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420, 430, 523 ], [ 232, 257, 314, 334, 340, 419, 421, 431, 524 ] ] }, "distance": { "d": 18, "X": { "value": 18, "confidence": "upper_bound", "witness": [ 213, 216, 219, 222, 223, 227, 250, 256, 259, 276, 284, 295, 331, 333, 338, 377, 378, 416 ] }, "Z": { "value": 18, "confidence": "upper_bound", "witness": [ 107, 114, 118, 136, 153, 168, 192, 200, 329, 335, 339, 341, 359, 390, 394, 405, 412, 417 ] } }, "provenance": { "authors": [ "@yifanhong" ], "origin": "submission", "novelty": "known_parameters", "construction": "Balanced/lifted product over Z_35 semidirect-product_11 Z_3, with weight-3 group-ring entries a=1+x^22+xy^2, b=1+x^4+x^16y^2, c=1+x^34+x^12y, d=1+x^28y+x^31y; reproduced from arXiv:2607.27644v1.", "model": "GPT 5.6 Sol", "references": [ "arXiv:2607.27644v1" ], "date": "2026-08-02", "notes": "Published in Table 8 (Appendix A) of arXiv:2607.27644v1; fresh QDistEvol witnesses reproduced for this contribution." }, "family": "balanced-product" }