Filled-end two-band L packings of unit squares in a square: 5134 certified upper bounds, n = 1182–9946

Certified upper bounds s(n) ≤ S for packing n unit squares in a square, 1182 ≤ 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. 5134 rows. Every row is strictly below the entry of franciscouzo/square-packing at commit 712c6a6 (certified_bounds.json) and the entry of Mishapolk/square-packing-records at commit ab8e833, where an entry exists. 4841 rows improve the author's earlier records (doi:10.5281/zenodo.23664800, v5); the other 293 are values of n not in v5. Together with v5, the author holds the best known certified side for 5601 distinct n in 1182–9946 relative to these two indices. Changes from V1.0. A finer search (containers K = 35–100, finer tilt grid, 20 lift splits) lowered or added 4536 sides. Each row is now compared with both indices. 40 rows of V1.0 that are not below Couzo's index are removed (listed in README_filled.md); 603 values of n are new. 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. 5134 accepted, 0 rejected. 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: 1cbfecf886a2000bd9d5f54304813d7422f785a2fb9a15655f2119a33f8c48f5 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.