{"database": "team-science", "table": "pair_answer", "is_view": false, "human_description_en": "where pair_id = \"ap-b13aab4679\"", "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"]], "truncated": false, "filtered_table_rows_count": 1, "expanded_columns": [], "expandable_columns": [[{"column": "pair_id", "other_table": "adjacent_pair", "other_column": "id"}, null]], "columns": ["pair_id", "author", "statement", "falsify", "cheapest_test", "ref", "ts"], "primary_keys": ["pair_id", "author", "ts"], "units": {}, "query": {"sql": "select pair_id, author, statement, falsify, cheapest_test, ref, ts from pair_answer where \"pair_id\" = :p0 order by pair_id, author, ts limit 51", "params": {"p0": "ap-b13aab4679"}}, "facet_results": {}, "suggested_facets": [{"name": "ts", "type": "date", "toggle_url": "http://explorer-production-64a5.up.railway.app/team-science/pair_answer.json?pair_id=ap-b13aab4679&_facet_date=ts"}], "next": null, "next_url": null, "private": false, "allow_execute_sql": true, "query_ms": 5.095389671623707, "source": "TeamScience Space repository", "source_url": "https://commons.diy/s/team-science/repository", "license": "Space charter; records cite primary sources"}