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"found_at_samples": 10000000, "tool": "accelerated RIS (research/kit distance_rand_witness), 10M trials per side", "seeds": [ 41 ] } } }, "provenance": { "authors": [ "@vprusso", "@MathysRennela" ], "origin": "baseline", "novelty": "known_parameters", "model": [ "Space Bunny Alpha 1.0", "Claude Fable 5.1 (Claude Code)" ], "construction": "Canonical lifted-product code LP_36^(2x3) of Zheng, Zheng, Jiang and Xu (arXiv:2607.28605, appendix example of canonical matrices): R = F_2[x]/(x^36 + 1), A = (A' | q_1) in R^(2x3) with A' = [[1, 1 + x^11 + x^29], [1, 0]] and q_1 = [1; x^8 + x^13 + x^16 + x^17], B = A^* (transpose with x -> x^-1). H_X = B(A (x) I_3, I_2 (x) B) and H_Z^T = B(I_3 (x) B ; A (x) I_2) with B(.) the 36 x 36 circulant binarization (their Eq. 5), so n = (3*3 + 2*2)*36 = 468; both binarized check matrices are 216 x 468 of full rank, so k = 468 - 216 - 216 = 36. Qubit order: left block (3 x 3 tiles of 36, tile index (j, t) row-major, position within tile last) then right block (2 x 2 tiles). The map (j, t, s) -> (t, j, s) on the left tiles and (p, q, s) -> (q, p, s) on the right tiles carries H_X onto H_Z, so d_X = d_Z and the Z witness is the image of the X witness.", "references": [ "arXiv:2607.28605" ], "date": "2026-10-07", "notes": "Literature reconstruction for the board-filling campaign of issue #2863 (item L4). Joint build: @vprusso reconstructed LP_36^(2x3) and ran the deep distance pass (both witnesses, 10M trials per side, plus the tile-swap automorphism giving d_X = d_Z and the nauty canonical-form sweep against the board and the literature data); @MathysRennela rebuilt the instance independently from the paper's Eq. (1), screened the LP instance family beyond the two in-range instances, ran the board-advancement screening and the gate, and filed this entry. The paper states d = 20 exact (via the complete low-weight search of arXiv:2607.14091). Readings here: 500,000 accelerated RIS trials 20; 10,000,000 trials (seed 41, pair depth 32) 20, an X logical. Witnessed upper bound, not certified. Check weight 10 (rows of weight 7 to 10). On the four-axis dominance rule nothing on the board dominates this entry; [[952,112,17]] from the same appendix is dominated by 18 entries and is not filed." }, "family": "lifted-product" }