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"confidence": "upper_bound", "witness": [ 14, 33, 59, 63, 90, 99, 105, 127, 130, 137, 138, 144, 145, 152, 167, 170, 208, 217, 234, 239, 258, 262, 290, 298, 304, 345, 346, 351 ], "witness_provenance": { "found_by": [ "@mathysrennela" ], "date": "2026-10-12", "found_at_samples": 200000, "survived_samples": 200000, "tool": "surrogate.distance_rand_witness (gf2_fast, 8 threads)", "seeds": [ 555001 ] } }, "Z": { "value": 27, "confidence": "upper_bound", "witness": [ 14, 53, 64, 71, 72, 78, 94, 106, 142, 148, 157, 168, 170, 178, 183, 195, 196, 216, 224, 273, 280, 288, 291, 309, 356, 365, 376 ], "witness_provenance": { "found_by": [ "@mathysrennela" ], "date": "2026-10-12", "found_at_samples": 200000, "survived_samples": 200000, "tool": "surrogate.distance_rand_witness (gf2_fast, 8 threads)", "seeds": [ 555002 ] } } }, "provenance": { "authors": [ "@mathysrennela" ], "construction": "Lifted product over G = M_27 x Z_7 with K = {e} (free action) and 1x1/1x1 boundary maps, from arXiv:2608.08996's Supplementary Information: M_27 = times Z_7 on generator u, with A = e + s^2u^3 + x^3su + x^5u^6 and B = s + x + x^2s^2u^5 + x^5su^3 in F_2[M_27 x Z_7], built with research/kit/group_algebra.build_2bga. n = 2|G| = 378, check weight 4 + 4 = 8.", "references": [ "arXiv:2608.08996v1" ], "date": "2026-10-12", "notes": "Reproduction of a code published in arXiv:2608.08996 Table 1 at n = 378, k = 18, w = 8 with a QDistEvol bound of 27; here the bound is measured at 27 on both sides rather than merely taken. No board entry shares (n, k), so this is a new parameter point rather than a distinct code at held parameters. Distance is a witness-backed upper bound at confidence upper_bound, not an exact certification.", "model": "Space Bunny Alpha 1.0", "origin": "submission", "search_budget": { "ris_trials_per_side": 1000000 } }, "family": "lifted-product" }