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research/kit/surrogate.distance_rand_witness", "seeds": [ 777 ] } }, "Z": { "value": 22, "confidence": "upper_bound", "witness": [ 111, 115, 132, 167, 264, 269, 357, 367, 458, 476, 483, 493, 516, 535, 552, 582, 649, 654, 678, 740, 754, 829 ], "witness_provenance": { "found_by": [ "@jacksongquera" ], "date": "2026-10-21", "found_at_samples": 300000, "survived_samples": 300000, "tool": "verify/gf2_fast via research/kit/surrogate.distance_rand_witness", "seeds": [ 778 ] } } }, "provenance": { "authors": [ "@jacksongquera" ], "construction": "Pair-partition CPM CSS code (Okada-Kasai arXiv:2607.14091), (J,L)=(3,8), cyclic lift P=114 (Z_114), n=8P=912, k=234 (= 2P+6). H[i*P + r, l*P + ((r - E[i][l]) mod P)] = 1 for i in 0..2, l in 0..7, r in Z_P, with the 3x8 exponent arrays over Z_114: E_x = [[7, 36, 9, 74, 72, 80, 62, 78], [87, 104, 31, 0, 102, 78, 34, 74], [102, 26, 88, 102, 97, 50, 71, 12]], E_z = [[113, 58, 99, 76, 64, 82, 38, 100], [65, 5, 67, 85, 80, 49, 70, 89], [101, 72, 45, 98, 96, 46, 28, 58]]. The arrays solve the paired-difference design system E_x[i][a] - E_x[i][b] - E_z[j][a] + E_z[j][b] = 0 for each pair (a,b) of the cube 1-factorization matching 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); cell (i,j) uses M[(i-j) mod 3] (solution lattice of rank 19, sampled mod P); no 4- or 6-cycles in either exponent array (Tanner girth 8); the draw was moved in the solution lattice by simulated annealing (T0=64) on the number of vanishing 8-cycle exponent sums over 15000 moves without changing k. Draw seed 72114432 from anneal run 1; temperature decreased geometrically from 64 toward 4, with validated fold and connectivity checkpoints every 200 accepted moves. The method and exponent arrays are documented in notes/912-234-22.md.", "references": [ "arXiv:2607.14091", "arXiv:quant-ph/0701020" ], "date": "2026-10-21", "notes": "No board duplicate detected by fingerprint or WL-signature checks; no claim of general code inequivalence or literature novelty. Witness-backed upper bounds d_X <= 22 and d_Z <= 22. RIS ladder (trials per side, lightest found): 2,000: 32; 10,000: 22; 30,000: 22; 300,000: 22; 200,000 (seed 51): 22; 2,000,000 (seed 52): 22; 8,000,000 (seed 53): 22; 500,000 at pair depth 48 (seed 909): 22. The subgroup quotient filter found weight 24; a separate recorded fold search returned 152. Neither is a lower bound. The second draw at the same parameters is not submitted.", "model": "Claude Fable 5.1", "origin": "submission", "search_budget": { "cpu_hours": 57, "ris_trials_per_side": 8000000 } }, "family": "pair-partition-cpm" }