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"confidence": "upper_bound", "witness": [ 2, 3, 23, 33, 40, 42, 70, 76, 79, 97, 113, 114, 134, 144, 151, 153, 181, 187, 190, 208, 224, 225, 245, 255, 262, 264, 292, 298, 301, 319, 362, 436, 473, 547, 584, 658 ], "witness_provenance": { "found_by": [ "@vprusso" ], "date": "2026-09-24", "found_at_samples": 1, "survived_samples": 1, "tool": "norm-word lift of a Z_111 quotient logical (exact algebra)", "seeds": [ 0 ] } } }, "provenance": { "authors": [ "@npdeep" ], "construction": "Lift-333 generalized-bicycle search with 16-term a(x) and 14-term b(x); six-stage cloud RIS deepening retained a validated weight-82 X logical, and PR #596 CI RIS-fast found the retained weight-81 Z logical.", "date": "2026-08-17", "model": "Magic State Labs (Custom) v0.1", "notes": "The X and Z witnesses were independently validated. The distance is corrected to the weight-81 Z logical found by PR #596 CI and remains a witness-backed upper bound, not an exact-distance claim. Refuted 2026-08-20: deep-RIS (full-basis + pair stage, --pair-depth 24) found lighter logicals on every seed \u2014 X: 81/81/80, Z: 79/79/76 at 30M deep trials per seed per side; best CPU-verified witnesses recorded. d: 81 -> 76 (score 1477.66 -> 1300.90). Distance corrected 2026-09-09: an independent GCD-ideal RIS search found and CSS-verified a weight-66 X logical at 65,536 trials per side (seed 29061169), lowering the witness-backed upper bound to d<=66 and the score to 150*66^2/666 = 980.18." }, "family": "generalized-bicycle" }