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346, 425, 676, 745 ], [ 9, 126, 218, 281, 347, 426, 677, 746 ], [ 10, 127, 219, 282, 348, 427, 678, 747 ], [ 11, 128, 220, 283, 349, 428, 679, 748 ], [ 12, 129, 221, 284, 350, 429, 680, 749 ] ] }, "distance": { "d": 34, "X": { "value": 34, "confidence": "upper_bound", "witness": [ 22, 36, 47, 60, 66, 110, 128, 169, 177, 202, 236, 313, 315, 319, 349, 360, 361, 365, 372, 374, 387, 451, 477, 520, 578, 615, 653, 691, 711, 822, 857, 892, 901, 926 ], "witness_provenance": { "found_by": [ "@jacksongquera" ], "date": "2026-10-24", "found_at_samples": 1000001, "survived_samples": 7127445, "tool": "Stern ISD p=2, multithreaded C++ (uncommitted; see the note)", "seeds": [ 81102433 ] } }, "Z": { "value": 34, "confidence": "upper_bound", "witness": [ 19, 25, 26, 56, 68, 75, 91, 108, 151, 183, 193, 205, 208, 253, 261, 302, 324, 326, 329, 334, 337, 369, 485, 527, 587, 618, 736, 793, 801, 814, 872, 890, 893, 963 ], "witness_provenance": { "found_by": [ "@jacksongquera" ], "date": "2026-10-24", "found_at_samples": 1000001, "survived_samples": 7126916, "tool": "Stern ISD p=2, multithreaded C++ (uncommitted; see the note)", "seeds": [ 81102434 ] } } }, "provenance": { "authors": [ "@jacksongquera" ], "construction": "Irregular pair-partition CPM CSS code (the pair-partition commutation rule of Okada-Kasai, arXiv:2607.14091) on PR #4045's irregular 5x12 'pair-complement-2' base template, the same on X and Z: block columns per block row [[4,5,6,7,8,9,10,11],[2,3,6,7,8,9,10,11],[0,1,6,7,8,9,10,11],[0,1,2,3,4,5,10,11],[0,1,2,3,4,5,8,9]], design rate 1/6. A new pairing, found by large-neighbourhood search from PR #4045's pairing: its square complex (rows, columns, one square per pair) is non-positively curved (every block row's link is triangle-free), it leaves 6 free exponent directions and forces 6 block hexagons per side, the minimum found over about 500 4-cycle-free pairings of this template. Pairing (X-row,Z-row -> column pairs): {\"0,2\":[[6,8],[7,10],[9,11]],\"1,0\":[[6,8],[7,10],[9,11]],\"1,1\":[[2,3],[6,7],[8,9],[10,11]],\"1,2\":[[6,11],[7,9],[8,10]],\"1,3\":[[2,10],[3,11]],\"2,2\":[[0,1],[6,7],[8,9],[10,11]],\"2,4\":[[0,9],[1,8]],\"3,0\":[[4,10],[5,11]],\"3,2\":[[0,10],[1,11]],\"3,3\":[[0,1],[2,3],[4,5],[10,11]],\"3,4\":[[0,5],[1,2],[3,4]],\"4,0\":[[4,9],[5,8]],\"4,3\":[[0,3],[1,4],[2,5]],\"4,4\":[[0,1],[2,3],[4,5],[8,9]],\"0,0\":[[4,5],[6,7],[8,9],[10,11]],\"2,0\":[[6,11],[7,9],[8,10]],\"2,1\":[[6,8],[7,10],[9,11]],\"0,1\":[[6,11],[7,9],[8,10]],\"2,3\":[[0,10],[1,11]],\"4,1\":[[2,9],[3,8]],\"0,3\":[[4,10],[5,11]],\"4,2\":[[0,9],[1,8]],\"1,4\":[[2,9],[3,8]],\"3,1\":[[2,10],[3,11]],\"0,4\":[[4,9],[5,8]]}. Composite lift P = 81 = 3^4 with a rank-deficient cocycle class: exponents are an integer cocycle (a Z-basis of the integer solution lattice of the pair-partition equations) reduced mod 81, with the class mod 3 fixed so that H_X and H_Z both lose rank on the Phi_3 component of F_2[x]/(x^81 - 1); this adds 4 logical qubits, k = 2P + 4 = 166 at n = 972. Exploratory quotient searches reported logical weights 6 for Z_9 and 14 for Z_27, with checked periodic lifts of weights 54 and 42. These are reported heuristic upper bounds, not exact quotient distances. Exponents drawn with no block 4-cycle (also none closing after 3 turns) and only the 6 forced block hexagons per side. H[i*P + r, c*P + ((r + s_ic) mod P)] = 1. Lift G = Z_81; block exponents: S_X = [[-, -, -, -, 49, 3, 4, 9, 11, 43, 51, 51], [-, -, 61, 49, -, -, 53, 10, 40, 22, 11, 9], [49, 51, -, -, -, -, 26, 43, 35, 57, 54, 32], [52, 65, 76, 55, 40, 64, -, -, -, -, 39, 28], [41, 77, 12, 75, 67, 65, -, -, 10, 79, -, -]], S_Z = [[-, -, -, -, 1, 36, 75, 80, 62, 13, 0, 0], [-, -, 31, 19, -, -, 26, 64, 35, 17, 75, 73], [21, 23, -, -, -, -, 30, 47, 37, 59, 8, 67], [48, 61, 22, 1, 51, 75, -, -, -, -, 53, 42], [13, 49, 60, 42, 27, 25, -, -, 33, 21, -, -]].", "references": [ "arXiv:2607.14091", "arXiv:2609.30069", "https://github.com/unitaryfoundation/qldpc-challenge/pull/4045" ], "date": "2026-10-24", "notes": "Distance is a witness-backed upper bound: d_X <= 34 and d_Z <= 34. Full-length Stern ISD (p = 2 per half) found no pure-X or pure-Z logical of weight <= 32 in 7,127,445 X and 7,126,916 Z iterations across three runs. Pure-X and pure-Z logicals have even weight. The independent round-1 X minimum was 36; its previously known upper bound stayed 34. Four draws were screened with a budget of up to 1,000,001 iterations per side; two stopped on weight-14 X logicals after two iterations, before Z. No cross-run distinct-witness total is claimed. The trusted gate found no exact fingerprint or WL-signature match on the checked board; literature novelty is unverified. See notes/972-166-34.md.", "model": "Claude Opus 5.5 (Claude Code)", "origin": "submission", "novelty": "unknown", "search_budget": { "cpu_hours": 40, "candidates_screened": 4, "tool": "Stern ISD, p = 2 per half, l = 16, 16 pivot swaps per iteration", "notes": "CPU-hours are an approximate session total; about 9 were spent on this candidate's screen and deep rounds. candidates_screened counts the four filtered draws of the selected P = 81 class, not the whole session. Full-length Stern iterations: X = 7,127,445; Z = 7,126,916. These are not RIS trials. Screen iterations X/Z = 1,000,001/1,000,001; round 1 = 3,048,292/3,066,137; round 2 = 3,079,152/3,060,778. The trusted gate is a separate validation search." } }, "family": "pair-partition-cpm" }