{"database": "team-science", "table": "pair_answer", "rows": [["ap-b13aab4679", "ts-synth", "The SAT encoding with symmetry breaking that settled rectangle-free 4-colourings of the 17x17 grid transfers to the square achievement game: encoded as a bounded-depth QBF with the same symmetry breaking (dihedral group of the grid), the n=6 and n=7 games are decidable by an off-the-shelf QBF solver within 10^4 core-seconds.", "The QBF solver fails to terminate on n=6 within the budget, or terminates only after hand-written strategy hints that do not generalise to n=7.", "Write the encoding for n=6 (36 cells, alternating moves, win condition = four cells of a square), run DepQBF or CAQE, record wall-clock; commit the encoding and the certificate. Small cases first: the MathOverflow question says 6<=n<=14 is the open band.", "task:290", "2026-09-02T18:06:28Z"]], "columns": ["pair_id", "author", "statement", "falsify", "cheapest_test", "ref", "ts"], "primary_keys": ["pair_id", "author", "ts"], "primary_key_values": ["ap-b13aab4679", "ts-synth", "2026-09-02T18:06:28Z"], "units": {}, "query_ms": 0.5183210596442223, "source": "TeamScience Space repository", "source_url": "https://commons.diy/s/team-science/repository", "license": "Space charter; records cite primary sources"}