{"license": "CC BY 4.0", "license_url": "https://creativecommons.org/licenses/by/4.0/", "word": {"id": "W-0099", "n": 9, "length": 408719, "sha256": "b00e0e9b64c5d4dd2cc9233b082b046e37eabcb18902c066ae48648fe0629728", "is_record": true, "tie": false, "letters_saved": 12, "repeated_occurrences": 371, "credited": [{"name": "Jay Pantone", "github_username": "jaypantone"}], "date": "2026-11-10T20:25:05Z", "date_precision": "day", "received_at": "2026-11-10T20:25:05Z", "source": "site", "source_url": null, "note": "Every n = 9 word of the 43/80 construction uses the same 52 closed trails, and an exact computation shows that no way of cutting and joining those trails beats 408,731. This word uses new trails. It starts from a selection on 8 symbols that is invariant under a group of order 9 (Q = 360, 15 walks). Four square flips using rows of charge 5 join walks: each adds 7 to Q but reduces the number of walks and trails by more. I applied the flips in random order among the improving ones, built a word from each resulting selection, and kept the shortest. Jakub Halfar's geng.py completed it into closed trails (Q = 388, 11 walks, 58 trails), and his trailsearch cut and joined them into this word.", "url": "https://superpermutations.com/w/W-0099", "permutation_windows": 363251, "check_elapsed_seconds": 0.35175, "deletable_letters": null, "begins": "012345678012345670812345670182345670128345670123845670123485670123458670123456870123456078123456071823456071283456071238", "checkers": {"classcheck": {"source_sha256": "fe9c2f7fd612f3311543038c96bfda84d9d81d84229417d35bb44102da78848f", "seconds": 0.004414224065840244}, "bitmapcheck": {"source_sha256": "98e62368f912a3a0735910b924314104681dc2ea55f283c32eb66d52748bf1f0", "seconds": 0.01306422334164381}, "wordhash": {"source_sha256": "cb47f567daa6634a3ebeb81f2d9eb7fb5c19659441fbb973bf29a36a784a1c95", "seconds": 0.005440502427518368}, "compiler": "rustc 1.89.0 (29483883e 2025-08-04)"}, "file": {"name": "W-0099.detour", "compression": "detour", "size": 676, "encoded_sha256": "1233b77b28a9a20747611b521839752996923e084d3badd798efba3c417a2b71", "metadata": {"schema_version": 1, "format": "detour", "encoded_sha256": "1233b77b28a9a20747611b521839752996923e084d3badd798efba3c417a2b71", "encoded_size": 676, "word_length": 408719, "word_sha256": "b00e0e9b64c5d4dd2cc9233b082b046e37eabcb18902c066ae48648fe0629728", "detour": {"version": 1, "n": 9, "alphabet": "012345678", "length": 408719, "sha256": "b00e0e9b64c5d4dd2cc9233b082b046e37eabcb18902c066ae48648fe0629728", "tokens": 1720, "starts": 1, "literal_bytes": 0, "steps_by_weight": [322931, 35248, 5024, 31, 9, 7, 0, 0, 0], "detours_by_weight": [0, 0, 1699, 4, 8, 8, 0, 0, 0]}}, "text_download": "https://superpermutations.com/w/W-0099/download/text", "download": "https://superpermutations.com/w/W-0099/download"}}}