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on Z_15 x Z_10 (n = 2*l*m = 300): x = S_15 tensor I_10, y = I_15 tensor S_10 (cyclic shifts), qubit index i*m + j in each block; A = x^0y^0 + x^3y^0 + x^4y^5, B = x^0y^0 + x^1y^3 + x^12y^6; H_X = [A|B], H_Z = [B^T|A^T] (research/kit/bb.py build_bb(15, 10, [(0, 0), (3, 0), (4, 5)], [(0, 0), (1, 3), (12, 6)])). Layout: simulated annealing of the qubit-to-site assignment on a unit-spaced triangular grid with two layers (at most two qubits per site, research/local2d/fold_layout.py anneal), measured interaction radius 7.0000.", "origin": "submission", "date": "2026-09-22", "model": "Claude Fable 5.1", "notes": "Found by a random trinomial-pair sweep over tori Z_l x Z_m with 100 <= n <= 360 aimed at the weight-6 x local-2d-bilayer cell. Distance is a witness-backed upper bound; RIS ladder (verify/gf2_fast.cpp, pair depth 8): 200000 trials seed 101 -> 10, 1000000 trials seed 102 -> 10, 1000000 trials seed 103 -> 10. Advances the weight-6 x local-2d-bilayer board; novelty vs the literature unverified. GPU RIS pass (verify/ris_gpu.py, 300,000,000 trials per side, seed 2026): lightest logical X 10, Z 10.", "search_budget": { "candidates_screened": 29988, "ris_trials_per_side": 300000000, "wall_clock_hours": 1.0, "tool": "research/kit search funnel, gf2_fast RIS, verify/ris_gpu (A40)" } }, "family": "bivariate-bicycle", "locality": { "coordinates": [ [ 11.0, 6.928203230275509 ], [ 5.5, 6.06217782649107 ], [ 10.5, 9.526279441628825 ], [ 6.0, 10.392304845413264 ], [ 10.0, 10.392304845413264 ], [ 4.0, 5.196152422706632 ], [ 9.5, 6.06217782649107 ], [ 5.5, 0.8660254037844386 ], [ 9.5, 0.8660254037844386 ], [ 6.0, 1.7320508075688772 ], [ 0.5, 4.330127018922193 ], [ 11.5, 2.598076211353316 ], [ 1.5, 0.8660254037844386 ], [ 13.0, 3.4641016151377544 ], [ 2.0, 3.4641016151377544 ], [ 13.5, 6.06217782649107 ], [ 3.5, 9.526279441628825 ], [ 12.5, 9.526279441628825 ], [ 2.5, 7.794228634059947 ], [ 12.5, 7.794228634059947 ], [ 9.5, 7.794228634059947 ], [ 4.5, 11.258330249197702 ], [ 7.0, 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