Filled-end two-band L packings of unit squares in a square: 4571 certified upper bounds, n = 1184–9946

Certified upper bounds s(n) ≤ S for packing n unit squares in a square, 1184 ≤ n ≤ 9946, from a filled-end two-band L packing with independent bands. Construction. An aligned grid and two tilted bands (Sungjoon Ryu's L-shaped packing, doi:10.5281/zenodo.23278927, Theorem 1.3). The ends of each band are filled with axis-parallel layers, an idea due to Evan Daniel (evand/square-packing, certificates/k2-minus-c/, 18 October 2026); the band and the fill follow Kevin Fang's note (doi:10.5281/zenodo.23624565, Sections 2–3). New here: independent width, tilt and lift split for each of the two bands, and a search over these parameters for each n. Rows. 4571 rows. 4261 of them improve the author's earlier records (doi:10.5281/zenodo.23664800, v5). The other 310 are values of n not in v5 whose side is below the entry of Mishapolk/square-packing-records at commit ab8e833. Not compared with Couzo's index or other registers. Verification. Every certificate is rebuilt in exact rational arithmetic from its row by regenerate_filled.py and is accepted by verify_bound_certificate.py of Mishapolk/square-packing-records (ab8e833): closed container, disjoint interiors. Files. filled_records.csv (n, K, exact side, previous best side and source, exact parameters), filled_ends.py (exact construction), regenerate_filled.py, check_cert.py (independent exact checker), README_filled.md. SHA-256 of filled_records.csv: f047c44b7d627d7d5e2e990136931a6d8cf4c19ded439482ab1ef9f8bd030b56 Code and computations were done with the assistance of Claude (Anthropic) under the author's direction; the search was run in MATLAB Online and reproduced in Python.