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649, 680, 681 ] ] }, "code_type": "CSS", "distance": { "X": { "confidence": "upper_bound", "value": 80, "witness": [ 1, 15, 16, 18, 22, 23, 24, 31, 33, 37, 40, 41, 42, 46, 50, 52, 54, 68, 71, 75, 77, 78, 103, 108, 114, 118, 128, 129, 133, 134, 142, 143, 145, 147, 149, 150, 160, 161, 162, 164, 171, 178, 184, 192, 193, 196, 207, 215, 217, 224, 226, 228, 242, 247, 252, 253, 254, 255, 257, 261, 264, 270, 271, 273, 274, 280, 281, 284, 285, 286, 288, 294, 302, 308, 309, 317, 319, 325, 334, 339 ], "witness_provenance": { "date": "2026-09-21", "found_at_samples": 400000, "found_by": [ "@DennisWayo" ], "seeds": [ 71077108993585715, 9218007 ], "survived_samples": 8000000, "tool": "gf2_fast circulant-GB structural gate" } }, "Z": { "value": 79, "confidence": "upper_bound", "witness": [ 9, 12, 17, 25, 26, 28, 37, 41, 42, 65, 66, 67, 69, 72, 81, 83, 84, 96, 97, 100, 113, 114, 117, 119, 122, 123, 125, 131, 136, 138, 147, 151, 152, 162, 168, 176, 179, 181, 186, 190, 193, 195, 196, 212, 213, 215, 217, 224, 226, 227, 230, 234, 236, 237, 239, 240, 241, 244, 250, 251, 253, 255, 259, 263, 267, 285, 293, 307, 310, 357, 426, 449, 482, 506, 508, 600, 629, 642, 652 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-24", "found_at_samples": 300000000, "survived_samples": 300000000, "tool": "verify/ris_gpu.py recover mode, pair depth 0 (GPU RIS, CPU re-verified)", "seeds": [ 4102 ] } }, "d": 79 }, "family": "generalized-bicycle", "k": 142, "n": 682, "name": "[[682,142,79]] Z_341 cyclic-ideal generalized-bicycle code", "provenance": { "authors": [ "@DennisWayo" ], "construction": "Cyclic generalized-bicycle code over Z_341; a=[0, 1, 32, 45, 71, 76, 132, 176, 226, 231, 275, 286]; b=[25, 33, 44, 58, 69, 128, 168, 179, 252, 267, 281, 292]; H_X=[circ(a)|circ(b)], H_Z=[circ(b)^T|circ(a)^T].", "date": "2026-09-21", "model": "OpenAI GPT-5 (Codex)", "notes": "Recovered from a collapsed-candidate bank and retained by a live-board Pareto filter on (n,k,d,max check weight). A 400000-trial circulant-GB structural search found the submitted X witness; the Z witness is its independently verified GB block-swap/index-reversal image. A final local CI-style pass at d<=80 completed another 400000 structural trials, the Python RIS pass, and 8000000 RIS-fast trials without finding a logical lighter than 80. Base-board validation reports no exact or WL duplicate. The current codes/682-142-82.json entry has d<=82 and maximum check weight 32; this distinct representation trades two distance points for a reduction to check weight 24 and remains Pareto non-dominated. This is an upper-bound claim, not an exact-distance certificate.", "novelty": "unknown", "origin": "submission", "references": [] }, "schema_version": "0.2" }