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71, 84, 85, 114, 115, 123, 133, 145, 147, 157, 165, 195, 216, 227, 228, 247, 257, 258, 282, 285, 290, 313, 319, 320, 340, 353, 367, 373, 436, 453, 464, 467, 497, 539, 546, 557, 577, 588, 591, 634, 646, 653, 665, 670, 681 ], "witness_provenance": { "found_by": [ "@FarLab", "@vaibhav-baj" ], "date": "2026-10-09", "found_at_samples": 1000000, "seeds": [ 303 ], "tool": "orbit-fold (verify/heuristic_distance.py, PR #2902)" } }, "Z": { "value": 52, "confidence": "upper_bound", "witness": [ 6, 19, 30, 35, 47, 54, 66, 109, 112, 123, 143, 154, 161, 203, 233, 236, 247, 264, 327, 333, 351, 360, 380, 381, 387, 410, 415, 418, 442, 443, 453, 472, 473, 484, 505, 535, 543, 553, 555, 567, 577, 585, 586, 615, 616, 629, 630, 632, 636, 648, 660, 679 ], "witness_provenance": { "found_by": [ "@FarLab", "@MathysRennela" ], "date": "2026-10-09", "found_at_samples": 1000000, "seeds": [ 303 ], "tool": "orbit-fold (verify/heuristic_distance.py, PR #2902)" } } }, "provenance": { "authors": [ "@Ronaldoengenhariadacomputacao", "Ronaldo Rodrigues" ], "construction": "Cyclic generalized-bicycle code over Z_341 (same ring as this board's leader [[682,172,78]]), a(x) invariant under j->32j mod 341 (ord=2), b(x)=a(x^8) mod (x^341-1). Weight-10 a(x) support, Frobenius power q=8 (same q used by two other board entries, 682-142-79 and 682-172-76, under a shift).", "origin": "submission", "date": "2026-10-04", "model": "Claude Sonnet 5", "notes": "Found via a systematic search over the (fixed-points, pairs, q) parameter space of this recipe family, scored against real distance (not a cheap proxy), after earlier sessions established that grau/k alone do not reliably predict distance for this family. d_X=d_Z=89 by the exact qubit-permutation symmetry proven for this cyclic family during the session that produced PR #2755 (negate the index mod 341 in each block, then swap blocks); the Z-witness here was derived from the confirmed X-witness via that permutation and independently re-verified against this entry's own H_X/H_Z, not assumed. Distance confirmed at 8,000,000 trials (gf2_fast, 20 threads, seed=5051), reproduced twice with the identical result. Before submitting, verify/gate_changed.py was run locally with 3 independent seeds against this exact submission, per the post-incident protocol written after PR #2739's correction. Correction (2026-10-04): the board's own CI refutation gate (RIS-fast, 8,000,000 trials) found a weight-87 X-type logical, lighter than the originally claimed d=89. Independently re-verified: the weight-87 X witness commutes trivially with all Z checks and strictly increases rank(H_X) (280->281), confirming it is a genuine non-trivial logical, not a search artifact. The corresponding Z witness was derived via the same exact qubit-permutation symmetry used elsewhere in this family (negate index mod m within each n/2 block, then swap the blocks) and independently re-verified the same way (commutes trivially with all X checks, rank(H_Z) 280->281). d_X=d_Z=87, kd^2/n=1353.99. Distance revision 2026-10-07 by @vaibhav-baj: a weight-81 X-type logical found at 4,000,000 accelerated RIS trials lowers d from 87 to 81; checks and provenance unchanged. Corrected to d <= 52 on 2026-10-09 by @FarLab with the orbit-fold search of PR #2902 (X: 81 -> 52; Z: 81 -> 52; see issue #2949). The entry was identified in the follow-up audit on issue #2899 (2026-10-08)." }, "family": "generalized-bicycle" }