{ "schema_version": "0.4", "name": "Cyclic XYZ binary-cube code (L=11)", "code_type": "stabilizer", "n": 88, "k": 36, "family": "other", "checks": { "S": [ { "X": [ 0, 11, 22, 33, 44, 55, 66, 77 ], "Z": [] }, { "X": [ 1, 12, 23, 34, 45, 56, 67, 78 ], "Z": [] }, { "X": [ 2, 13, 24, 35, 46, 57, 68, 79 ], "Z": [] }, { "X": [ 3, 14, 25, 36, 47, 58, 69, 80 ], "Z": [] }, { "X": [ 4, 15, 26, 37, 48, 59, 70, 81 ], "Z": [] }, { "X": [ 5, 16, 27, 38, 49, 60, 71, 82 ], "Z": [] }, { "X": [ 6, 17, 28, 39, 50, 61, 72, 83 ], "Z": [] }, { "X": [ 7, 18, 29, 40, 51, 62, 73, 84 ], "Z": [] }, { "X": [ 8, 19, 30, 41, 52, 63, 74, 85 ], "Z": [] }, { "X": [ 9, 20, 31, 42, 53, 64, 75, 86 ], "Z": [] }, { "X": [ 10, 21, 32, 43, 54, 65, 76, 87 ], "Z": [] }, { "X": [ 0, 14, 24, 38, 45, 59, 69, 83 ], "Z": [] }, { "X": [ 1, 15, 25, 39, 46, 60, 70, 84 ], "Z": [] }, { "X": [ 2, 16, 26, 40, 47, 61, 71, 85 ], "Z": [] }, { "X": [ 3, 17, 27, 41, 48, 62, 72, 86 ], "Z": [] }, { "X": [ 4, 18, 28, 42, 49, 63, 73, 87 ], "Z": [] }, { "X": [ 5, 19, 29, 43, 50, 64, 74, 77 ], "Z": [] }, { "X": [ 6, 20, 30, 33, 51, 65, 75, 78 ], "Z": [] }, { "X": [ 7, 21, 31, 34, 52, 55, 76, 79 ], "Z": [] }, { "X": [ 8, 11, 32, 35, 53, 56, 66, 80 ], "Z": [] }, { "X": [ 9, 12, 22, 36, 54, 57, 67, 81 ], "Z": [] }, { "X": [ 10, 13, 23, 37, 44, 58, 68, 82 ], "Z": [] }, { "X": [], "Z": [ 0, 11, 22, 33, 45, 56, 67, 78 ] }, { "X": [], "Z": [ 1, 12, 23, 34, 46, 57, 68, 79 ] }, { "X": [], "Z": [ 2, 13, 24, 35, 47, 58, 69, 80 ] }, { "X": [], "Z": [ 3, 14, 25, 36, 48, 59, 70, 81 ] }, { "X": [], "Z": [ 4, 15, 26, 37, 49, 60, 71, 82 ] }, { "X": [], "Z": [ 5, 16, 27, 38, 50, 61, 72, 83 ] }, { "X": [], "Z": [ 6, 17, 28, 39, 51, 62, 73, 84 ] }, { "X": [], "Z": [ 7, 18, 29, 40, 52, 63, 74, 85 ] }, { "X": [], "Z": [ 8, 19, 30, 41, 53, 64, 75, 86 ] }, { "X": [], "Z": [ 9, 20, 31, 42, 54, 65, 76, 87 ] }, { "X": [], "Z": [ 10, 21, 32, 43, 44, 55, 66, 77 ] }, { "X": [], "Z": [ 0, 14, 24, 38, 44, 58, 68, 82 ] }, { "X": [], "Z": [ 1, 15, 25, 39, 45, 59, 69, 83 ] }, { "X": [], "Z": [ 2, 16, 26, 40, 46, 60, 70, 84 ] }, { "X": [], "Z": [ 3, 17, 27, 41, 47, 61, 71, 85 ] }, { "X": [], "Z": [ 4, 18, 28, 42, 48, 62, 72, 86 ] }, { "X": [], "Z": [ 5, 19, 29, 43, 49, 63, 73, 87 ] }, { "X": [], "Z": [ 6, 20, 30, 33, 50, 64, 74, 77 ] }, { "X": [], "Z": [ 7, 21, 31, 34, 51, 65, 75, 78 ] }, { "X": [], "Z": [ 8, 11, 32, 35, 52, 55, 76, 79 ] }, { "X": [], "Z": [ 9, 12, 22, 36, 53, 56, 66, 80 ] }, { "X": [], "Z": [ 10, 13, 23, 37, 54, 57, 67, 81 ] }, { "X": [ 0, 11, 24, 35, 44, 55, 68, 79 ], "Z": [ 0, 11, 24, 35, 44, 55, 68, 79 ] }, { "X": [ 1, 12, 25, 36, 45, 56, 69, 80 ], "Z": [ 1, 12, 25, 36, 45, 56, 69, 80 ] }, { "X": [ 2, 13, 26, 37, 46, 57, 70, 81 ], "Z": [ 2, 13, 26, 37, 46, 57, 70, 81 ] }, { "X": [ 3, 14, 27, 38, 47, 58, 71, 82 ], "Z": [ 3, 14, 27, 38, 47, 58, 71, 82 ] }, { "X": [ 4, 15, 28, 39, 48, 59, 72, 83 ], "Z": [ 4, 15, 28, 39, 48, 59, 72, 83 ] }, { "X": [ 5, 16, 29, 40, 49, 60, 73, 84 ], "Z": [ 5, 16, 29, 40, 49, 60, 73, 84 ] }, { "X": [ 6, 17, 30, 41, 50, 61, 74, 85 ], "Z": [ 6, 17, 30, 41, 50, 61, 74, 85 ] }, { "X": [ 7, 18, 31, 42, 51, 62, 75, 86 ], "Z": [ 7, 18, 31, 42, 51, 62, 75, 86 ] }, { "X": [ 8, 19, 32, 43, 52, 63, 76, 87 ], "Z": [ 8, 19, 32, 43, 52, 63, 76, 87 ] }, { "X": [ 9, 20, 22, 33, 53, 64, 66, 77 ], "Z": [ 9, 20, 22, 33, 53, 64, 66, 77 ] }, { "X": [ 10, 21, 23, 34, 54, 65, 67, 78 ], "Z": [ 10, 21, 23, 34, 54, 65, 67, 78 ] } ] }, "distance": { "d": 4, "P": { "value": 4, "confidence": "upper_bound", "witness": { "X": [], "Z": [ 22, 33, 54, 65 ] } } }, "provenance": { "model": "GPT-6 Astra", "authors": [ "@hirobumii" ], "date": "2026-10-17", "construction": "{\"column_labels\": [[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 1, 1], [1, 0, 0], [1, 0, 1], [1, 1, 0], [1, 1, 1]], \"construction\": \"degree-five monochromatic XYZ binary-cube template\", \"ell\": 11, \"row_labels\": [[0, 0, 0], [1, 1, 1], [1, 0, 0], [0, 1, 1], [0, 1, 0]], \"row_types\": [\"X\", \"X\", \"Z\", \"Z\", \"Y\"], \"shifts\": [1, 2, 3]}", "origin": "submission", "novelty": "unknown", "references": [ "Baldelli, Orsucci, Lazaro and Battaglioni, Quantum XYZ Stabilizer Codes, arXiv:2607.14988v1, Sections III-V. https://arxiv.org/abs/2607.14988v1", "Lee, Okada, Maskara, Kasai and Zhou, Design Principles for Ultra-High-Rate Quantum Codes, arXiv:2609.30069v1, Sections III-IV. https://arxiv.org/abs/2609.30069v1", "Finite proof sources, input binding, non-LC-CSS argument and deep-search receipts: https://github.com/hirobumii/qldpc-cyclic-xyz-evidence/tree/3c673081df60df2b708781ff561da857da898cf7" ], "notes": "Known XYZ check-space framework; fixed cyclic instance, max check weight 8 and qubit degree 5. Current gate found no exact/WL duplicate and advances the weight-8 unrestricted stabilizer frontier at upstream 0433d4ff5ff371976c0c03b02b103770f9fe0ee9. Global novelty and general code equivalence remain unestablished; not constructed by applying a Clifford to a board entry. Two new seeds 2026101781/2026101782 each ran 20000 Python Pauli RIS trials plus a 2000000-trial gf2_fast doubling request and 50000-trial orbit-fold budget; lightest found 4 throughout. Exact finite binary-symplectic parameter proof is supplementary; the challenge field remains upper_bound, with no circuit claim. AI tools: GPT-6 Astra with OpenAI Codex, used for exploration, review, validation and drafting. See notes/88-36-4.md." } }