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244, 258, 329, 364, 405, 439, 479, 537, 549 ] ] }, "distance": { "d": 18, "X": { "value": 18, "confidence": "upper_bound", "witness": [ 220, 221, 225, 234, 260, 273, 276, 297, 300, 306, 319, 352, 358, 386, 392, 405, 436, 439 ] }, "Z": { "value": 18, "confidence": "upper_bound", "witness": [ 1, 7, 13, 25, 35, 41, 47, 83, 224, 227, 243, 245, 261, 271, 277, 294, 295, 303 ] } }, "provenance": { "authors": [ "@yifanhong" ], "origin": "submission", "novelty": "known_parameters", "construction": "Balanced/lifted product over Z_22 semidirect-product_3 Z_5, with weight-3 group-ring entries a=1+x^10+x^5y^2, b=1+x^8+x^2y^3, c=1+x^7+x^16y, d=1+x+x^6y^4; reproduced from arXiv:2607.27644v1.", "model": "GPT 5.6 Sol", "references": [ "arXiv:2607.27644v1" ], "date": "2026-08-02", "notes": "Published in Table 1 of arXiv:2607.27644v1; fresh QDistEvol witnesses reproduced for this contribution." }, "family": "balanced-product" }