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746 ], [ 48, 101, 271, 357, 475, 495, 588, 747 ], [ 49, 102, 272, 358, 476, 496, 589, 748 ], [ 50, 103, 273, 359, 477, 497, 590, 749 ] ] }, "distance": { "d": 20, "X": { "value": 20, "confidence": "upper_bound", "witness": [ 51, 70, 128, 147, 184, 196, 264, 309, 315, 368, 440, 478, 506, 544, 578, 643, 650, 696, 740, 774 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-23", "found_at_samples": 1000000, "seeds": [ 61000005600 ], "tool": "GPU deep kernel (full basis, pair depth 8), screen stage 3", "survived_samples": 59000000 } }, "Z": { "value": 20, "confidence": "upper_bound", "witness": [ 106, 119, 141, 205, 283, 290, 300, 384, 394, 430, 500, 519, 566, 569, 657, 659, 669, 699, 737, 753 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-23", "found_at_samples": 1000000, "seeds": [ 61000005601 ], "tool": "GPU deep kernel (full basis, pair depth 8), screen stage 3", "survived_samples": 59000000 } } }, "family": "pair-partition-cpm", "provenance": { "authors": [ "@vprusso" ], "origin": "submission", "novelty": "new_parameters", "model": "Claude Fable 5.1 (Claude Code)", "construction": "Pair-partition CPM CSS code (Okada-Kasai arXiv:2607.14091), (J,L)=(3,8), prime lift P=97, n=8P=776, k=2P+4=198. H[i*P + r, j*P + ((r - E[i][j]) mod P)] = 1 with 3x8 exponent arrays over Z_97: E_x = [[29, 20, 44, 46, 25, 49, 53, 9], [91, 93, 62, 65, 12, 87, 93, 63], [88, 45, 40, 58, 49, 17, 14, 78]], E_z = [[68, 51, 20, 20, 64, 23, 29, 40], [71, 91, 86, 1, 89, 23, 20, 61], [46, 90, 17, 28, 7, 84, 88, 26]]. The arrays solve the joint design system E_x[i][j] - E_x[i][j'] - E_z[i'][j] + E_z[i'][j'] = 0 for each column pair of the matching M[(i-i') mod 3], M0=(0,4)(1,7)(2,6)(3,5), M1=(0,7)(1,2)(3,4)(5,6), M2=(0,2)(1,5)(3,7)(4,6); girth 8 (no 4- or 6-cycles in either exponent array). Same construction and design system as the board's [[808,206,20]] (P = 101), [[664,170,18]] (P = 83), [[632,162,18]] (P = 79), and [[584,150,18]] (P = 73).", "references": [ "arXiv:2607.14091", "arXiv:2111.03654" ], "date": "2026-09-23", "notes": "Found by a GPU random-information-set screen (deep kernel: full-basis RREF plus pair sums) over pair-partition CPM (3,8) codes at prime lifts P in {89, 97, 101, 103, 107, 109, 113} at n in [702, 1000]; see the research note for the ladder. Lightest logicals: X 20, Z 20; deep-kernel GPU passes (full basis, pair depth 8): X 20 at 50,000,000 trials (seed 777); Z 20 at 50,000,000 trials (seed 778); board fast pass 20 at 8,000,000 trials. Every operator re-verified with verify/gf2.py. Distance is a witness-backed upper bound. Novelty: no isomorphic code found by a nauty canonical-form check against the board and the 2BGA, GB, BB, QECDB, and codetables data (submitter claim). Generator spec: {\"family\": \"cpm38\", \"P\": 97, \"E\": [[29, 20, 44, 46, 25, 49, 53, 9], [91, 93, 62, 65, 12, 87, 93, 63], [88, 45, 40, 58, 49, 17, 14, 78]], \"D\": [[68, 51, 20, 20, 64, 23, 29, 40], [71, 91, 86, 1, 89, 23, 20, 61], [46, 90, 17, 28, 7, 84, 88, 26]]}" } }