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518, 548, 559, 571 ] }, "Z": { "value": 24, "confidence": "upper_bound", "witness": [ 39, 48, 86, 115, 170, 182, 201, 239, 243, 310, 322, 323, 351, 406, 417, 429, 472, 481, 517, 572, 590, 612, 634, 647 ] } }, "provenance": { "authors": [ "@MathysRennela" ], "construction": "Quadricycle code (rank-4 generalized bicycle on the abelian torus G = Z_7 x Z_4 x Z_4 x Z_3): H_X = [A | B], H_Z = [B^T | A^T] with A = x1 x2 x3 x4 + x1^4 and B = x1^3 x2^2 x3 + x1^6 x4, monomials of the four independent cyclic shifts over F_2; check weight 4. Found by uniform random sampling of weight-2+2 monomial sets (1,200 candidates, dims in [2,11] with prod <= 350) screened with a staged RIS funnel (300 -> 3,000 -> 20,000 trials, gf2_fast) and confirmed with a 1M-sample adversarial ladder. Generalizes the bivariate bicycles (arXiv:2308.07915) and the trivariate codes (arXiv:2406.19151) to four independent shifts.", "origin": "submission", "date": "2026-09-20", "model": "GLM 5.3 Flash (Zed agent)", "notes": "Checked against the current board by the validation gate: verifies, not refuted, and no exact or WL-equivalent duplicate of any existing entry; not known to be equivalent to any existing entry under a code symmetry.", "search_budget": { "candidates_screened": 1800, "wall_clock_hours": 0.9 } }, "family": "generalized-bicycle" }