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2027101105 ] } }, "Z": { "value": 18, "confidence": "upper_bound", "witness": [ 94, 139, 153, 167, 173, 181, 184, 195, 201, 212, 218, 240, 243, 246, 249, 252, 449, 479 ], "witness_provenance": { "found_by": [ "@MathysRennela" ], "date": "2026-10-10", "found_at_samples": 50000, "survived_samples": 16172640, "tool": "Clifford transform + gf2_fast RIS", "seeds": [ 20261011, 2026101102, 2027101105 ] } } }, "provenance": { "authors": [ "@DennisWayo" ], "construction": "One-qubit Clifford reduction of the board entry codes/512-18-18.json, whose open-boundary weight-8 planar tile construction, bilayer layout, and X/Z witnesses are credited to @MathysRennela. Use source X row 0 as S={0,3,34,48,258,275,288,307} and choose a=0. Clear a from the only other incident X generator by R_169 <- R_169 + S. Apply CNOT fan-out from control 0 to targets {3,34,48,258,275,288,307}; this maps S to X_0 and maps column 0 of H_Z to zero by CSS commutation. Delete X_0 and qubit 0, then renumber every surviving source qubit q>0 as q-1. This is a Clifford equivalence followed by removal of a disentangled qubit, so k remains 18. Surviving qubits keep their source coordinates; maximum check weight remains 8, interaction radius remains 4.242640687119285, and the layout remains bilayer.", "references": [ "arXiv:2504.09171", "arXiv:2504.08887", "arXiv:2410.11942" ], "date": "2026-10-11", "notes": "Derivative contribution, not an independent tile construction. The source [[512,18,d<=18]] code, layout, weight-20 X witness, and weight-18 Z witness are credited to @MathysRennela; this contribution is the explicit one-qubit stabilizer reduction to n=511. The current official verifier recomputes k=18, maximum check weight 8, bilayer locality, and interaction radius 4.242640687119285. Two independent CI-style fire passes used seeds 2026101102 and 2027101105. Each pass ran the structural detector, the 50000-trial orbit-fold gate, 86320 ordinary RIS trials, and 8000000 RIS-fast trials. Neither pass found a logical below weight 18; the lightest observed weight was 18 in every ordinary and fast pass. Total post-reduction RIS search: 16172640 trials. Distance remains a witness-backed upper bound, not an exact-distance claim.", "model": "GPT-5 (Codex)", "origin": "submission", "search_budget": { "cpu_hours": 0.6, "ris_trials_per_side": 16172640, "tool": "current CI-style orbit-fold and gf2_fast RIS", "candidates_screened": 10 }, "novelty": "new_parameters" }, "family": "tile", "locality": { "coordinates": [ [ 0.0, 1.0 ], [ 0.0, 2.0 ], [ 0.0, 3.0 ], [ 0.0, 4.0 ], [ 0.0, 5.0 ], [ 0.0, 6.0 ], [ 0.0, 7.0 ], [ 0.0, 8.0 ], [ 0.0, 9.0 ], [ 0.0, 10.0 ], [ 0.0, 11.0 ], [ 0.0, 12.0 ], [ 0.0, 13.0 ], [ 0.0, 14.0 ], [ 0.0, 15.0 ], [ 1.0, 0.0 ], [ 1.0, 1.0 ], [ 1.0, 2.0 ], [ 1.0, 3.0 ], [ 1.0, 4.0 ], [ 1.0, 5.0 ], [ 1.0, 6.0 ], [ 1.0, 7.0 ], [ 1.0, 8.0 ], [ 1.0, 9.0 ], [ 1.0, 10.0 ], [ 1.0, 11.0 ], [ 1.0, 12.0 ], [ 1.0, 13.0 ], [ 1.0, 14.0 ], [ 1.0, 15.0 ], [ 2.0, 0.0 ], [ 2.0, 1.0 ], [ 2.0, 2.0 ], [ 2.0, 3.0 ], [ 2.0, 4.0 ], [ 2.0, 5.0 ], [ 2.0, 6.0 ], [ 2.0, 7.0 ], [ 2.0, 8.0 ], [ 2.0, 9.0 ], [ 2.0, 10.0 ], [ 2.0, 11.0 ], [ 2.0, 12.0 ], [ 2.0, 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