Two-strip square packings: improved upper bounds for s(n), n = 1182–9944

Two-strip square packings: 5308 improved upper bounds for s(n), n = 1182–9944, K = 35–100, with exact certificates, plus the full search and verification code. Author: Mohsen Karimi (Independent researcher, Zanjan, Iran), ORCID 0009-0004-1055-8267. The construction was found by the author independently of S. Ryu's L-shaped packing (doi:10.5281/zenodo.23278927, Theorem 1.3), of which it is an instance with independent widths, angles and phases for the two bands. Code and computations were done with the assistance of Claude (Anthropic) under the author's direction; part of the search was run by the author in MATLAB Online. Each packing improves the best side listed for its n in the catalogues Mishapolk/square-packing-records (commit 7e82c64) and franciscouzo/square-packing (commit 1c17153), compared with their verified entries. Improvements range from 0.00016 to 0.204. For 51 of the 5308 values, a side derived from a Kaggle leaderboard value without coordinates is smaller; these rows are marked in records.csv (column below_all_reported). Version 3 of the data (this version, v5 of the record): the search was extended from sides in [K − 0.1, K) to [K − 0.5, K). This adds 2484 new values of n and lowers the side of 1434 of the 2824 records of the previous data version. Files: 1) karimi_two_strip_records_v3_lite.zip — records.csv (one row per n: new side exact and decimal, previous best side, construction parameters K, mH, tH, phH, mV, tV, phV, below_all_reported) and regenerate.py, which rebuilds all 5308 certificates exactly (Python standard library only). 2) karimi_two_strip_code_v1_lite.zip — search and verification code (Python and MATLAB) with an unchanged copy of the exact rational verifier verify_bound_certificate.py (MIT, E. Daniel, modifications by F. Couzo). To rebuild certificates with it, copy records.csv from file 1 into its python folder. 3) karimi_near_integer_v2.pdf — the earlier theorem note, version 2 (also deposited separately, https://doi.org/10.5281/zenodo.23627827); it predates the comparison with Ryu's work, which the paper now cites, and its conjecture on the optimality of the order sqrt(K) is withdrawn. Every certificate was checked with the exact verifier (closed container, disjoint interiors, exact rational arithmetic); all 5308 were accepted. License: data CC BY 4.0; code MIT.