50 for reliable upload SHA256SUMS: SHA-256 of both .xz files and both decompressed .jsonl files Reassembly and verification Clone https://github.com/SupersonicMan12/g5-upper-bound, download all files from this record into its data folder, then run in that folder: cat certificates_K4p15.jsonl.xz.part* > certificates_K4p15.jsonl.xzxz -dk certificates_K4p5.jsonl.xz certificates_K4p15.jsonl.xzshasum -a 256 -c SHA256SUMScd ..python3 checker.py 9/2 data/logs_K4p5 data/certificates_K4p5.jsonlpython3 checker.py 2175795/524288 data/logs_K4p15 data/certificates_K4p15.jsonl Measured checker times on an Apple M4 with Python 3.11.9: 51 s (K = 9/2) and 32.5 min (K = 2175795/2¹⁹). Use of AI. The method (24-parameter LU normal form, linear relaxation, branch-and-bound with LP-duality certificates) and an initial proof draft were produced by an AI coding agent (Claude Opus 5.5 on Devin, Cognition AI), which also wrote the search and certificate-generation code. The author rewrote and checked the proof for the paper, and independently wrote checker.py, which re-verifies every certificate in exact arithmetic. The certificates in this record were produced by the AI-written generators and are trusted only because they pass checker.py.