{"abstract":"The bounded pairing pass certificate reports an incorrect pairs.","category":"Heap invariants","checks":7,"contract":"For delete-min pairing pass, children are [id,key]. Pair adjacent children left-to-right, keeping the left on equal keys. An odd last child survives. Return pair indices, winning ids, losing ids, odd carry id, second-pass traversal order, and comparison count. The second pass folds from right to left.","evaluation_group":"s3-heap-model-pairing-pass","failed_approach":"The local patch uses [[i,i+1] for i in range(1,len(a)-1,2)] and still violates the stated relation.","family":"s3-heap-pairing-pass-pairs","id":"FA-40141","implementations":{"attempt":{"sha256":"34cd4dab7c06b3c00e6a37e25674a11a1c824f9ac23c45cdc7f7a880c9e4e4bc","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(d):\n    a=d['children']; pairs=[(a[i],a[i+1]) for i in range(0,len(a)-1,2)]\n    wins=[x if x[1]<=y[1] else y for x,y in pairs]\n    loses=[y if x[1]<=y[1] else x for x,y in pairs]\n    first=wins+([a[-1]] if len(a)%2 else [])\n    return {'pairs': [[i,i+1] for i in range(1,len(a)-1,2)],\n    'winners': [x[0] for x in wins],\n    'losers': [x[0] for x in loses],\n    'carry': a[-1][0] if len(a)%2 else None,\n    'fold_order': [x[0] for x in reversed(first)],\n    'comparisons': len(pairs)+max(0,len(first)-1)}\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncases = [[({'children': []}, {'pairs': [], 'winners': [], 'losers': [], 'carry': None, 'fold_order': [], 'comparisons': 0}), ({'children': [[8, 3]]}, {'pairs': [], 'winners': [], 'losers': [], 'carry': 8, 'fold_order': [8], 'comparisons': 0}), ({'children': [[8, 9], [2, 1]]}, {'pairs': [[0, 1]], 'winners': [2], 'losers': [8], 'carry': None, 'fold_order': [2], 'comparisons': 1}), ({'children': [[4, 5], [7, 2], [1, 9]]}, {'pairs': [[0, 1]], 'winners': [7], 'losers': [4], 'carry': 1, 'fold_order': [1, 7], 'comparisons': 2}), ({'children': [[4, 2], [7, 2], [1, 6], [9, 3]]}, {'pairs': [[0, 1], [2, 3]], 'winners': [4, 9], 'losers': [7, 1], 'carry': None, 'fold_order': [9, 4], 'comparisons': 3}), ({'children': [[9, 8], [8, 2], [7, 7], [6, 1], [5, 3], [4, 6]]}, {'pairs': [[0, 1], [2, 3], [4, 5]], 'winners': [8, 6, 5], 'losers': [9, 7, 4], 'carry': None, 'fold_order': [5, 6, 8], 'comparisons': 5}), ({'children': [[9, 8], [8, 2], [7, 7], [6, 1], [5, 3], [4, 6], [100, 1]]}, {'pairs': [[0, 1], [2, 3], [4, 5]], 'winners': [8, 6, 5], 'losers': [9, 7, 4], 'carry': 100, 'fold_order': [100, 5, 6, 8], 'comparisons': 6})], [({'children': []}, {'pairs': [], 'winners': [], 'losers': [], 'carry': None, 'fold_order': [], 'comparisons': 0}), ({'children': [[8, 3]]}, {'pairs': [], 'winners': [], 'losers': [], 'carry': 8, 'fold_order': [8], 'comparisons': 0}), ({'children': [[8, 9], [2, 1]]}, {'pairs': [[0, 1]], 'winners': [2], 'losers': [8], 'carry': None, 'fold_order': [2], 'comparisons': 1}), ({'children': [[4, 5], [7, 2], [1, 9]]}, {'pairs': [[0, 1]], 'winners': [7], 'losers': [4], 'carry': 1, 'fold_order': [1, 7], 'comparisons': 2}), ({'children': [[4, 2], [7, 2], [1, 6], [9, 3]]}, {'pairs': [[0, 1], [2, 3]], 'winners': [4, 9], 'losers': [7, 1], 'carry': None, 'fold_order': [9, 4], 'comparisons': 3}), ({'children': [[9, 8], [8, 2], [7, 7], [6, 1], [5, 3], [4, 6]]}, {'pairs': [[0, 1], [2, 3], [4, 5]], 'winners': [8, 6, 5], 'losers': [9, 7, 4], 'carry': None, 'fold_order': [5, 6, 8], 'comparisons': 5}), ({'children': [[9, 8], [8, 2], [7, 7], [6, 1], [5, 3], [4, 6], [100, 2], [101, 1]]}, {'pairs': [[0, 1], [2, 3], [4, 5], [6, 7]], 'winners': [8, 6, 5, 101], 'losers': [9, 7, 4, 100], 'carry': None, 'fold_order': [101, 5, 6, 8], 'comparisons': 7})], [({'children': []}, {'pairs': [], 'winners': [], 'losers': [], 'carry': None, 'fold_order': [], 'comparisons': 0}), ({'children': [[8, 3]]}, {'pairs': [], 'winners': [], 'losers': [], 'carry': 8, 'fold_order': [8], 'comparisons': 0}), ({'children': [[8, 9], [2, 1]]}, {'pairs': [[0, 1]], 'winners': [2], 'losers': [8], 'carry': None, 'fold_order': [2], 'comparisons': 1}), ({'children': [[4, 5], [7, 2], [1, 9]]}, {'pairs': [[0, 1]], 'winners': [7], 'losers': [4], 'carry': 1, 'fold_order': [1, 7], 'comparisons': 2}), ({'children': [[4, 2], [7, 2], [1, 6], [9, 3]]}, {'pairs': [[0, 1], [2, 3]], 'winners': [4, 9], 'losers': [7, 1], 'carry': None, 'fold_order': [9, 4], 'comparisons': 3}), ({'children': [[9, 8], [8, 2], [7, 7], [6, 1], [5, 3], [4, 6]]}, {'pairs': [[0, 1], [2, 3], [4, 5]], 'winners': [8, 6, 5], 'losers': [9, 7, 4], 'carry': None, 'fold_order': [5, 6, 8], 'comparisons': 5}), ({'children': [[9, 8], [8, 2], [7, 7], [6, 1], [5, 3], [4, 6], [100, 3], [101, 2], [102, 1]]}, {'pairs': [[0, 1], [2, 3], [4, 5], [6, 7]], 'winners': [8, 6, 5, 101], 'losers': [9, 7, 4, 100], 'carry': 102, 'fold_order': [102, 101, 5, 6, 8], 'comparisons': 8})], [({'children': []}, {'pairs': [], 'winners': [], 'losers': [], 'carry': None, 'fold_order': [], 'comparisons': 0}), ({'children': [[8, 3]]}, {'pairs': [], 'winners': [], 'losers': [], 'carry': 8, 'fold_order': [8], 'comparisons': 0}), ({'children': [[8, 9], [2, 1]]}, {'pairs': [[0, 1]], 'winners': [2], 'losers': [8], 'carry': None, 'fold_order': [2], 'comparisons': 1}), ({'children': [[4, 5], [7, 2], [1, 9]]}, {'pairs': [[0, 1]], 'winners': [7], 'losers': [4], 'carry': 1, 'fold_order': [1, 7], 'comparisons': 2}), ({'children': [[4, 2], [7, 2], [1, 6], [9, 3]]}, {'pairs': [[0, 1], [2, 3]], 'winners': [4, 9], 'losers': [7, 1], 'carry': None, 'fold_order': [9, 4], 'comparisons': 3}), ({'children': [[9, 8], [8, 2], [7, 7], [6, 1], [5, 3], [4, 6]]}, {'pairs': [[0, 1], [2, 3], [4, 5]], 'winners': [8, 6, 5], 'losers': [9, 7, 4], 'carry': None, 'fold_order': [5, 6, 8], 'comparisons': 5}), ({'children': [[9, 8], [8, 2], [7, 7], [6, 1], [5, 3], [4, 6], [100, 4], [101, 3], [102, 2], [103, 1]]}, {'pairs': [[0, 1], [2, 3], [4, 5], [6, 7], [8, 9]], 'winners': [8, 6, 5, 101, 103], 'losers': [9, 7, 4, 100, 102], 'carry': None, 'fold_order': [103, 101, 5, 6, 8], 'comparisons': 9})], [({'children': []}, {'pairs': [], 'winners': [], 'losers': [], 'carry': None, 'fold_order': [], 'comparisons': 0}), ({'children': [[8, 3]]}, {'pairs': [], 'winners': [], 'losers': [], 'carry': 8, 'fold_order': [8], 'comparisons': 0}), ({'children': [[8, 9], [2, 1]]}, {'pairs': [[0, 1]], 'winners': [2], 'losers': [8], 'carry': None, 'fold_order': [2], 'comparisons': 1}), ({'children': [[4, 5], [7, 2], [1, 9]]}, {'pairs': [[0, 1]], 'winners': [7], 'losers': [4], 'carry': 1, 'fold_order': [1, 7], 'comparisons': 2}), ({'children': [[4, 2], [7, 2], [1, 6], [9, 3]]}, {'pairs': [[0, 1], [2, 3]], 'winners': [4, 9], 'losers': [7, 1], 'carry': None, 'fold_order': [9, 4], 'comparisons': 3}), ({'children': [[9, 8], [8, 2], [7, 7], [6, 1], [5, 3], [4, 6]]}, {'pairs': [[0, 1], [2, 3], [4, 5]], 'winners': [8, 6, 5], 'losers': [9, 7, 4], 'carry': None, 'fold_order': [5, 6, 8], 'comparisons': 5}), ({'children': [[9, 8], [8, 2], [7, 7], [6, 1], [5, 3], [4, 6], [100, 5], [101, 4], [102, 3], [103, 2], [104, 1]]}, {'pairs': [[0, 1], [2, 3], [4, 5], [6, 7], [8, 9]], 'winners': [8, 6, 5, 101, 103], 'losers': [9, 7, 4, 100, 102], 'carry': 104, 'fold_order': [104, 103, 101, 5, 6, 8], 'comparisons': 10})]][N-1]\ncheck('regression certificate 1', solve(cases[0][0]), cases[0][1])\ncheck('regression certificate 2', solve(cases[1][0]), cases[1][1])\ncheck('regression certificate 3', solve(cases[2][0]), cases[2][1])\ncheck('regression certificate 4', solve(cases[3][0]), cases[3][1])\ncheck('regression certificate 5', solve(cases[4][0]), cases[4][1])\ncheck('regression certificate 6', solve(cases[5][0]), cases[5][1])\ncheck('variant-dependent certificate', solve(cases[6][0]), cases[6][1])\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"},"broken":{"sha256":"1b59ce2afe42f6b4f20d26d3372132337ee263fa50b13e70c72df5320aae8ad8","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(d):\n    a=d['children']; pairs=[(a[i],a[i+1]) for i in range(0,len(a)-1,2)]\n    wins=[x if x[1]<=y[1] else y for x,y in pairs]\n    loses=[y if x[1]<=y[1] else x for x,y in pairs]\n    first=wins+([a[-1]] if len(a)%2 else [])\n    return {'pairs': [[i,i+1] for i in range(len(a)-1)],\n    'winners': [x[0] for x in wins],\n    'losers': [x[0] for x in loses],\n    'carry': a[-1][0] if len(a)%2 else None,\n    'fold_order': [x[0] for x in reversed(first)],\n    'comparisons': len(pairs)+max(0,len(first)-1)}\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncases = [[({'children': []}, {'pairs': [], 'winners': [], 'losers': [], 'carry': None, 'fold_order': [], 'comparisons': 0}), ({'children': [[8, 3]]}, {'pairs': [], 'winners': [], 'losers': [], 'carry': 8, 'fold_order': [8], 'comparisons': 0}), ({'children': [[8, 9], [2, 1]]}, {'pairs': [[0, 1]], 'winners': [2], 'losers': [8], 'carry': None, 'fold_order': [2], 'comparisons': 1}), ({'children': [[4, 5], [7, 2], [1, 9]]}, {'pairs': [[0, 1]], 'winners': [7], 'losers': [4], 'carry': 1, 'fold_order': [1, 7], 'comparisons': 2}), ({'children': [[4, 2], [7, 2], [1, 6], [9, 3]]}, {'pairs': [[0, 1], [2, 3]], 'winners': [4, 9], 'losers': [7, 1], 'carry': None, 'fold_order': [9, 4], 'comparisons': 3}), ({'children': [[9, 8], [8, 2], [7, 7], [6, 1], [5, 3], [4, 6]]}, {'pairs': [[0, 1], [2, 3], [4, 5]], 'winners': [8, 6, 5], 'losers': [9, 7, 4], 'carry': None, 'fold_order': [5, 6, 8], 'comparisons': 5}), ({'children': [[9, 8], [8, 2], [7, 7], [6, 1], [5, 3], [4, 6], [100, 1]]}, {'pairs': [[0, 1], [2, 3], [4, 5]], 'winners': [8, 6, 5], 'losers': [9, 7, 4], 'carry': 100, 'fold_order': [100, 5, 6, 8], 'comparisons': 6})], [({'children': []}, {'pairs': [], 'winners': [], 'losers': [], 'carry': None, 'fold_order': [], 'comparisons': 0}), ({'children': [[8, 3]]}, {'pairs': [], 'winners': [], 'losers': [], 'carry': 8, 'fold_order': [8], 'comparisons': 0}), ({'children': [[8, 9], [2, 1]]}, {'pairs': [[0, 1]], 'winners': [2], 'losers': [8], 'carry': None, 'fold_order': [2], 'comparisons': 1}), ({'children': [[4, 5], [7, 2], [1, 9]]}, {'pairs': [[0, 1]], 'winners': [7], 'losers': [4], 'carry': 1, 'fold_order': [1, 7], 'comparisons': 2}), ({'children': [[4, 2], [7, 2], [1, 6], [9, 3]]}, {'pairs': [[0, 1], [2, 3]], 'winners': [4, 9], 'losers': [7, 1], 'carry': None, 'fold_order': [9, 4], 'comparisons': 3}), ({'children': [[9, 8], [8, 2], [7, 7], [6, 1], [5, 3], [4, 6]]}, {'pairs': [[0, 1], [2, 3], [4, 5]], 'winners': [8, 6, 5], 'losers': [9, 7, 4], 'carry': None, 'fold_order': [5, 6, 8], 'comparisons': 5}), ({'children': [[9, 8], [8, 2], [7, 7], [6, 1], [5, 3], [4, 6], [100, 2], [101, 1]]}, {'pairs': [[0, 1], [2, 3], [4, 5], [6, 7]], 'winners': [8, 6, 5, 101], 'losers': [9, 7, 4, 100], 'carry': None, 'fold_order': [101, 5, 6, 8], 'comparisons': 7})], [({'children': []}, {'pairs': [], 'winners': [], 'losers': [], 'carry': None, 'fold_order': [], 'comparisons': 0}), ({'children': [[8, 3]]}, {'pairs': [], 'winners': [], 'losers': [], 'carry': 8, 'fold_order': [8], 'comparisons': 0}), ({'children': [[8, 9], [2, 1]]}, {'pairs': [[0, 1]], 'winners': [2], 'losers': [8], 'carry': None, 'fold_order': [2], 'comparisons': 1}), ({'children': [[4, 5], [7, 2], [1, 9]]}, {'pairs': [[0, 1]], 'winners': [7], 'losers': [4], 'carry': 1, 'fold_order': [1, 7], 'comparisons': 2}), ({'children': [[4, 2], [7, 2], [1, 6], [9, 3]]}, {'pairs': [[0, 1], [2, 3]], 'winners': [4, 9], 'losers': [7, 1], 'carry': None, 'fold_order': [9, 4], 'comparisons': 3}), ({'children': [[9, 8], [8, 2], [7, 7], [6, 1], [5, 3], [4, 6]]}, {'pairs': [[0, 1], [2, 3], [4, 5]], 'winners': [8, 6, 5], 'losers': [9, 7, 4], 'carry': None, 'fold_order': [5, 6, 8], 'comparisons': 5}), ({'children': [[9, 8], [8, 2], [7, 7], [6, 1], [5, 3], [4, 6], [100, 3], [101, 2], [102, 1]]}, {'pairs': [[0, 1], [2, 3], [4, 5], [6, 7]], 'winners': [8, 6, 5, 101], 'losers': [9, 7, 4, 100], 'carry': 102, 'fold_order': [102, 101, 5, 6, 8], 'comparisons': 8})], [({'children': []}, {'pairs': [], 'winners': [], 'losers': [], 'carry': None, 'fold_order': [], 'comparisons': 0}), ({'children': [[8, 3]]}, {'pairs': [], 'winners': [], 'losers': [], 'carry': 8, 'fold_order': [8], 'comparisons': 0}), ({'children': [[8, 9], [2, 1]]}, {'pairs': [[0, 1]], 'winners': [2], 'losers': [8], 'carry': None, 'fold_order': [2], 'comparisons': 1}), ({'children': [[4, 5], [7, 2], [1, 9]]}, {'pairs': [[0, 1]], 'winners': [7], 'losers': [4], 'carry': 1, 'fold_order': [1, 7], 'comparisons': 2}), ({'children': [[4, 2], [7, 2], [1, 6], [9, 3]]}, {'pairs': [[0, 1], [2, 3]], 'winners': [4, 9], 'losers': [7, 1], 'carry': None, 'fold_order': [9, 4], 'comparisons': 3}), ({'children': [[9, 8], [8, 2], [7, 7], [6, 1], [5, 3], [4, 6]]}, {'pairs': [[0, 1], [2, 3], [4, 5]], 'winners': [8, 6, 5], 'losers': [9, 7, 4], 'carry': None, 'fold_order': [5, 6, 8], 'comparisons': 5}), ({'children': [[9, 8], [8, 2], [7, 7], [6, 1], [5, 3], [4, 6], [100, 4], [101, 3], [102, 2], [103, 1]]}, {'pairs': [[0, 1], [2, 3], [4, 5], [6, 7], [8, 9]], 'winners': [8, 6, 5, 101, 103], 'losers': [9, 7, 4, 100, 102], 'carry': None, 'fold_order': [103, 101, 5, 6, 8], 'comparisons': 9})], [({'children': []}, {'pairs': [], 'winners': [], 'losers': [], 'carry': None, 'fold_order': [], 'comparisons': 0}), ({'children': [[8, 3]]}, {'pairs': [], 'winners': [], 'losers': [], 'carry': 8, 'fold_order': [8], 'comparisons': 0}), ({'children': [[8, 9], [2, 1]]}, {'pairs': [[0, 1]], 'winners': [2], 'losers': [8], 'carry': None, 'fold_order': [2], 'comparisons': 1}), ({'children': [[4, 5], [7, 2], [1, 9]]}, {'pairs': [[0, 1]], 'winners': [7], 'losers': [4], 'carry': 1, 'fold_order': [1, 7], 'comparisons': 2}), ({'children': [[4, 2], [7, 2], [1, 6], [9, 3]]}, {'pairs': [[0, 1], [2, 3]], 'winners': [4, 9], 'losers': [7, 1], 'carry': None, 'fold_order': [9, 4], 'comparisons': 3}), ({'children': [[9, 8], [8, 2], [7, 7], [6, 1], [5, 3], [4, 6]]}, {'pairs': [[0, 1], [2, 3], [4, 5]], 'winners': [8, 6, 5], 'losers': [9, 7, 4], 'carry': None, 'fold_order': [5, 6, 8], 'comparisons': 5}), ({'children': [[9, 8], [8, 2], [7, 7], [6, 1], [5, 3], [4, 6], [100, 5], [101, 4], [102, 3], [103, 2], [104, 1]]}, {'pairs': [[0, 1], [2, 3], [4, 5], [6, 7], [8, 9]], 'winners': [8, 6, 5, 101, 103], 'losers': [9, 7, 4, 100, 102], 'carry': 104, 'fold_order': [104, 103, 101, 5, 6, 8], 'comparisons': 10})]][N-1]\ncheck('regression certificate 1', solve(cases[0][0]), cases[0][1])\ncheck('regression certificate 2', solve(cases[1][0]), cases[1][1])\ncheck('regression certificate 3', solve(cases[2][0]), cases[2][1])\ncheck('regression certificate 4', solve(cases[3][0]), cases[3][1])\ncheck('regression certificate 5', solve(cases[4][0]), cases[4][1])\ncheck('regression certificate 6', solve(cases[5][0]), cases[5][1])\ncheck('variant-dependent certificate', solve(cases[6][0]), cases[6][1])\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"},"fixed":{"sha256":"0ae528ca62ac7c5f2183f60441cf0d55270d8552aefc0c0f6a74a1f8ffd532bd","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(d):\n    a=d['children']; pairs=[(a[i],a[i+1]) for i in range(0,len(a)-1,2)]\n    wins=[x if x[1]<=y[1] else y for x,y in pairs]\n    loses=[y if x[1]<=y[1] else x for x,y in pairs]\n    first=wins+([a[-1]] if len(a)%2 else [])\n    return {'pairs': [[i,i+1] for i in range(0,len(a)-1,2)],\n    'winners': [x[0] for x in wins],\n    'losers': [x[0] for x in loses],\n    'carry': a[-1][0] if len(a)%2 else None,\n    'fold_order': [x[0] for x in reversed(first)],\n    'comparisons': len(pairs)+max(0,len(first)-1)}\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncases = [[({'children': []}, {'pairs': [], 'winners': [], 'losers': [], 'carry': None, 'fold_order': [], 'comparisons': 0}), ({'children': [[8, 3]]}, {'pairs': [], 'winners': [], 'losers': [], 'carry': 8, 'fold_order': [8], 'comparisons': 0}), ({'children': [[8, 9], [2, 1]]}, {'pairs': [[0, 1]], 'winners': [2], 'losers': [8], 'carry': None, 'fold_order': [2], 'comparisons': 1}), ({'children': [[4, 5], [7, 2], [1, 9]]}, {'pairs': [[0, 1]], 'winners': [7], 'losers': [4], 'carry': 1, 'fold_order': [1, 7], 'comparisons': 2}), ({'children': [[4, 2], [7, 2], [1, 6], [9, 3]]}, {'pairs': [[0, 1], [2, 3]], 'winners': [4, 9], 'losers': [7, 1], 'carry': None, 'fold_order': [9, 4], 'comparisons': 3}), ({'children': [[9, 8], [8, 2], [7, 7], [6, 1], [5, 3], [4, 6]]}, {'pairs': [[0, 1], [2, 3], [4, 5]], 'winners': [8, 6, 5], 'losers': [9, 7, 4], 'carry': None, 'fold_order': [5, 6, 8], 'comparisons': 5}), ({'children': [[9, 8], [8, 2], [7, 7], [6, 1], [5, 3], [4, 6], [100, 1]]}, {'pairs': [[0, 1], [2, 3], [4, 5]], 'winners': [8, 6, 5], 'losers': [9, 7, 4], 'carry': 100, 'fold_order': [100, 5, 6, 8], 'comparisons': 6})], [({'children': []}, {'pairs': [], 'winners': [], 'losers': [], 'carry': None, 'fold_order': [], 'comparisons': 0}), ({'children': [[8, 3]]}, {'pairs': [], 'winners': [], 'losers': [], 'carry': 8, 'fold_order': [8], 'comparisons': 0}), ({'children': [[8, 9], [2, 1]]}, {'pairs': [[0, 1]], 'winners': [2], 'losers': [8], 'carry': None, 'fold_order': [2], 'comparisons': 1}), ({'children': [[4, 5], [7, 2], [1, 9]]}, {'pairs': [[0, 1]], 'winners': [7], 'losers': [4], 'carry': 1, 'fold_order': [1, 7], 'comparisons': 2}), ({'children': [[4, 2], [7, 2], [1, 6], [9, 3]]}, {'pairs': [[0, 1], [2, 3]], 'winners': [4, 9], 'losers': [7, 1], 'carry': None, 'fold_order': [9, 4], 'comparisons': 3}), ({'children': [[9, 8], [8, 2], [7, 7], [6, 1], [5, 3], [4, 6]]}, {'pairs': [[0, 1], [2, 3], [4, 5]], 'winners': [8, 6, 5], 'losers': [9, 7, 4], 'carry': None, 'fold_order': [5, 6, 8], 'comparisons': 5}), ({'children': [[9, 8], [8, 2], [7, 7], [6, 1], [5, 3], [4, 6], [100, 2], [101, 1]]}, {'pairs': [[0, 1], [2, 3], [4, 5], [6, 7]], 'winners': [8, 6, 5, 101], 'losers': [9, 7, 4, 100], 'carry': None, 'fold_order': [101, 5, 6, 8], 'comparisons': 7})], [({'children': []}, {'pairs': [], 'winners': [], 'losers': [], 'carry': None, 'fold_order': [], 'comparisons': 0}), ({'children': [[8, 3]]}, {'pairs': [], 'winners': [], 'losers': [], 'carry': 8, 'fold_order': [8], 'comparisons': 0}), ({'children': [[8, 9], [2, 1]]}, {'pairs': [[0, 1]], 'winners': [2], 'losers': [8], 'carry': None, 'fold_order': [2], 'comparisons': 1}), ({'children': [[4, 5], [7, 2], [1, 9]]}, {'pairs': [[0, 1]], 'winners': [7], 'losers': [4], 'carry': 1, 'fold_order': [1, 7], 'comparisons': 2}), ({'children': [[4, 2], [7, 2], [1, 6], [9, 3]]}, {'pairs': [[0, 1], [2, 3]], 'winners': [4, 9], 'losers': [7, 1], 'carry': None, 'fold_order': [9, 4], 'comparisons': 3}), ({'children': [[9, 8], [8, 2], [7, 7], [6, 1], [5, 3], [4, 6]]}, {'pairs': [[0, 1], [2, 3], [4, 5]], 'winners': [8, 6, 5], 'losers': [9, 7, 4], 'carry': None, 'fold_order': [5, 6, 8], 'comparisons': 5}), ({'children': [[9, 8], [8, 2], [7, 7], [6, 1], [5, 3], [4, 6], [100, 3], [101, 2], [102, 1]]}, {'pairs': [[0, 1], [2, 3], [4, 5], [6, 7]], 'winners': [8, 6, 5, 101], 'losers': [9, 7, 4, 100], 'carry': 102, 'fold_order': [102, 101, 5, 6, 8], 'comparisons': 8})], [({'children': []}, {'pairs': [], 'winners': [], 'losers': [], 'carry': None, 'fold_order': [], 'comparisons': 0}), ({'children': [[8, 3]]}, {'pairs': [], 'winners': [], 'losers': [], 'carry': 8, 'fold_order': [8], 'comparisons': 0}), ({'children': [[8, 9], [2, 1]]}, {'pairs': [[0, 1]], 'winners': [2], 'losers': [8], 'carry': None, 'fold_order': [2], 'comparisons': 1}), ({'children': [[4, 5], [7, 2], [1, 9]]}, {'pairs': [[0, 1]], 'winners': [7], 'losers': [4], 'carry': 1, 'fold_order': [1, 7], 'comparisons': 2}), ({'children': [[4, 2], [7, 2], [1, 6], [9, 3]]}, {'pairs': [[0, 1], [2, 3]], 'winners': [4, 9], 'losers': [7, 1], 'carry': None, 'fold_order': [9, 4], 'comparisons': 3}), ({'children': [[9, 8], [8, 2], [7, 7], [6, 1], [5, 3], [4, 6]]}, {'pairs': [[0, 1], [2, 3], [4, 5]], 'winners': [8, 6, 5], 'losers': [9, 7, 4], 'carry': None, 'fold_order': [5, 6, 8], 'comparisons': 5}), ({'children': [[9, 8], [8, 2], [7, 7], [6, 1], [5, 3], [4, 6], [100, 4], [101, 3], [102, 2], [103, 1]]}, {'pairs': [[0, 1], [2, 3], [4, 5], [6, 7], [8, 9]], 'winners': [8, 6, 5, 101, 103], 'losers': [9, 7, 4, 100, 102], 'carry': None, 'fold_order': [103, 101, 5, 6, 8], 'comparisons': 9})], [({'children': []}, {'pairs': [], 'winners': [], 'losers': [], 'carry': None, 'fold_order': [], 'comparisons': 0}), ({'children': [[8, 3]]}, {'pairs': [], 'winners': [], 'losers': [], 'carry': 8, 'fold_order': [8], 'comparisons': 0}), ({'children': [[8, 9], [2, 1]]}, {'pairs': [[0, 1]], 'winners': [2], 'losers': [8], 'carry': None, 'fold_order': [2], 'comparisons': 1}), ({'children': [[4, 5], [7, 2], [1, 9]]}, {'pairs': [[0, 1]], 'winners': [7], 'losers': [4], 'carry': 1, 'fold_order': [1, 7], 'comparisons': 2}), ({'children': [[4, 2], [7, 2], [1, 6], [9, 3]]}, {'pairs': [[0, 1], [2, 3]], 'winners': [4, 9], 'losers': [7, 1], 'carry': None, 'fold_order': [9, 4], 'comparisons': 3}), ({'children': [[9, 8], [8, 2], [7, 7], [6, 1], [5, 3], [4, 6]]}, {'pairs': [[0, 1], [2, 3], [4, 5]], 'winners': [8, 6, 5], 'losers': [9, 7, 4], 'carry': None, 'fold_order': [5, 6, 8], 'comparisons': 5}), ({'children': [[9, 8], [8, 2], [7, 7], [6, 1], [5, 3], [4, 6], [100, 5], [101, 4], [102, 3], [103, 2], [104, 1]]}, {'pairs': [[0, 1], [2, 3], [4, 5], [6, 7], [8, 9]], 'winners': [8, 6, 5, 101, 103], 'losers': [9, 7, 4, 100, 102], 'carry': 104, 'fold_order': [104, 103, 101, 5, 6, 8], 'comparisons': 10})]][N-1]\ncheck('regression certificate 1', solve(cases[0][0]), cases[0][1])\ncheck('regression certificate 2', solve(cases[1][0]), cases[1][1])\ncheck('regression certificate 3', solve(cases[2][0]), cases[2][1])\ncheck('regression certificate 4', solve(cases[3][0]), cases[3][1])\ncheck('regression certificate 5', solve(cases[4][0]), cases[4][1])\ncheck('regression certificate 6', solve(cases[5][0]), cases[5][1])\ncheck('variant-dependent certificate', solve(cases[6][0]), cases[6][1])\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"}},"limitations":"A stipulated offline diagnostic model; it does not implement a production allocator, concurrency protocol, or complete heap library. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.","method":"Deterministic executable model with adversarial boundary fixtures.","provenance":{"created_by":"Failure Map","dependencies":"Python standard library","family":"s3-heap-pairing-pass-pairs","generated_at":"2026-09-29T14:43:28.150956+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"This isolates an internal heap representation or priority-structure invariant using deterministic finite records.","repair":"Derive pairs using [[i,i+1] for i in range(0,len(a)-1,2)] under the stated bounded certificate contract.","root_cause":"Pairing first pass consumes disjoint pairs beginning at the first child.","sha256":"06f3069ff104ec85370f9b65a89e8d1484939f8be29618faadc4e09f15690f00","title":"Pairing first pass consumes disjoint pairs beginning at the first child · case 01","variant":1,"variant_policy":"Six explicit regression certificates are retained; a seventh changes structural size, position, priority, or bounds with N.","verification":{"attempt":{"elapsed_ms":45.172,"exit_code":1,"observations":[{"actual":{"carry":null,"comparisons":0,"fold_order":[],"losers":[],"pairs":[],"winners":[]},"check":"regression certificate 1","expected":{"carry":null,"comparisons":0,"fold_order":[],"losers":[],"pairs":[],"winners":[]},"passed":true},{"actual":{"carry":8,"comparisons":0,"fold_order":[8],"losers":[],"pairs":[],"winners":[]},"check":"regression certificate 2","expected":{"carry":8,"comparisons":0,"fold_order":[8],"losers":[],"pairs":[],"winners":[]},"passed":true},{"actual":{"carry":null,"comparisons":1,"fold_order":[2],"losers":[8],"pairs":[],"winners":[2]},"check":"regression certificate 3","expected":{"carry":null,"comparisons":1,"fold_order":[2],"losers":[8],"pairs":[[0,1]],"winners":[2]},"passed":false},{"actual":{"carry":1,"comparisons":2,"fold_order":[1,7],"losers":[4],"pairs":[[1,2]],"winners":[7]},"check":"regression certificate 4","expected":{"carry":1,"comparisons":2,"fold_order":[1,7],"losers":[4],"pairs":[[0,1]],"winners":[7]},"passed":false},{"actual":{"carry":null,"comparisons":3,"fold_order":[9,4],"losers":[7,1],"pairs":[[1,2]],"winners":[4,9]},"check":"regression certificate 5","expected":{"carry":null,"comparisons":3,"fold_order":[9,4],"losers":[7,1],"pairs":[[0,1],[2,3]],"winners":[4,9]},"passed":false},{"actual":{"carry":null,"comparisons":5,"fold_order":[5,6,8],"losers":[9,7,4],"pairs":[[1,2],[3,4]],"winners":[8,6,5]},"check":"regression certificate 6","expected":{"carry":null,"comparisons":5,"fold_order":[5,6,8],"losers":[9,7,4],"pairs":[[0,1],[2,3],[4,5]],"winners":[8,6,5]},"passed":false},{"actual":{"carry":100,"comparisons":6,"fold_order":[100,5,6,8],"losers":[9,7,4],"pairs":[[1,2],[3,4],[5,6]],"winners":[8,6,5]},"check":"variant-dependent certificate","expected":{"carry":100,"comparisons":6,"fold_order":[100,5,6,8],"losers":[9,7,4],"pairs":[[0,1],[2,3],[4,5]],"winners":[8,6,5]},"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression certificate 1\", \"actual\": {\"pairs\": [], \"winners\": [], \"losers\": [], \"carry\": null, \"fold_order\": [], \"comparisons\": 0}, \"expected\": {\"pairs\": [], \"winners\": [], \"losers\": [], \"carry\": null, \"fold_order\": [], \"comparisons\": 0}, \"passed\": true}, {\"check\": \"regression certificate 2\", \"actual\": {\"pairs\": [], \"winners\": [], \"losers\": [], \"carry\": 8, \"fold_order\": [8], \"comparisons\": 0}, \"expected\": {\"pairs\": [], \"winners\": [], \"losers\": [], \"carry\": 8, \"fold_order\": [8], \"comparisons\": 0}, \"passed\": true}, {\"check\": \"regression certificate 3\", \"actual\": {\"pairs\": [], \"winners\": [2], \"losers\": [8], \"carry\": null, \"fold_order\": [2], \"comparisons\": 1}, \"expected\": {\"pairs\": [[0, 1]], \"winners\": [2], \"losers\": [8], \"carry\": null, \"fold_order\": [2], \"comparisons\": 1}, \"passed\": false}, {\"check\": \"regression certificate 4\", \"actual\": {\"pairs\": [[1, 2]], \"winners\": [7], \"losers\": [4], \"carry\": 1, \"fold_order\": [1, 7], \"comparisons\": 2}, \"expected\": {\"pairs\": [[0, 1]], \"winners\": [7], \"losers\": [4], \"carry\": 1, \"fold_order\": [1, 7], \"comparisons\": 2}, \"passed\": false}, {\"check\": \"regression certificate 5\", \"actual\": {\"pairs\": [[1, 2]], \"winners\": [4, 9], \"losers\": [7, 1], \"carry\": null, \"fold_order\": [9, 4], \"comparisons\": 3}, \"expected\": {\"pairs\": [[0, 1], [2, 3]], \"winners\": [4, 9], \"losers\": [7, 1], \"carry\": null, \"fold_order\": [9, 4], \"comparisons\": 3}, \"passed\": false}, {\"check\": \"regression certificate 6\", \"actual\": {\"pairs\": [[1, 2], [3, 4]], \"winners\": [8, 6, 5], \"losers\": [9, 7, 4], \"carry\": null, \"fold_order\": [5, 6, 8], \"comparisons\": 5}, \"expected\": {\"pairs\": [[0, 1], [2, 3], [4, 5]], \"winners\": [8, 6, 5], \"losers\": [9, 7, 4], \"carry\": null, \"fold_order\": [5, 6, 8], \"comparisons\": 5}, \"passed\": false}, {\"check\": \"variant-dependent certificate\", \"actual\": {\"pairs\": [[1, 2], [3, 4], [5, 6]], \"winners\": [8, 6, 5], \"losers\": [9, 7, 4], \"carry\": 100, \"fold_order\": [100, 5, 6, 8], \"comparisons\": 6}, \"expected\": {\"pairs\": [[0, 1], [2, 3], [4, 5]], \"winners\": [8, 6, 5], \"losers\": [9, 7, 4], \"carry\": 100, \"fold_order\": [100, 5, 6, 8], \"comparisons\": 6}, \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":47.565,"exit_code":1,"observations":[{"actual":{"carry":null,"comparisons":0,"fold_order":[],"losers":[],"pairs":[],"winners":[]},"check":"regression certificate 1","expected":{"carry":null,"comparisons":0,"fold_order":[],"losers":[],"pairs":[],"winners":[]},"passed":true},{"actual":{"carry":8,"comparisons":0,"fold_order":[8],"losers":[],"pairs":[],"winners":[]},"check":"regression certificate 2","expected":{"carry":8,"comparisons":0,"fold_order":[8],"losers":[],"pairs":[],"winners":[]},"passed":true},{"actual":{"carry":null,"comparisons":1,"fold_order":[2],"losers":[8],"pairs":[[0,1]],"winners":[2]},"check":"regression certificate 3","expected":{"carry":null,"comparisons":1,"fold_order":[2],"losers":[8],"pairs":[[0,1]],"winners":[2]},"passed":true},{"actual":{"carry":1,"comparisons":2,"fold_order":[1,7],"losers":[4],"pairs":[[0,1],[1,2]],"winners":[7]},"check":"regression certificate 4","expected":{"carry":1,"comparisons":2,"fold_order":[1,7],"losers":[4],"pairs":[[0,1]],"winners":[7]},"passed":false},{"actual":{"carry":null,"comparisons":3,"fold_order":[9,4],"losers":[7,1],"pairs":[[0,1],[1,2],[2,3]],"winners":[4,9]},"check":"regression certificate 5","expected":{"carry":null,"comparisons":3,"fold_order":[9,4],"losers":[7,1],"pairs":[[0,1],[2,3]],"winners":[4,9]},"passed":false},{"actual":{"carry":null,"comparisons":5,"fold_order":[5,6,8],"losers":[9,7,4],"pairs":[[0,1],[1,2],[2,3],[3,4],[4,5]],"winners":[8,6,5]},"check":"regression certificate 6","expected":{"carry":null,"comparisons":5,"fold_order":[5,6,8],"losers":[9,7,4],"pairs":[[0,1],[2,3],[4,5]],"winners":[8,6,5]},"passed":false},{"actual":{"carry":100,"comparisons":6,"fold_order":[100,5,6,8],"losers":[9,7,4],"pairs":[[0,1],[1,2],[2,3],[3,4],[4,5],[5,6]],"winners":[8,6,5]},"check":"variant-dependent certificate","expected":{"carry":100,"comparisons":6,"fold_order":[100,5,6,8],"losers":[9,7,4],"pairs":[[0,1],[2,3],[4,5]],"winners":[8,6,5]},"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression certificate 1\", \"actual\": {\"pairs\": [], \"winners\": [], \"losers\": [], \"carry\": null, \"fold_order\": [], \"comparisons\": 0}, \"expected\": {\"pairs\": [], \"winners\": [], \"losers\": [], \"carry\": null, \"fold_order\": [], \"comparisons\": 0}, \"passed\": true}, {\"check\": \"regression certificate 2\", \"actual\": {\"pairs\": [], \"winners\": [], \"losers\": [], \"carry\": 8, \"fold_order\": [8], \"comparisons\": 0}, \"expected\": {\"pairs\": [], \"winners\": [], \"losers\": [], \"carry\": 8, \"fold_order\": [8], \"comparisons\": 0}, \"passed\": true}, {\"check\": \"regression certificate 3\", \"actual\": {\"pairs\": [[0, 1]], \"winners\": [2], \"losers\": [8], \"carry\": null, \"fold_order\": [2], \"comparisons\": 1}, \"expected\": {\"pairs\": [[0, 1]], \"winners\": [2], \"losers\": [8], \"carry\": null, \"fold_order\": [2], \"comparisons\": 1}, \"passed\": true}, {\"check\": \"regression certificate 4\", \"actual\": {\"pairs\": [[0, 1], [1, 2]], \"winners\": [7], \"losers\": [4], \"carry\": 1, \"fold_order\": [1, 7], \"comparisons\": 2}, \"expected\": {\"pairs\": [[0, 1]], \"winners\": [7], \"losers\": [4], \"carry\": 1, \"fold_order\": [1, 7], \"comparisons\": 2}, \"passed\": false}, {\"check\": \"regression certificate 5\", \"actual\": {\"pairs\": [[0, 1], [1, 2], [2, 3]], \"winners\": [4, 9], \"losers\": [7, 1], \"carry\": null, \"fold_order\": [9, 4], \"comparisons\": 3}, \"expected\": {\"pairs\": [[0, 1], [2, 3]], \"winners\": [4, 9], \"losers\": [7, 1], \"carry\": null, \"fold_order\": [9, 4], \"comparisons\": 3}, \"passed\": false}, {\"check\": \"regression certificate 6\", \"actual\": {\"pairs\": [[0, 1], [1, 2], [2, 3], [3, 4], [4, 5]], \"winners\": [8, 6, 5], \"losers\": [9, 7, 4], \"carry\": null, \"fold_order\": [5, 6, 8], \"comparisons\": 5}, \"expected\": {\"pairs\": [[0, 1], [2, 3], [4, 5]], \"winners\": [8, 6, 5], \"losers\": [9, 7, 4], \"carry\": null, \"fold_order\": [5, 6, 8], \"comparisons\": 5}, \"passed\": false}, {\"check\": \"variant-dependent certificate\", \"actual\": {\"pairs\": [[0, 1], [1, 2], [2, 3], [3, 4], [4, 5], [5, 6]], \"winners\": [8, 6, 5], \"losers\": [9, 7, 4], \"carry\": 100, \"fold_order\": [100, 5, 6, 8], \"comparisons\": 6}, \"expected\": {\"pairs\": [[0, 1], [2, 3], [4, 5]], \"winners\": [8, 6, 5], \"losers\": [9, 7, 4], \"carry\": 100, \"fold_order\": [100, 5, 6, 8], \"comparisons\": 6}, \"passed\": false}], \"passed\": false}\n"},"fixed":{"elapsed_ms":44.986,"exit_code":0,"observations":[{"actual":{"carry":null,"comparisons":0,"fold_order":[],"losers":[],"pairs":[],"winners":[]},"check":"regression certificate 1","expected":{"carry":null,"comparisons":0,"fold_order":[],"losers":[],"pairs":[],"winners":[]},"passed":true},{"actual":{"carry":8,"comparisons":0,"fold_order":[8],"losers":[],"pairs":[],"winners":[]},"check":"regression certificate 2","expected":{"carry":8,"comparisons":0,"fold_order":[8],"losers":[],"pairs":[],"winners":[]},"passed":true},{"actual":{"carry":null,"comparisons":1,"fold_order":[2],"losers":[8],"pairs":[[0,1]],"winners":[2]},"check":"regression certificate 3","expected":{"carry":null,"comparisons":1,"fold_order":[2],"losers":[8],"pairs":[[0,1]],"winners":[2]},"passed":true},{"actual":{"carry":1,"comparisons":2,"fold_order":[1,7],"losers":[4],"pairs":[[0,1]],"winners":[7]},"check":"regression certificate 4","expected":{"carry":1,"comparisons":2,"fold_order":[1,7],"losers":[4],"pairs":[[0,1]],"winners":[7]},"passed":true},{"actual":{"carry":null,"comparisons":3,"fold_order":[9,4],"losers":[7,1],"pairs":[[0,1],[2,3]],"winners":[4,9]},"check":"regression certificate 5","expected":{"carry":null,"comparisons":3,"fold_order":[9,4],"losers":[7,1],"pairs":[[0,1],[2,3]],"winners":[4,9]},"passed":true},{"actual":{"carry":null,"comparisons":5,"fold_order":[5,6,8],"losers":[9,7,4],"pairs":[[0,1],[2,3],[4,5]],"winners":[8,6,5]},"check":"regression certificate 6","expected":{"carry":null,"comparisons":5,"fold_order":[5,6,8],"losers":[9,7,4],"pairs":[[0,1],[2,3],[4,5]],"winners":[8,6,5]},"passed":true},{"actual":{"carry":100,"comparisons":6,"fold_order":[100,5,6,8],"losers":[9,7,4],"pairs":[[0,1],[2,3],[4,5]],"winners":[8,6,5]},"check":"variant-dependent certificate","expected":{"carry":100,"comparisons":6,"fold_order":[100,5,6,8],"losers":[9,7,4],"pairs":[[0,1],[2,3],[4,5]],"winners":[8,6,5]},"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression certificate 1\", \"actual\": {\"pairs\": [], \"winners\": [], \"losers\": [], \"carry\": null, \"fold_order\": [], \"comparisons\": 0}, \"expected\": {\"pairs\": [], \"winners\": [], \"losers\": [], \"carry\": null, \"fold_order\": [], \"comparisons\": 0}, \"passed\": true}, {\"check\": \"regression certificate 2\", \"actual\": {\"pairs\": [], \"winners\": [], \"losers\": [], \"carry\": 8, \"fold_order\": [8], \"comparisons\": 0}, \"expected\": {\"pairs\": [], \"winners\": [], \"losers\": [], \"carry\": 8, \"fold_order\": [8], \"comparisons\": 0}, \"passed\": true}, {\"check\": \"regression certificate 3\", \"actual\": {\"pairs\": [[0, 1]], \"winners\": [2], \"losers\": [8], \"carry\": null, \"fold_order\": [2], \"comparisons\": 1}, \"expected\": {\"pairs\": [[0, 1]], \"winners\": [2], \"losers\": [8], \"carry\": null, \"fold_order\": [2], \"comparisons\": 1}, \"passed\": true}, {\"check\": \"regression certificate 4\", \"actual\": {\"pairs\": [[0, 1]], \"winners\": [7], \"losers\": [4], \"carry\": 1, \"fold_order\": [1, 7], \"comparisons\": 2}, \"expected\": {\"pairs\": [[0, 1]], \"winners\": [7], \"losers\": [4], \"carry\": 1, \"fold_order\": [1, 7], \"comparisons\": 2}, \"passed\": true}, {\"check\": \"regression certificate 5\", \"actual\": {\"pairs\": [[0, 1], [2, 3]], \"winners\": [4, 9], \"losers\": [7, 1], \"carry\": null, \"fold_order\": [9, 4], \"comparisons\": 3}, \"expected\": {\"pairs\": [[0, 1], [2, 3]], \"winners\": [4, 9], \"losers\": [7, 1], \"carry\": null, \"fold_order\": [9, 4], \"comparisons\": 3}, \"passed\": true}, {\"check\": \"regression certificate 6\", \"actual\": {\"pairs\": [[0, 1], [2, 3], [4, 5]], \"winners\": [8, 6, 5], \"losers\": [9, 7, 4], \"carry\": null, \"fold_order\": [5, 6, 8], \"comparisons\": 5}, \"expected\": {\"pairs\": [[0, 1], [2, 3], [4, 5]], \"winners\": [8, 6, 5], \"losers\": [9, 7, 4], \"carry\": null, \"fold_order\": [5, 6, 8], \"comparisons\": 5}, \"passed\": true}, {\"check\": \"variant-dependent certificate\", \"actual\": {\"pairs\": [[0, 1], [2, 3], [4, 5]], \"winners\": [8, 6, 5], \"losers\": [9, 7, 4], \"carry\": 100, \"fold_order\": [100, 5, 6, 8], \"comparisons\": 6}, \"expected\": {\"pairs\": [[0, 1], [2, 3], [4, 5]], \"winners\": [8, 6, 5], \"losers\": [9, 7, 4], \"carry\": 100, \"fold_order\": [100, 5, 6, 8], \"comparisons\": 6}, \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}