{"abstract":"The bounded minmax levels certificate reports an incorrect min violations.","category":"Heap invariants","checks":7,"contract":"A min-max heap certificate is a complete zero-based binary array. Even depth is a minimum level, odd depth a maximum level. Report level parities, grandparent indices, minimum-level grandchild violations, maximum-level grandchild violations, maximum endpoint, and immediate-child level alternation pairs. Empty maximum is None.","evaluation_group":"s3-heap-model-minmax-levels","failed_approach":"The local patch uses [[i,j] for i in range(n) if depth(i)%2==0 for j in grandchildren(i) if a[j]<=a[i]] and still violates the stated relation.","family":"s3-heap-minmax-levels-min_violations","id":"FA-40391","implementations":{"attempt":{"sha256":"0fdce6aee3b18c6d79004aeb6ac3d3f8209887edbd0a2dc53f1e11cfce5275a8","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(d):\n    a=d['keys']; n=len(a)\n    def depth(i): return (i+1).bit_length()-1\n    def grandchildren(i): return [j for j in range(4*i+3,4*i+7) if j<n]\n    return {'parity': [depth(i)%2 for i in range(n)],\n    'grandparents': [None if i<3 else (i-3)//4 for i in range(n)],\n    'min_violations': [[i,j] for i in range(n) if depth(i)%2==0 for j in grandchildren(i) if a[j]<=a[i]],\n    'max_violations': [[i,j] for i in range(n) if depth(i)%2==1 for j in grandchildren(i) if a[j]>a[i]],\n    'maximum': None if not a else max(a[1:3] or a),\n    'edges': [[i,j] for i in range(n) for j in (2*i+1,2*i+2) if j<n]}\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncases = [[({'keys': []}, {'parity': [], 'grandparents': [], 'min_violations': [], 'max_violations': [], 'maximum': None, 'edges': []}), ({'keys': [4]}, {'parity': [0], 'grandparents': [None], 'min_violations': [], 'max_violations': [], 'maximum': 4, 'edges': []}), ({'keys': [1, 8, 9]}, {'parity': [0, 1, 1], 'grandparents': [None, None, None], 'min_violations': [], 'max_violations': [], 'maximum': 9, 'edges': [[0, 1], [0, 2]]}), ({'keys': [2, 9, 8, 3, 2, 4, 7]}, {'parity': [0, 1, 1, 0, 0, 0, 0], 'grandparents': [None, None, None, 0, 0, 0, 0], 'min_violations': [], 'max_violations': [], 'maximum': 9, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6]]}), ({'keys': [5, 4, 9, 1, 8, 2, 6, 10, 3, 8, 7, 6, 5, 4, 3]}, {'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'min_violations': [[0, 3], [0, 5]], 'max_violations': [[1, 7], [1, 9], [1, 10]], 'maximum': 9, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]}), ({'keys': [0, 7, 8, 2, 3, 1, 4, 7, 7, 7, 9, 8, 8, 8, 8]}, {'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'min_violations': [], 'max_violations': [[1, 10]], 'maximum': 8, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]}), ({'keys': [0, 8, 8, 2, 3, 1, 4, 7, 7, 7, 9, 8, 8, 8, 8]}, {'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'min_violations': [], 'max_violations': [[1, 10]], 'maximum': 8, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]})], [({'keys': []}, {'parity': [], 'grandparents': [], 'min_violations': [], 'max_violations': [], 'maximum': None, 'edges': []}), ({'keys': [4]}, {'parity': [0], 'grandparents': [None], 'min_violations': [], 'max_violations': [], 'maximum': 4, 'edges': []}), ({'keys': [1, 8, 9]}, {'parity': [0, 1, 1], 'grandparents': [None, None, None], 'min_violations': [], 'max_violations': [], 'maximum': 9, 'edges': [[0, 1], [0, 2]]}), ({'keys': [2, 9, 8, 3, 2, 4, 7]}, {'parity': [0, 1, 1, 0, 0, 0, 0], 'grandparents': [None, None, None, 0, 0, 0, 0], 'min_violations': [], 'max_violations': [], 'maximum': 9, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6]]}), ({'keys': [5, 4, 9, 1, 8, 2, 6, 10, 3, 8, 7, 6, 5, 4, 3]}, {'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'min_violations': [[0, 3], [0, 5]], 'max_violations': [[1, 7], [1, 9], [1, 10]], 'maximum': 9, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]}), ({'keys': [0, 7, 8, 2, 3, 1, 4, 7, 7, 7, 9, 8, 8, 8, 8]}, {'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'min_violations': [], 'max_violations': [[1, 10]], 'maximum': 8, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]}), ({'keys': [0, 9, 8, 2, 3, 1, 4, 7, 7, 7, 9, 8, 8, 8, 8]}, {'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'min_violations': [], 'max_violations': [], 'maximum': 9, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]})], [({'keys': []}, {'parity': [], 'grandparents': [], 'min_violations': [], 'max_violations': [], 'maximum': None, 'edges': []}), ({'keys': [4]}, {'parity': [0], 'grandparents': [None], 'min_violations': [], 'max_violations': [], 'maximum': 4, 'edges': []}), ({'keys': [1, 8, 9]}, {'parity': [0, 1, 1], 'grandparents': [None, None, None], 'min_violations': [], 'max_violations': [], 'maximum': 9, 'edges': [[0, 1], [0, 2]]}), ({'keys': [2, 9, 8, 3, 2, 4, 7]}, {'parity': [0, 1, 1, 0, 0, 0, 0], 'grandparents': [None, None, None, 0, 0, 0, 0], 'min_violations': [], 'max_violations': [], 'maximum': 9, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6]]}), ({'keys': [5, 4, 9, 1, 8, 2, 6, 10, 3, 8, 7, 6, 5, 4, 3]}, {'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'min_violations': [[0, 3], [0, 5]], 'max_violations': [[1, 7], [1, 9], [1, 10]], 'maximum': 9, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]}), ({'keys': [0, 7, 8, 2, 3, 1, 4, 7, 7, 7, 9, 8, 8, 8, 8]}, {'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'min_violations': [], 'max_violations': [[1, 10]], 'maximum': 8, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]}), ({'keys': [0, 10, 8, 2, 3, 1, 4, 7, 7, 7, 9, 8, 8, 8, 8]}, {'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'min_violations': [], 'max_violations': [], 'maximum': 10, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]})], [({'keys': []}, {'parity': [], 'grandparents': [], 'min_violations': [], 'max_violations': [], 'maximum': None, 'edges': []}), ({'keys': [4]}, {'parity': [0], 'grandparents': [None], 'min_violations': [], 'max_violations': [], 'maximum': 4, 'edges': []}), ({'keys': [1, 8, 9]}, {'parity': [0, 1, 1], 'grandparents': [None, None, None], 'min_violations': [], 'max_violations': [], 'maximum': 9, 'edges': [[0, 1], [0, 2]]}), ({'keys': [2, 9, 8, 3, 2, 4, 7]}, {'parity': [0, 1, 1, 0, 0, 0, 0], 'grandparents': [None, None, None, 0, 0, 0, 0], 'min_violations': [], 'max_violations': [], 'maximum': 9, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6]]}), ({'keys': [5, 4, 9, 1, 8, 2, 6, 10, 3, 8, 7, 6, 5, 4, 3]}, {'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'min_violations': [[0, 3], [0, 5]], 'max_violations': [[1, 7], [1, 9], [1, 10]], 'maximum': 9, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]}), ({'keys': [0, 7, 8, 2, 3, 1, 4, 7, 7, 7, 9, 8, 8, 8, 8]}, {'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'min_violations': [], 'max_violations': [[1, 10]], 'maximum': 8, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]}), ({'keys': [0, 11, 8, 2, 3, 1, 4, 7, 7, 7, 9, 8, 8, 8, 8]}, {'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'min_violations': [], 'max_violations': [], 'maximum': 11, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]})], [({'keys': []}, {'parity': [], 'grandparents': [], 'min_violations': [], 'max_violations': [], 'maximum': None, 'edges': []}), ({'keys': [4]}, {'parity': [0], 'grandparents': [None], 'min_violations': [], 'max_violations': [], 'maximum': 4, 'edges': []}), ({'keys': [1, 8, 9]}, {'parity': [0, 1, 1], 'grandparents': [None, None, None], 'min_violations': [], 'max_violations': [], 'maximum': 9, 'edges': [[0, 1], [0, 2]]}), ({'keys': [2, 9, 8, 3, 2, 4, 7]}, {'parity': [0, 1, 1, 0, 0, 0, 0], 'grandparents': [None, None, None, 0, 0, 0, 0], 'min_violations': [], 'max_violations': [], 'maximum': 9, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6]]}), ({'keys': [5, 4, 9, 1, 8, 2, 6, 10, 3, 8, 7, 6, 5, 4, 3]}, {'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'min_violations': [[0, 3], [0, 5]], 'max_violations': [[1, 7], [1, 9], [1, 10]], 'maximum': 9, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]}), ({'keys': [0, 7, 8, 2, 3, 1, 4, 7, 7, 7, 9, 8, 8, 8, 8]}, {'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'min_violations': [], 'max_violations': [[1, 10]], 'maximum': 8, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]}), ({'keys': [0, 12, 8, 2, 3, 1, 4, 7, 7, 7, 9, 8, 8, 8, 8]}, {'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'min_violations': [], 'max_violations': [], 'maximum': 12, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]})]][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":"d69eefd7ebe2303404d511de13741f197ba8a447866c10da653c334a163efdb1","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(d):\n    a=d['keys']; n=len(a)\n    def depth(i): return (i+1).bit_length()-1\n    def grandchildren(i): return [j for j in range(4*i+3,4*i+7) if j<n]\n    return {'parity': [depth(i)%2 for i in range(n)],\n    'grandparents': [None if i<3 else (i-3)//4 for i in range(n)],\n    'min_violations': [[i,j] for i in range(n) if depth(i)%2==1 for j in grandchildren(i) if a[j]<a[i]],\n    'max_violations': [[i,j] for i in range(n) if depth(i)%2==1 for j in grandchildren(i) if a[j]>a[i]],\n    'maximum': None if not a else max(a[1:3] or a),\n    'edges': [[i,j] for i in range(n) for j in (2*i+1,2*i+2) if j<n]}\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncases = [[({'keys': []}, {'parity': [], 'grandparents': [], 'min_violations': [], 'max_violations': [], 'maximum': None, 'edges': []}), ({'keys': [4]}, {'parity': [0], 'grandparents': [None], 'min_violations': [], 'max_violations': [], 'maximum': 4, 'edges': []}), ({'keys': [1, 8, 9]}, {'parity': [0, 1, 1], 'grandparents': [None, None, None], 'min_violations': [], 'max_violations': [], 'maximum': 9, 'edges': [[0, 1], [0, 2]]}), ({'keys': [2, 9, 8, 3, 2, 4, 7]}, {'parity': [0, 1, 1, 0, 0, 0, 0], 'grandparents': [None, None, None, 0, 0, 0, 0], 'min_violations': [], 'max_violations': [], 'maximum': 9, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6]]}), ({'keys': [5, 4, 9, 1, 8, 2, 6, 10, 3, 8, 7, 6, 5, 4, 3]}, {'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'min_violations': [[0, 3], [0, 5]], 'max_violations': [[1, 7], [1, 9], [1, 10]], 'maximum': 9, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]}), ({'keys': [0, 7, 8, 2, 3, 1, 4, 7, 7, 7, 9, 8, 8, 8, 8]}, {'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'min_violations': [], 'max_violations': [[1, 10]], 'maximum': 8, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]}), ({'keys': [0, 8, 8, 2, 3, 1, 4, 7, 7, 7, 9, 8, 8, 8, 8]}, {'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'min_violations': [], 'max_violations': [[1, 10]], 'maximum': 8, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]})], [({'keys': []}, {'parity': [], 'grandparents': [], 'min_violations': [], 'max_violations': [], 'maximum': None, 'edges': []}), ({'keys': [4]}, {'parity': [0], 'grandparents': [None], 'min_violations': [], 'max_violations': [], 'maximum': 4, 'edges': []}), ({'keys': [1, 8, 9]}, {'parity': [0, 1, 1], 'grandparents': [None, None, None], 'min_violations': [], 'max_violations': [], 'maximum': 9, 'edges': [[0, 1], [0, 2]]}), ({'keys': [2, 9, 8, 3, 2, 4, 7]}, {'parity': [0, 1, 1, 0, 0, 0, 0], 'grandparents': [None, None, None, 0, 0, 0, 0], 'min_violations': [], 'max_violations': [], 'maximum': 9, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6]]}), ({'keys': [5, 4, 9, 1, 8, 2, 6, 10, 3, 8, 7, 6, 5, 4, 3]}, {'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'min_violations': [[0, 3], [0, 5]], 'max_violations': [[1, 7], [1, 9], [1, 10]], 'maximum': 9, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]}), ({'keys': [0, 7, 8, 2, 3, 1, 4, 7, 7, 7, 9, 8, 8, 8, 8]}, {'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'min_violations': [], 'max_violations': [[1, 10]], 'maximum': 8, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]}), ({'keys': [0, 9, 8, 2, 3, 1, 4, 7, 7, 7, 9, 8, 8, 8, 8]}, {'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'min_violations': [], 'max_violations': [], 'maximum': 9, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]})], [({'keys': []}, {'parity': [], 'grandparents': [], 'min_violations': [], 'max_violations': [], 'maximum': None, 'edges': []}), ({'keys': [4]}, {'parity': [0], 'grandparents': [None], 'min_violations': [], 'max_violations': [], 'maximum': 4, 'edges': []}), ({'keys': [1, 8, 9]}, {'parity': [0, 1, 1], 'grandparents': [None, None, None], 'min_violations': [], 'max_violations': [], 'maximum': 9, 'edges': [[0, 1], [0, 2]]}), ({'keys': [2, 9, 8, 3, 2, 4, 7]}, {'parity': [0, 1, 1, 0, 0, 0, 0], 'grandparents': [None, None, None, 0, 0, 0, 0], 'min_violations': [], 'max_violations': [], 'maximum': 9, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6]]}), ({'keys': [5, 4, 9, 1, 8, 2, 6, 10, 3, 8, 7, 6, 5, 4, 3]}, {'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'min_violations': [[0, 3], [0, 5]], 'max_violations': [[1, 7], [1, 9], [1, 10]], 'maximum': 9, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]}), ({'keys': [0, 7, 8, 2, 3, 1, 4, 7, 7, 7, 9, 8, 8, 8, 8]}, {'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'min_violations': [], 'max_violations': [[1, 10]], 'maximum': 8, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]}), ({'keys': [0, 10, 8, 2, 3, 1, 4, 7, 7, 7, 9, 8, 8, 8, 8]}, {'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'min_violations': [], 'max_violations': [], 'maximum': 10, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]})], [({'keys': []}, {'parity': [], 'grandparents': [], 'min_violations': [], 'max_violations': [], 'maximum': None, 'edges': []}), ({'keys': [4]}, {'parity': [0], 'grandparents': [None], 'min_violations': [], 'max_violations': [], 'maximum': 4, 'edges': []}), ({'keys': [1, 8, 9]}, {'parity': [0, 1, 1], 'grandparents': [None, None, None], 'min_violations': [], 'max_violations': [], 'maximum': 9, 'edges': [[0, 1], [0, 2]]}), ({'keys': [2, 9, 8, 3, 2, 4, 7]}, {'parity': [0, 1, 1, 0, 0, 0, 0], 'grandparents': [None, None, None, 0, 0, 0, 0], 'min_violations': [], 'max_violations': [], 'maximum': 9, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6]]}), ({'keys': [5, 4, 9, 1, 8, 2, 6, 10, 3, 8, 7, 6, 5, 4, 3]}, {'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'min_violations': [[0, 3], [0, 5]], 'max_violations': [[1, 7], [1, 9], [1, 10]], 'maximum': 9, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]}), ({'keys': [0, 7, 8, 2, 3, 1, 4, 7, 7, 7, 9, 8, 8, 8, 8]}, {'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'min_violations': [], 'max_violations': [[1, 10]], 'maximum': 8, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]}), ({'keys': [0, 11, 8, 2, 3, 1, 4, 7, 7, 7, 9, 8, 8, 8, 8]}, {'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'min_violations': [], 'max_violations': [], 'maximum': 11, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]})], [({'keys': []}, {'parity': [], 'grandparents': [], 'min_violations': [], 'max_violations': [], 'maximum': None, 'edges': []}), ({'keys': [4]}, {'parity': [0], 'grandparents': [None], 'min_violations': [], 'max_violations': [], 'maximum': 4, 'edges': []}), ({'keys': [1, 8, 9]}, {'parity': [0, 1, 1], 'grandparents': [None, None, None], 'min_violations': [], 'max_violations': [], 'maximum': 9, 'edges': [[0, 1], [0, 2]]}), ({'keys': [2, 9, 8, 3, 2, 4, 7]}, {'parity': [0, 1, 1, 0, 0, 0, 0], 'grandparents': [None, None, None, 0, 0, 0, 0], 'min_violations': [], 'max_violations': [], 'maximum': 9, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6]]}), ({'keys': [5, 4, 9, 1, 8, 2, 6, 10, 3, 8, 7, 6, 5, 4, 3]}, {'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'min_violations': [[0, 3], [0, 5]], 'max_violations': [[1, 7], [1, 9], [1, 10]], 'maximum': 9, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]}), ({'keys': [0, 7, 8, 2, 3, 1, 4, 7, 7, 7, 9, 8, 8, 8, 8]}, {'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'min_violations': [], 'max_violations': [[1, 10]], 'maximum': 8, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]}), ({'keys': [0, 12, 8, 2, 3, 1, 4, 7, 7, 7, 9, 8, 8, 8, 8]}, {'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'min_violations': [], 'max_violations': [], 'maximum': 12, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]})]][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":"6cdf3075ba45f3441d9cc01e779db03bdb44f414ee457672e010befa88b92b90","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(d):\n    a=d['keys']; n=len(a)\n    def depth(i): return (i+1).bit_length()-1\n    def grandchildren(i): return [j for j in range(4*i+3,4*i+7) if j<n]\n    return {'parity': [depth(i)%2 for i in range(n)],\n    'grandparents': [None if i<3 else (i-3)//4 for i in range(n)],\n    'min_violations': [[i,j] for i in range(n) if depth(i)%2==0 for j in grandchildren(i) if a[j]<a[i]],\n    'max_violations': [[i,j] for i in range(n) if depth(i)%2==1 for j in grandchildren(i) if a[j]>a[i]],\n    'maximum': None if not a else max(a[1:3] or a),\n    'edges': [[i,j] for i in range(n) for j in (2*i+1,2*i+2) if j<n]}\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncases = [[({'keys': []}, {'parity': [], 'grandparents': [], 'min_violations': [], 'max_violations': [], 'maximum': None, 'edges': []}), ({'keys': [4]}, {'parity': [0], 'grandparents': [None], 'min_violations': [], 'max_violations': [], 'maximum': 4, 'edges': []}), ({'keys': [1, 8, 9]}, {'parity': [0, 1, 1], 'grandparents': [None, None, None], 'min_violations': [], 'max_violations': [], 'maximum': 9, 'edges': [[0, 1], [0, 2]]}), ({'keys': [2, 9, 8, 3, 2, 4, 7]}, {'parity': [0, 1, 1, 0, 0, 0, 0], 'grandparents': [None, None, None, 0, 0, 0, 0], 'min_violations': [], 'max_violations': [], 'maximum': 9, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6]]}), ({'keys': [5, 4, 9, 1, 8, 2, 6, 10, 3, 8, 7, 6, 5, 4, 3]}, {'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'min_violations': [[0, 3], [0, 5]], 'max_violations': [[1, 7], [1, 9], [1, 10]], 'maximum': 9, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]}), ({'keys': [0, 7, 8, 2, 3, 1, 4, 7, 7, 7, 9, 8, 8, 8, 8]}, {'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'min_violations': [], 'max_violations': [[1, 10]], 'maximum': 8, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]}), ({'keys': [0, 8, 8, 2, 3, 1, 4, 7, 7, 7, 9, 8, 8, 8, 8]}, {'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'min_violations': [], 'max_violations': [[1, 10]], 'maximum': 8, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]})], [({'keys': []}, {'parity': [], 'grandparents': [], 'min_violations': [], 'max_violations': [], 'maximum': None, 'edges': []}), ({'keys': [4]}, {'parity': [0], 'grandparents': [None], 'min_violations': [], 'max_violations': [], 'maximum': 4, 'edges': []}), ({'keys': [1, 8, 9]}, {'parity': [0, 1, 1], 'grandparents': [None, None, None], 'min_violations': [], 'max_violations': [], 'maximum': 9, 'edges': [[0, 1], [0, 2]]}), ({'keys': [2, 9, 8, 3, 2, 4, 7]}, {'parity': [0, 1, 1, 0, 0, 0, 0], 'grandparents': [None, None, None, 0, 0, 0, 0], 'min_violations': [], 'max_violations': [], 'maximum': 9, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6]]}), ({'keys': [5, 4, 9, 1, 8, 2, 6, 10, 3, 8, 7, 6, 5, 4, 3]}, {'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'min_violations': [[0, 3], [0, 5]], 'max_violations': [[1, 7], [1, 9], [1, 10]], 'maximum': 9, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]}), ({'keys': [0, 7, 8, 2, 3, 1, 4, 7, 7, 7, 9, 8, 8, 8, 8]}, {'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'min_violations': [], 'max_violations': [[1, 10]], 'maximum': 8, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]}), ({'keys': [0, 9, 8, 2, 3, 1, 4, 7, 7, 7, 9, 8, 8, 8, 8]}, {'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'min_violations': [], 'max_violations': [], 'maximum': 9, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]})], [({'keys': []}, {'parity': [], 'grandparents': [], 'min_violations': [], 'max_violations': [], 'maximum': None, 'edges': []}), ({'keys': [4]}, {'parity': [0], 'grandparents': [None], 'min_violations': [], 'max_violations': [], 'maximum': 4, 'edges': []}), ({'keys': [1, 8, 9]}, {'parity': [0, 1, 1], 'grandparents': [None, None, None], 'min_violations': [], 'max_violations': [], 'maximum': 9, 'edges': [[0, 1], [0, 2]]}), ({'keys': [2, 9, 8, 3, 2, 4, 7]}, {'parity': [0, 1, 1, 0, 0, 0, 0], 'grandparents': [None, None, None, 0, 0, 0, 0], 'min_violations': [], 'max_violations': [], 'maximum': 9, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6]]}), ({'keys': [5, 4, 9, 1, 8, 2, 6, 10, 3, 8, 7, 6, 5, 4, 3]}, {'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'min_violations': [[0, 3], [0, 5]], 'max_violations': [[1, 7], [1, 9], [1, 10]], 'maximum': 9, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]}), ({'keys': [0, 7, 8, 2, 3, 1, 4, 7, 7, 7, 9, 8, 8, 8, 8]}, {'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'min_violations': [], 'max_violations': [[1, 10]], 'maximum': 8, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]}), ({'keys': [0, 10, 8, 2, 3, 1, 4, 7, 7, 7, 9, 8, 8, 8, 8]}, {'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'min_violations': [], 'max_violations': [], 'maximum': 10, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]})], [({'keys': []}, {'parity': [], 'grandparents': [], 'min_violations': [], 'max_violations': [], 'maximum': None, 'edges': []}), ({'keys': [4]}, {'parity': [0], 'grandparents': [None], 'min_violations': [], 'max_violations': [], 'maximum': 4, 'edges': []}), ({'keys': [1, 8, 9]}, {'parity': [0, 1, 1], 'grandparents': [None, None, None], 'min_violations': [], 'max_violations': [], 'maximum': 9, 'edges': [[0, 1], [0, 2]]}), ({'keys': [2, 9, 8, 3, 2, 4, 7]}, {'parity': [0, 1, 1, 0, 0, 0, 0], 'grandparents': [None, None, None, 0, 0, 0, 0], 'min_violations': [], 'max_violations': [], 'maximum': 9, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6]]}), ({'keys': [5, 4, 9, 1, 8, 2, 6, 10, 3, 8, 7, 6, 5, 4, 3]}, {'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'min_violations': [[0, 3], [0, 5]], 'max_violations': [[1, 7], [1, 9], [1, 10]], 'maximum': 9, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]}), ({'keys': [0, 7, 8, 2, 3, 1, 4, 7, 7, 7, 9, 8, 8, 8, 8]}, {'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'min_violations': [], 'max_violations': [[1, 10]], 'maximum': 8, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]}), ({'keys': [0, 11, 8, 2, 3, 1, 4, 7, 7, 7, 9, 8, 8, 8, 8]}, {'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'min_violations': [], 'max_violations': [], 'maximum': 11, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]})], [({'keys': []}, {'parity': [], 'grandparents': [], 'min_violations': [], 'max_violations': [], 'maximum': None, 'edges': []}), ({'keys': [4]}, {'parity': [0], 'grandparents': [None], 'min_violations': [], 'max_violations': [], 'maximum': 4, 'edges': []}), ({'keys': [1, 8, 9]}, {'parity': [0, 1, 1], 'grandparents': [None, None, None], 'min_violations': [], 'max_violations': [], 'maximum': 9, 'edges': [[0, 1], [0, 2]]}), ({'keys': [2, 9, 8, 3, 2, 4, 7]}, {'parity': [0, 1, 1, 0, 0, 0, 0], 'grandparents': [None, None, None, 0, 0, 0, 0], 'min_violations': [], 'max_violations': [], 'maximum': 9, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6]]}), ({'keys': [5, 4, 9, 1, 8, 2, 6, 10, 3, 8, 7, 6, 5, 4, 3]}, {'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'min_violations': [[0, 3], [0, 5]], 'max_violations': [[1, 7], [1, 9], [1, 10]], 'maximum': 9, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]}), ({'keys': [0, 7, 8, 2, 3, 1, 4, 7, 7, 7, 9, 8, 8, 8, 8]}, {'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'min_violations': [], 'max_violations': [[1, 10]], 'maximum': 8, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]}), ({'keys': [0, 12, 8, 2, 3, 1, 4, 7, 7, 7, 9, 8, 8, 8, 8]}, {'parity': [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], 'grandparents': [None, None, None, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], 'min_violations': [], 'max_violations': [], 'maximum': 12, 'edges': [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]})]][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-minmax-levels-min_violations","generated_at":"2026-09-29T14:43:30.758788+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 min violations using [[i,j] for i in range(n) if depth(i)%2==0 for j in grandchildren(i) if a[j]<a[i]] under the stated bounded certificate contract.","root_cause":"Min-level bubbling compares grandchildren and allows equal priorities.","sha256":"476d6eab05fded399d124233d302ae875e4ddbdb326fb71019fe8f94ca644c7e","title":"Min-level bubbling compares grandchildren and allows equal priorities · 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":44.271,"exit_code":1,"observations":[{"actual":{"edges":[],"grandparents":[],"max_violations":[],"maximum":null,"min_violations":[],"parity":[]},"check":"regression certificate 1","expected":{"edges":[],"grandparents":[],"max_violations":[],"maximum":null,"min_violations":[],"parity":[]},"passed":true},{"actual":{"edges":[],"grandparents":[null],"max_violations":[],"maximum":4,"min_violations":[],"parity":[0]},"check":"regression certificate 2","expected":{"edges":[],"grandparents":[null],"max_violations":[],"maximum":4,"min_violations":[],"parity":[0]},"passed":true},{"actual":{"edges":[[0,1],[0,2]],"grandparents":[null,null,null],"max_violations":[],"maximum":9,"min_violations":[],"parity":[0,1,1]},"check":"regression certificate 3","expected":{"edges":[[0,1],[0,2]],"grandparents":[null,null,null],"max_violations":[],"maximum":9,"min_violations":[],"parity":[0,1,1]},"passed":true},{"actual":{"edges":[[0,1],[0,2],[1,3],[1,4],[2,5],[2,6]],"grandparents":[null,null,null,0,0,0,0],"max_violations":[],"maximum":9,"min_violations":[[0,4]],"parity":[0,1,1,0,0,0,0]},"check":"regression certificate 4","expected":{"edges":[[0,1],[0,2],[1,3],[1,4],[2,5],[2,6]],"grandparents":[null,null,null,0,0,0,0],"max_violations":[],"maximum":9,"min_violations":[],"parity":[0,1,1,0,0,0,0]},"passed":false},{"actual":{"edges":[[0,1],[0,2],[1,3],[1,4],[2,5],[2,6],[3,7],[3,8],[4,9],[4,10],[5,11],[5,12],[6,13],[6,14]],"grandparents":[null,null,null,0,0,0,0,1,1,1,1,2,2,2,2],"max_violations":[[1,7],[1,9],[1,10]],"maximum":9,"min_violations":[[0,3],[0,5]],"parity":[0,1,1,0,0,0,0,1,1,1,1,1,1,1,1]},"check":"regression certificate 5","expected":{"edges":[[0,1],[0,2],[1,3],[1,4],[2,5],[2,6],[3,7],[3,8],[4,9],[4,10],[5,11],[5,12],[6,13],[6,14]],"grandparents":[null,null,null,0,0,0,0,1,1,1,1,2,2,2,2],"max_violations":[[1,7],[1,9],[1,10]],"maximum":9,"min_violations":[[0,3],[0,5]],"parity":[0,1,1,0,0,0,0,1,1,1,1,1,1,1,1]},"passed":true},{"actual":{"edges":[[0,1],[0,2],[1,3],[1,4],[2,5],[2,6],[3,7],[3,8],[4,9],[4,10],[5,11],[5,12],[6,13],[6,14]],"grandparents":[null,null,null,0,0,0,0,1,1,1,1,2,2,2,2],"max_violations":[[1,10]],"maximum":8,"min_violations":[],"parity":[0,1,1,0,0,0,0,1,1,1,1,1,1,1,1]},"check":"regression certificate 6","expected":{"edges":[[0,1],[0,2],[1,3],[1,4],[2,5],[2,6],[3,7],[3,8],[4,9],[4,10],[5,11],[5,12],[6,13],[6,14]],"grandparents":[null,null,null,0,0,0,0,1,1,1,1,2,2,2,2],"max_violations":[[1,10]],"maximum":8,"min_violations":[],"parity":[0,1,1,0,0,0,0,1,1,1,1,1,1,1,1]},"passed":true},{"actual":{"edges":[[0,1],[0,2],[1,3],[1,4],[2,5],[2,6],[3,7],[3,8],[4,9],[4,10],[5,11],[5,12],[6,13],[6,14]],"grandparents":[null,null,null,0,0,0,0,1,1,1,1,2,2,2,2],"max_violations":[[1,10]],"maximum":8,"min_violations":[],"parity":[0,1,1,0,0,0,0,1,1,1,1,1,1,1,1]},"check":"variant-dependent certificate","expected":{"edges":[[0,1],[0,2],[1,3],[1,4],[2,5],[2,6],[3,7],[3,8],[4,9],[4,10],[5,11],[5,12],[6,13],[6,14]],"grandparents":[null,null,null,0,0,0,0,1,1,1,1,2,2,2,2],"max_violations":[[1,10]],"maximum":8,"min_violations":[],"parity":[0,1,1,0,0,0,0,1,1,1,1,1,1,1,1]},"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression certificate 1\", \"actual\": {\"parity\": [], \"grandparents\": [], \"min_violations\": [], \"max_violations\": [], \"maximum\": null, \"edges\": []}, \"expected\": {\"parity\": [], \"grandparents\": [], \"min_violations\": [], \"max_violations\": [], \"maximum\": null, \"edges\": []}, \"passed\": true}, {\"check\": \"regression certificate 2\", \"actual\": {\"parity\": [0], \"grandparents\": [null], \"min_violations\": [], \"max_violations\": [], \"maximum\": 4, \"edges\": []}, \"expected\": {\"parity\": [0], \"grandparents\": [null], \"min_violations\": [], \"max_violations\": [], \"maximum\": 4, \"edges\": []}, \"passed\": true}, {\"check\": \"regression certificate 3\", \"actual\": {\"parity\": [0, 1, 1], \"grandparents\": [null, null, null], \"min_violations\": [], \"max_violations\": [], \"maximum\": 9, \"edges\": [[0, 1], [0, 2]]}, \"expected\": {\"parity\": [0, 1, 1], \"grandparents\": [null, null, null], \"min_violations\": [], \"max_violations\": [], \"maximum\": 9, \"edges\": [[0, 1], [0, 2]]}, \"passed\": true}, {\"check\": \"regression certificate 4\", \"actual\": {\"parity\": [0, 1, 1, 0, 0, 0, 0], \"grandparents\": [null, null, null, 0, 0, 0, 0], \"min_violations\": [[0, 4]], \"max_violations\": [], \"maximum\": 9, \"edges\": [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6]]}, \"expected\": {\"parity\": [0, 1, 1, 0, 0, 0, 0], \"grandparents\": [null, null, null, 0, 0, 0, 0], \"min_violations\": [], \"max_violations\": [], \"maximum\": 9, \"edges\": [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6]]}, \"passed\": false}, {\"check\": \"regression certificate 5\", \"actual\": {\"parity\": [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], \"grandparents\": [null, null, null, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], \"min_violations\": [[0, 3], [0, 5]], \"max_violations\": [[1, 7], [1, 9], [1, 10]], \"maximum\": 9, \"edges\": [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]}, \"expected\": {\"parity\": [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], \"grandparents\": [null, null, null, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], \"min_violations\": [[0, 3], [0, 5]], \"max_violations\": [[1, 7], [1, 9], [1, 10]], \"maximum\": 9, \"edges\": [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]}, \"passed\": true}, {\"check\": \"regression certificate 6\", \"actual\": {\"parity\": [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], \"grandparents\": [null, null, null, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], \"min_violations\": [], \"max_violations\": [[1, 10]], \"maximum\": 8, \"edges\": [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]}, \"expected\": {\"parity\": [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], \"grandparents\": [null, null, null, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], \"min_violations\": [], \"max_violations\": [[1, 10]], \"maximum\": 8, \"edges\": [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]}, \"passed\": true}, {\"check\": \"variant-dependent certificate\", \"actual\": {\"parity\": [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], \"grandparents\": [null, null, null, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], \"min_violations\": [], \"max_violations\": [[1, 10]], \"maximum\": 8, \"edges\": [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]}, \"expected\": {\"parity\": [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], \"grandparents\": [null, null, null, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], \"min_violations\": [], \"max_violations\": [[1, 10]], \"maximum\": 8, \"edges\": [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]}, \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":47.545,"exit_code":1,"observations":[{"actual":{"edges":[],"grandparents":[],"max_violations":[],"maximum":null,"min_violations":[],"parity":[]},"check":"regression certificate 1","expected":{"edges":[],"grandparents":[],"max_violations":[],"maximum":null,"min_violations":[],"parity":[]},"passed":true},{"actual":{"edges":[],"grandparents":[null],"max_violations":[],"maximum":4,"min_violations":[],"parity":[0]},"check":"regression certificate 2","expected":{"edges":[],"grandparents":[null],"max_violations":[],"maximum":4,"min_violations":[],"parity":[0]},"passed":true},{"actual":{"edges":[[0,1],[0,2]],"grandparents":[null,null,null],"max_violations":[],"maximum":9,"min_violations":[],"parity":[0,1,1]},"check":"regression certificate 3","expected":{"edges":[[0,1],[0,2]],"grandparents":[null,null,null],"max_violations":[],"maximum":9,"min_violations":[],"parity":[0,1,1]},"passed":true},{"actual":{"edges":[[0,1],[0,2],[1,3],[1,4],[2,5],[2,6]],"grandparents":[null,null,null,0,0,0,0],"max_violations":[],"maximum":9,"min_violations":[],"parity":[0,1,1,0,0,0,0]},"check":"regression certificate 4","expected":{"edges":[[0,1],[0,2],[1,3],[1,4],[2,5],[2,6]],"grandparents":[null,null,null,0,0,0,0],"max_violations":[],"maximum":9,"min_violations":[],"parity":[0,1,1,0,0,0,0]},"passed":true},{"actual":{"edges":[[0,1],[0,2],[1,3],[1,4],[2,5],[2,6],[3,7],[3,8],[4,9],[4,10],[5,11],[5,12],[6,13],[6,14]],"grandparents":[null,null,null,0,0,0,0,1,1,1,1,2,2,2,2],"max_violations":[[1,7],[1,9],[1,10]],"maximum":9,"min_violations":[[1,8],[2,11],[2,12],[2,13],[2,14]],"parity":[0,1,1,0,0,0,0,1,1,1,1,1,1,1,1]},"check":"regression certificate 5","expected":{"edges":[[0,1],[0,2],[1,3],[1,4],[2,5],[2,6],[3,7],[3,8],[4,9],[4,10],[5,11],[5,12],[6,13],[6,14]],"grandparents":[null,null,null,0,0,0,0,1,1,1,1,2,2,2,2],"max_violations":[[1,7],[1,9],[1,10]],"maximum":9,"min_violations":[[0,3],[0,5]],"parity":[0,1,1,0,0,0,0,1,1,1,1,1,1,1,1]},"passed":false},{"actual":{"edges":[[0,1],[0,2],[1,3],[1,4],[2,5],[2,6],[3,7],[3,8],[4,9],[4,10],[5,11],[5,12],[6,13],[6,14]],"grandparents":[null,null,null,0,0,0,0,1,1,1,1,2,2,2,2],"max_violations":[[1,10]],"maximum":8,"min_violations":[],"parity":[0,1,1,0,0,0,0,1,1,1,1,1,1,1,1]},"check":"regression certificate 6","expected":{"edges":[[0,1],[0,2],[1,3],[1,4],[2,5],[2,6],[3,7],[3,8],[4,9],[4,10],[5,11],[5,12],[6,13],[6,14]],"grandparents":[null,null,null,0,0,0,0,1,1,1,1,2,2,2,2],"max_violations":[[1,10]],"maximum":8,"min_violations":[],"parity":[0,1,1,0,0,0,0,1,1,1,1,1,1,1,1]},"passed":true},{"actual":{"edges":[[0,1],[0,2],[1,3],[1,4],[2,5],[2,6],[3,7],[3,8],[4,9],[4,10],[5,11],[5,12],[6,13],[6,14]],"grandparents":[null,null,null,0,0,0,0,1,1,1,1,2,2,2,2],"max_violations":[[1,10]],"maximum":8,"min_violations":[[1,7],[1,8],[1,9]],"parity":[0,1,1,0,0,0,0,1,1,1,1,1,1,1,1]},"check":"variant-dependent certificate","expected":{"edges":[[0,1],[0,2],[1,3],[1,4],[2,5],[2,6],[3,7],[3,8],[4,9],[4,10],[5,11],[5,12],[6,13],[6,14]],"grandparents":[null,null,null,0,0,0,0,1,1,1,1,2,2,2,2],"max_violations":[[1,10]],"maximum":8,"min_violations":[],"parity":[0,1,1,0,0,0,0,1,1,1,1,1,1,1,1]},"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression certificate 1\", \"actual\": {\"parity\": [], \"grandparents\": [], \"min_violations\": [], \"max_violations\": [], \"maximum\": null, \"edges\": []}, \"expected\": {\"parity\": [], \"grandparents\": [], \"min_violations\": [], \"max_violations\": [], \"maximum\": null, \"edges\": []}, \"passed\": true}, {\"check\": \"regression certificate 2\", \"actual\": {\"parity\": [0], \"grandparents\": [null], \"min_violations\": [], \"max_violations\": [], \"maximum\": 4, \"edges\": []}, \"expected\": {\"parity\": [0], \"grandparents\": [null], \"min_violations\": [], \"max_violations\": [], \"maximum\": 4, \"edges\": []}, \"passed\": true}, {\"check\": \"regression certificate 3\", \"actual\": {\"parity\": [0, 1, 1], \"grandparents\": [null, null, null], \"min_violations\": [], \"max_violations\": [], \"maximum\": 9, \"edges\": [[0, 1], [0, 2]]}, \"expected\": {\"parity\": [0, 1, 1], \"grandparents\": [null, null, null], \"min_violations\": [], \"max_violations\": [], \"maximum\": 9, \"edges\": [[0, 1], [0, 2]]}, \"passed\": true}, {\"check\": \"regression certificate 4\", \"actual\": {\"parity\": [0, 1, 1, 0, 0, 0, 0], \"grandparents\": [null, null, null, 0, 0, 0, 0], \"min_violations\": [], \"max_violations\": [], \"maximum\": 9, \"edges\": [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6]]}, \"expected\": {\"parity\": [0, 1, 1, 0, 0, 0, 0], \"grandparents\": [null, null, null, 0, 0, 0, 0], \"min_violations\": [], \"max_violations\": [], \"maximum\": 9, \"edges\": [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6]]}, \"passed\": true}, {\"check\": \"regression certificate 5\", \"actual\": {\"parity\": [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], \"grandparents\": [null, null, null, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], \"min_violations\": [[1, 8], [2, 11], [2, 12], [2, 13], [2, 14]], \"max_violations\": [[1, 7], [1, 9], [1, 10]], \"maximum\": 9, \"edges\": [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]}, \"expected\": {\"parity\": [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], \"grandparents\": [null, null, null, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], \"min_violations\": [[0, 3], [0, 5]], \"max_violations\": [[1, 7], [1, 9], [1, 10]], \"maximum\": 9, \"edges\": [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]}, \"passed\": false}, {\"check\": \"regression certificate 6\", \"actual\": {\"parity\": [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], \"grandparents\": [null, null, null, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], \"min_violations\": [], \"max_violations\": [[1, 10]], \"maximum\": 8, \"edges\": [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]}, \"expected\": {\"parity\": [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], \"grandparents\": [null, null, null, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], \"min_violations\": [], \"max_violations\": [[1, 10]], \"maximum\": 8, 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{\"check\": \"regression certificate 4\", \"actual\": {\"parity\": [0, 1, 1, 0, 0, 0, 0], \"grandparents\": [null, null, null, 0, 0, 0, 0], \"min_violations\": [], \"max_violations\": [], \"maximum\": 9, \"edges\": [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6]]}, \"expected\": {\"parity\": [0, 1, 1, 0, 0, 0, 0], \"grandparents\": [null, null, null, 0, 0, 0, 0], \"min_violations\": [], \"max_violations\": [], \"maximum\": 9, \"edges\": [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6]]}, \"passed\": true}, {\"check\": \"regression certificate 5\", \"actual\": {\"parity\": [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1], \"grandparents\": [null, null, null, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2], \"min_violations\": [[0, 3], [0, 5]], \"max_violations\": [[1, 7], [1, 9], [1, 10]], \"maximum\": 9, \"edges\": [[0, 1], [0, 2], [1, 3], [1, 4], [2, 5], [2, 6], [3, 7], [3, 8], [4, 9], [4, 10], [5, 11], [5, 12], [6, 13], [6, 14]]}, \"expected\": {\"parity\": [0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 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