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 "distance": {
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   "confidence": "upper_bound",
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 "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\": 7, \"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 2026101701/2026101702 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/56-24-4.md."
 }
}