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184, 199, 202, 206, 215, 230, 233, 237, 246, 261, 264, 268, 277, 292, 295, 299, 308, 323, 326, 330, 339, 342, 346, 349, 373, 377, 380, 404, 408, 411, 435, 439, 442, 466, 470, 473, 497, 501, 504, 528, 532, 535, 559, 563, 566, 590, 594, 597, 621, 625, 628, 652, 656, 659 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-26", "found_at_samples": 1, "survived_samples": 1, "tool": "norm-word lift of a Z_31 quotient logical (exact algebra)", "seeds": [ 0 ] } }, "d": 76 }, "family": "generalized-bicycle", "k": 172, "n": 682, "name": "[[682,172,d<=76]] Z_341 cyclic-ideal generalized-bicycle code", "provenance": { "authors": [ "@DennisWayo" ], "construction": "Cyclic generalized-bicycle code over Z_341; divisor ideal degree 86 from x^341+1 over GF(2); a=[0, 1, 4, 11, 32, 44, 88, 128, 143, 146, 159, 239, 275, 314]; b=[5, 12, 97, 98, 105, 108, 119, 129, 185, 218, 222, 242, 251, 304]; H_X=[circ(a)|circ(b)], H_Z=[circ(b)^T|circ(a)^T].", "date": "2026-09-21", "model": "OpenAI GPT-5 (Codex)", "notes": "Cyclic-ideal generalized-bicycle candidate with an honest witness-backed upper bound. Heavier staging claims collapsed from d<=89 to 79, then 77, and finally to the submitted weight-76 X witness under the trusted circulant-GB structural gate. A final local CI-style pass at d<=76 ran 400000 structural trials, the Python RIS pass, and 8000000 RIS-fast trials without finding a logical lighter than 76. This entry has a distinct exact fingerprint but the same verifier WL signature as codes/682-172-79.json, so possible equivalence is disclosed rather than excluded. Its maximum check weight is 28 instead of 32, which advances the unrestricted weight-9plus frontier on the check-weight axis. This is not an exact-distance claim. The sibling entry cited above as codes/682-172-79.json has since been refiled as codes/682-172-72.json on github.com/unitaryfoundation/qldpc-challenge.", "novelty": "unknown", "origin": "submission", "references": [] }, "schema_version": "0.2" }