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347, 471, 510, 598 ], [ 19, 97, 101, 310, 349, 466, 509, 604 ], [ 20, 98, 102, 311, 351, 461, 508, 591 ], [ 21, 99, 103, 312, 353, 456, 507, 597 ], [ 22, 100, 104, 313, 355, 470, 506, 603 ], [ 23, 101, 105, 314, 357, 465, 505, 590 ], [ 24, 102, 106, 315, 359, 460, 504, 596 ], [ 25, 103, 107, 316, 342, 474, 503, 602 ], [ 26, 104, 108, 317, 344, 469, 502, 589 ], [ 27, 105, 109, 318, 346, 464, 501, 595 ] ] }, "distance": { "d": 40, "X": { "value": 40, "confidence": "upper_bound", "witness": [ 73, 84, 164, 174, 207, 209, 317, 331, 344, 350, 367, 379, 388, 399, 405, 417, 426, 437, 443, 455, 464, 475, 481, 493, 502, 513, 519, 531, 540, 569, 585, 589, 595, 607, 616, 627, 645, 665, 671, 683 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-23", "found_at_samples": 80000000, "survived_samples": 80000000, "seeds": [ 3505 ], "tool": "verify/ris_gpu.cu deep kernel, pair depth 8, CPU re-verified (gf2)" } }, "Z": { "value": 48, "confidence": "upper_bound", "witness": [ 21, 26, 73, 128, 206, 235, 259, 294, 325, 338, 343, 344, 346, 357, 363, 366, 380, 384, 401, 408, 430, 431, 435, 455, 467, 468, 478, 491, 493, 501, 505, 529, 539, 542, 556, 559, 565, 580, 589, 611, 619, 621, 627, 628, 659, 661, 666, 670 ], "witness_provenance": { "found_by": [ "@e-eight" ], "date": "2026-09-18", "found_at_samples": 8000000, "tool": "verify/gf2_fast distance_rand_witness", "seeds": [ 71 ] } } }, "provenance": { "authors": [ "@EthanFeld" ], "origin": "submission", "novelty": "unknown", "construction": "two-block-group-algebra CSS construction over semidirect(19,18,2); with A=[[25,136,177,278]]; and B=[[35,233,240,309]]; generated by the non-cyclic Stage 1 search.", "references": [], "model": "GPT-5.6 Luna", "date": "2026-09-11", "notes": "Witness-backed upper bound only. Native validation ran 20,000,000 X trials and 20,000,000 Z trials; observed X=74, Z=72. REVISED 2026-09-18: Relation to existing entries: this is a distance revision of the board's own [[684,20,72]] entry, which it supersedes -- same code, same checks, same provenance and authorship, corrected distance only. A deep fresh-seed RIS ladder (bit-packed verify/gf2_fast, both Pauli sides searched jointly) exhibits a weight-48 Z-logical, so the previous witness-backed bound d <= 72 was overstated by 24 and the honest parameter set is [[684,20,48]], kd^2/n = 67.37 (previously 151.58). The weight-48 Z-side witness is carried in this entry. The X side is unchanged at 74: it is not refuted, and d is the minimum over the two sides. The earlier bound came from a different RIS implementation (`cpp_fast.css_ris_parallel`, 20,000 trials per side); the repository's own accelerator reaches the lighter logical at 8,000,000 trials, so the gap is a search-depth difference rather than a disagreement about the code. Distance remains a witness-backed upper bound, not an exact claim. No other board entry carries this (n, k, d, w); the change strictly tightens the entry and removes no other frontier point. Tightened 2026-09-23 by @vprusso: a GPU random-information-set audit (verify/ris_gpu.cu deep kernel: full kernel basis plus pair sums, pair depth 8, recover mode; 80,000,000 X and 80,000,000 Z trials in chunks with fresh seeds 3500 to 3507) exhibits a weight-40 X-type logical, so d <= 40 (X 74 -> 40). Per chunk: X 86 at 1,000,000 trials (seed 3500); Z 84 at 1,000,000 trials (seed 3501); X 44 at 29,126,225 trials (seed 3502); Z 72 at 29,065,548 trials (seed 3503); Z 76 at 30,378,639 trials (seed 3504); X 40 at 30,348,767 trials (seed 3505); Z 76 at 19,555,813 trials (seed 3506); X 42 at 19,525,008 trials (seed 3507). Every GPU operator was re-verified on the CPU with verify/gf2.py. Distance remains a witness-backed upper bound." }, "family": "other" }