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486, 495, 496, 516, 518, 524, 525, 526, 532, 536, 540 ], "witness_provenance": { "found_by": [ "@Ming-yuan-Liang" ], "date": "2026-11-07", "found_at_samples": 30000000, "survived_samples": 30000000, "tool": "research/kit/surrogate.distance_rand_witness (gf2_fast backend)", "seeds": [ 20270507, 20270505 ] } }, "Z": { "value": 84, "confidence": "upper_bound", "witness": [ 1, 3, 14, 25, 41, 43, 48, 51, 73, 79, 81, 86, 90, 95, 99, 109, 128, 136, 141, 151, 155, 158, 172, 184, 187, 193, 198, 200, 204, 213, 214, 231, 235, 238, 249, 253, 258, 263, 272, 278, 281, 305, 317, 321, 322, 323, 326, 330, 334, 339, 347, 352, 359, 366, 373, 376, 377, 391, 410, 414, 415, 418, 425, 431, 433, 434, 443, 453, 461, 470, 479, 482, 483, 484, 486, 487, 490, 500, 511, 513, 516, 521, 528, 530 ], "witness_provenance": { "found_by": [ "@Ming-yuan-Liang" ], "date": "2026-11-07", "found_at_samples": 1000000, "survived_samples": 1000000, "tool": "research/kit/surrogate.distance_rand_witness (gf2_fast backend)", "seeds": [ 20270504 ] } } }, "provenance": { "authors": [ "@Ming-yuan-Liang" ], "construction": "Kasai affine 2BGA: a two-block group-algebra code over the affine group Aff(F_q) in its metacyclic realization Z_q x| Z_{q-1} (order q(q-1); 272 for q=17, so n = 2*272 = 544). With research/kit/group_algebra.py: mul, _ = metacyclic(q, q-1, r) where r is the smallest primitive root mod q (3 for q=17), then HX, HZ = build_2bga(mul, a, b) for the two exponent sets a, b recorded in the reproduction section.", "references": [], "date": "2026-11-06", "notes": "Checked against the board at the gate: no exact-fingerprint or WL-signature collision (gates.dedup reports neither), so the entry is declared not equivalent to any existing entry.", "model": "GLM-5.3-Flash", "origin": "submission", "search_budget": { "candidates_screened": 253, "wall_clock_hours": 16, "tool": "research/kit search lane (numpy RIS screen + 20k rungs; numpy 1M deep rung; gf2_fast 1M-30M deep probes; gate_changed fast batteries)", "ris_trials_per_side": 30000000 } }, "family": "generalized-bicycle" }