{"abstract":"The bounded bottomup schedule certificate reports an incorrect leaves.","category":"Heap invariants","checks":7,"contract":"For building a complete zero-based binary heap of n nodes, report descending internal-node repair schedule, leaf indices, level spans as inclusive [start,end], right-child-less internal node, parent dependency edges [child,parent], and number of internal nodes. This describes the build work graph, not sorted output.","evaluation_group":"s3-heap-model-bottomup-schedule","failed_approach":"The local patch uses list(range((n+1)//2,n)) and still violates the stated relation.","family":"s3-heap-bottomup-schedule-leaves","id":"FA-40596","implementations":{"attempt":{"sha256":"9db456534ba9176d7c96f1f791433eeb601d84cc148026b5f7c7771b835cd521","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(d):\n    n=d['size']; internal=list(range(n//2-1,-1,-1)); levels=[]; start=0; width=1\n    while start<n:\n        levels.append([start,min(n-1,start+width-1)]); start+=width; width*=2\n    return {'schedule': internal,\n    'leaves': list(range((n+1)//2,n)),\n    'levels': levels,\n    'unpaired_parent': n//2-1 if n>0 and n%2==0 else None,\n    'dependencies': [[i,(i-1)//2] for i in range(1,n//2)],\n    'internal_count': n//2}\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncases = [[({'size': 0}, {'schedule': [], 'leaves': [], 'levels': [], 'unpaired_parent': None, 'dependencies': [], 'internal_count': 0}), ({'size': 1}, {'schedule': [], 'leaves': [0], 'levels': [[0, 0]], 'unpaired_parent': None, 'dependencies': [], 'internal_count': 0}), ({'size': 2}, {'schedule': [0], 'leaves': [1], 'levels': [[0, 0], [1, 1]], 'unpaired_parent': 0, 'dependencies': [], 'internal_count': 1}), ({'size': 5}, {'schedule': [1, 0], 'leaves': [2, 3, 4], 'levels': [[0, 0], [1, 2], [3, 4]], 'unpaired_parent': None, 'dependencies': [[1, 0]], 'internal_count': 2}), ({'size': 8}, {'schedule': [3, 2, 1, 0], 'leaves': [4, 5, 6, 7], 'levels': [[0, 0], [1, 2], [3, 6], [7, 7]], 'unpaired_parent': 3, 'dependencies': [[1, 0], [2, 0], [3, 1]], 'internal_count': 4}), ({'size': 15}, {'schedule': [6, 5, 4, 3, 2, 1, 0], 'leaves': [7, 8, 9, 10, 11, 12, 13, 14], 'levels': [[0, 0], [1, 2], [3, 6], [7, 14]], 'unpaired_parent': None, 'dependencies': [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2]], 'internal_count': 7}), ({'size': 16}, {'schedule': [7, 6, 5, 4, 3, 2, 1, 0], 'leaves': [8, 9, 10, 11, 12, 13, 14, 15], 'levels': [[0, 0], [1, 2], [3, 6], [7, 14], [15, 15]], 'unpaired_parent': 7, 'dependencies': [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2], [7, 3]], 'internal_count': 8})], [({'size': 0}, {'schedule': [], 'leaves': [], 'levels': [], 'unpaired_parent': None, 'dependencies': [], 'internal_count': 0}), ({'size': 1}, {'schedule': [], 'leaves': [0], 'levels': [[0, 0]], 'unpaired_parent': None, 'dependencies': [], 'internal_count': 0}), ({'size': 2}, {'schedule': [0], 'leaves': [1], 'levels': [[0, 0], [1, 1]], 'unpaired_parent': 0, 'dependencies': [], 'internal_count': 1}), ({'size': 5}, {'schedule': [1, 0], 'leaves': [2, 3, 4], 'levels': [[0, 0], [1, 2], [3, 4]], 'unpaired_parent': None, 'dependencies': [[1, 0]], 'internal_count': 2}), ({'size': 8}, {'schedule': [3, 2, 1, 0], 'leaves': [4, 5, 6, 7], 'levels': [[0, 0], [1, 2], [3, 6], [7, 7]], 'unpaired_parent': 3, 'dependencies': [[1, 0], [2, 0], [3, 1]], 'internal_count': 4}), ({'size': 15}, {'schedule': [6, 5, 4, 3, 2, 1, 0], 'leaves': [7, 8, 9, 10, 11, 12, 13, 14], 'levels': [[0, 0], [1, 2], [3, 6], [7, 14]], 'unpaired_parent': None, 'dependencies': [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2]], 'internal_count': 7}), ({'size': 17}, {'schedule': [7, 6, 5, 4, 3, 2, 1, 0], 'leaves': [8, 9, 10, 11, 12, 13, 14, 15, 16], 'levels': [[0, 0], [1, 2], [3, 6], [7, 14], [15, 16]], 'unpaired_parent': None, 'dependencies': [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2], [7, 3]], 'internal_count': 8})], [({'size': 0}, {'schedule': [], 'leaves': [], 'levels': [], 'unpaired_parent': None, 'dependencies': [], 'internal_count': 0}), ({'size': 1}, {'schedule': [], 'leaves': [0], 'levels': [[0, 0]], 'unpaired_parent': None, 'dependencies': [], 'internal_count': 0}), ({'size': 2}, {'schedule': [0], 'leaves': [1], 'levels': [[0, 0], [1, 1]], 'unpaired_parent': 0, 'dependencies': [], 'internal_count': 1}), ({'size': 5}, {'schedule': [1, 0], 'leaves': [2, 3, 4], 'levels': [[0, 0], [1, 2], [3, 4]], 'unpaired_parent': None, 'dependencies': [[1, 0]], 'internal_count': 2}), ({'size': 8}, {'schedule': [3, 2, 1, 0], 'leaves': [4, 5, 6, 7], 'levels': [[0, 0], [1, 2], [3, 6], [7, 7]], 'unpaired_parent': 3, 'dependencies': [[1, 0], [2, 0], [3, 1]], 'internal_count': 4}), ({'size': 15}, {'schedule': [6, 5, 4, 3, 2, 1, 0], 'leaves': [7, 8, 9, 10, 11, 12, 13, 14], 'levels': [[0, 0], [1, 2], [3, 6], [7, 14]], 'unpaired_parent': None, 'dependencies': [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2]], 'internal_count': 7}), ({'size': 18}, {'schedule': [8, 7, 6, 5, 4, 3, 2, 1, 0], 'leaves': [9, 10, 11, 12, 13, 14, 15, 16, 17], 'levels': [[0, 0], [1, 2], [3, 6], [7, 14], [15, 17]], 'unpaired_parent': 8, 'dependencies': [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2], [7, 3], [8, 3]], 'internal_count': 9})], [({'size': 0}, {'schedule': [], 'leaves': [], 'levels': [], 'unpaired_parent': None, 'dependencies': [], 'internal_count': 0}), ({'size': 1}, {'schedule': [], 'leaves': [0], 'levels': [[0, 0]], 'unpaired_parent': None, 'dependencies': [], 'internal_count': 0}), ({'size': 2}, {'schedule': [0], 'leaves': [1], 'levels': [[0, 0], [1, 1]], 'unpaired_parent': 0, 'dependencies': [], 'internal_count': 1}), ({'size': 5}, {'schedule': [1, 0], 'leaves': [2, 3, 4], 'levels': [[0, 0], [1, 2], [3, 4]], 'unpaired_parent': None, 'dependencies': [[1, 0]], 'internal_count': 2}), ({'size': 8}, {'schedule': [3, 2, 1, 0], 'leaves': [4, 5, 6, 7], 'levels': [[0, 0], [1, 2], [3, 6], [7, 7]], 'unpaired_parent': 3, 'dependencies': [[1, 0], [2, 0], [3, 1]], 'internal_count': 4}), ({'size': 15}, {'schedule': [6, 5, 4, 3, 2, 1, 0], 'leaves': [7, 8, 9, 10, 11, 12, 13, 14], 'levels': [[0, 0], [1, 2], [3, 6], [7, 14]], 'unpaired_parent': None, 'dependencies': [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2]], 'internal_count': 7}), ({'size': 19}, {'schedule': [8, 7, 6, 5, 4, 3, 2, 1, 0], 'leaves': [9, 10, 11, 12, 13, 14, 15, 16, 17, 18], 'levels': [[0, 0], [1, 2], [3, 6], [7, 14], [15, 18]], 'unpaired_parent': None, 'dependencies': [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2], [7, 3], [8, 3]], 'internal_count': 9})], [({'size': 0}, {'schedule': [], 'leaves': [], 'levels': [], 'unpaired_parent': None, 'dependencies': [], 'internal_count': 0}), ({'size': 1}, {'schedule': [], 'leaves': [0], 'levels': [[0, 0]], 'unpaired_parent': None, 'dependencies': [], 'internal_count': 0}), ({'size': 2}, {'schedule': [0], 'leaves': [1], 'levels': [[0, 0], [1, 1]], 'unpaired_parent': 0, 'dependencies': [], 'internal_count': 1}), ({'size': 5}, {'schedule': [1, 0], 'leaves': [2, 3, 4], 'levels': [[0, 0], [1, 2], [3, 4]], 'unpaired_parent': None, 'dependencies': [[1, 0]], 'internal_count': 2}), ({'size': 8}, {'schedule': [3, 2, 1, 0], 'leaves': [4, 5, 6, 7], 'levels': [[0, 0], [1, 2], [3, 6], [7, 7]], 'unpaired_parent': 3, 'dependencies': [[1, 0], [2, 0], [3, 1]], 'internal_count': 4}), ({'size': 15}, {'schedule': [6, 5, 4, 3, 2, 1, 0], 'leaves': [7, 8, 9, 10, 11, 12, 13, 14], 'levels': [[0, 0], [1, 2], [3, 6], [7, 14]], 'unpaired_parent': None, 'dependencies': [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2]], 'internal_count': 7}), ({'size': 20}, {'schedule': [9, 8, 7, 6, 5, 4, 3, 2, 1, 0], 'leaves': [10, 11, 12, 13, 14, 15, 16, 17, 18, 19], 'levels': [[0, 0], [1, 2], [3, 6], [7, 14], [15, 19]], 'unpaired_parent': 9, 'dependencies': [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2], [7, 3], [8, 3], [9, 4]], 'internal_count': 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":"8336c1ffeb8cbd8f1fdfd8a8e9d436803e59588be107927290c45df4775fffea","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(d):\n    n=d['size']; internal=list(range(n//2-1,-1,-1)); levels=[]; start=0; width=1\n    while start<n:\n        levels.append([start,min(n-1,start+width-1)]); start+=width; width*=2\n    return {'schedule': internal,\n    'leaves': list(range(n//2+1,n)),\n    'levels': levels,\n    'unpaired_parent': n//2-1 if n>0 and n%2==0 else None,\n    'dependencies': [[i,(i-1)//2] for i in range(1,n//2)],\n    'internal_count': n//2}\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncases = [[({'size': 0}, {'schedule': [], 'leaves': [], 'levels': [], 'unpaired_parent': None, 'dependencies': [], 'internal_count': 0}), ({'size': 1}, {'schedule': [], 'leaves': [0], 'levels': [[0, 0]], 'unpaired_parent': None, 'dependencies': [], 'internal_count': 0}), ({'size': 2}, {'schedule': [0], 'leaves': [1], 'levels': [[0, 0], [1, 1]], 'unpaired_parent': 0, 'dependencies': [], 'internal_count': 1}), ({'size': 5}, {'schedule': [1, 0], 'leaves': [2, 3, 4], 'levels': [[0, 0], [1, 2], [3, 4]], 'unpaired_parent': None, 'dependencies': [[1, 0]], 'internal_count': 2}), ({'size': 8}, {'schedule': [3, 2, 1, 0], 'leaves': [4, 5, 6, 7], 'levels': [[0, 0], [1, 2], [3, 6], [7, 7]], 'unpaired_parent': 3, 'dependencies': [[1, 0], [2, 0], [3, 1]], 'internal_count': 4}), ({'size': 15}, {'schedule': [6, 5, 4, 3, 2, 1, 0], 'leaves': [7, 8, 9, 10, 11, 12, 13, 14], 'levels': [[0, 0], [1, 2], [3, 6], [7, 14]], 'unpaired_parent': None, 'dependencies': [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2]], 'internal_count': 7}), ({'size': 16}, {'schedule': [7, 6, 5, 4, 3, 2, 1, 0], 'leaves': [8, 9, 10, 11, 12, 13, 14, 15], 'levels': [[0, 0], [1, 2], [3, 6], [7, 14], [15, 15]], 'unpaired_parent': 7, 'dependencies': [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2], [7, 3]], 'internal_count': 8})], [({'size': 0}, {'schedule': [], 'leaves': [], 'levels': [], 'unpaired_parent': None, 'dependencies': [], 'internal_count': 0}), ({'size': 1}, {'schedule': [], 'leaves': [0], 'levels': [[0, 0]], 'unpaired_parent': None, 'dependencies': [], 'internal_count': 0}), ({'size': 2}, {'schedule': [0], 'leaves': [1], 'levels': [[0, 0], [1, 1]], 'unpaired_parent': 0, 'dependencies': [], 'internal_count': 1}), ({'size': 5}, {'schedule': [1, 0], 'leaves': [2, 3, 4], 'levels': [[0, 0], [1, 2], [3, 4]], 'unpaired_parent': None, 'dependencies': [[1, 0]], 'internal_count': 2}), ({'size': 8}, {'schedule': [3, 2, 1, 0], 'leaves': [4, 5, 6, 7], 'levels': [[0, 0], [1, 2], [3, 6], [7, 7]], 'unpaired_parent': 3, 'dependencies': [[1, 0], [2, 0], [3, 1]], 'internal_count': 4}), ({'size': 15}, {'schedule': [6, 5, 4, 3, 2, 1, 0], 'leaves': [7, 8, 9, 10, 11, 12, 13, 14], 'levels': [[0, 0], [1, 2], [3, 6], [7, 14]], 'unpaired_parent': None, 'dependencies': [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2]], 'internal_count': 7}), ({'size': 17}, {'schedule': [7, 6, 5, 4, 3, 2, 1, 0], 'leaves': [8, 9, 10, 11, 12, 13, 14, 15, 16], 'levels': [[0, 0], [1, 2], [3, 6], [7, 14], [15, 16]], 'unpaired_parent': None, 'dependencies': [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2], [7, 3]], 'internal_count': 8})], [({'size': 0}, {'schedule': [], 'leaves': [], 'levels': [], 'unpaired_parent': None, 'dependencies': [], 'internal_count': 0}), ({'size': 1}, {'schedule': [], 'leaves': [0], 'levels': [[0, 0]], 'unpaired_parent': None, 'dependencies': [], 'internal_count': 0}), ({'size': 2}, {'schedule': [0], 'leaves': [1], 'levels': [[0, 0], [1, 1]], 'unpaired_parent': 0, 'dependencies': [], 'internal_count': 1}), ({'size': 5}, {'schedule': [1, 0], 'leaves': [2, 3, 4], 'levels': [[0, 0], [1, 2], [3, 4]], 'unpaired_parent': None, 'dependencies': [[1, 0]], 'internal_count': 2}), ({'size': 8}, {'schedule': [3, 2, 1, 0], 'leaves': [4, 5, 6, 7], 'levels': [[0, 0], [1, 2], [3, 6], [7, 7]], 'unpaired_parent': 3, 'dependencies': [[1, 0], [2, 0], [3, 1]], 'internal_count': 4}), ({'size': 15}, {'schedule': [6, 5, 4, 3, 2, 1, 0], 'leaves': [7, 8, 9, 10, 11, 12, 13, 14], 'levels': [[0, 0], [1, 2], [3, 6], [7, 14]], 'unpaired_parent': None, 'dependencies': [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2]], 'internal_count': 7}), ({'size': 18}, {'schedule': [8, 7, 6, 5, 4, 3, 2, 1, 0], 'leaves': [9, 10, 11, 12, 13, 14, 15, 16, 17], 'levels': [[0, 0], [1, 2], [3, 6], [7, 14], [15, 17]], 'unpaired_parent': 8, 'dependencies': [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2], [7, 3], [8, 3]], 'internal_count': 9})], [({'size': 0}, {'schedule': [], 'leaves': [], 'levels': [], 'unpaired_parent': None, 'dependencies': [], 'internal_count': 0}), ({'size': 1}, {'schedule': [], 'leaves': [0], 'levels': [[0, 0]], 'unpaired_parent': None, 'dependencies': [], 'internal_count': 0}), ({'size': 2}, {'schedule': [0], 'leaves': [1], 'levels': [[0, 0], [1, 1]], 'unpaired_parent': 0, 'dependencies': [], 'internal_count': 1}), ({'size': 5}, {'schedule': [1, 0], 'leaves': [2, 3, 4], 'levels': [[0, 0], [1, 2], [3, 4]], 'unpaired_parent': None, 'dependencies': [[1, 0]], 'internal_count': 2}), ({'size': 8}, {'schedule': [3, 2, 1, 0], 'leaves': [4, 5, 6, 7], 'levels': [[0, 0], [1, 2], [3, 6], [7, 7]], 'unpaired_parent': 3, 'dependencies': [[1, 0], [2, 0], [3, 1]], 'internal_count': 4}), ({'size': 15}, {'schedule': [6, 5, 4, 3, 2, 1, 0], 'leaves': [7, 8, 9, 10, 11, 12, 13, 14], 'levels': [[0, 0], [1, 2], [3, 6], [7, 14]], 'unpaired_parent': None, 'dependencies': [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2]], 'internal_count': 7}), ({'size': 19}, {'schedule': [8, 7, 6, 5, 4, 3, 2, 1, 0], 'leaves': [9, 10, 11, 12, 13, 14, 15, 16, 17, 18], 'levels': [[0, 0], [1, 2], [3, 6], [7, 14], [15, 18]], 'unpaired_parent': None, 'dependencies': [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2], [7, 3], [8, 3]], 'internal_count': 9})], [({'size': 0}, {'schedule': [], 'leaves': [], 'levels': [], 'unpaired_parent': None, 'dependencies': [], 'internal_count': 0}), ({'size': 1}, {'schedule': [], 'leaves': [0], 'levels': [[0, 0]], 'unpaired_parent': None, 'dependencies': [], 'internal_count': 0}), ({'size': 2}, {'schedule': [0], 'leaves': [1], 'levels': [[0, 0], [1, 1]], 'unpaired_parent': 0, 'dependencies': [], 'internal_count': 1}), ({'size': 5}, {'schedule': [1, 0], 'leaves': [2, 3, 4], 'levels': [[0, 0], [1, 2], [3, 4]], 'unpaired_parent': None, 'dependencies': [[1, 0]], 'internal_count': 2}), ({'size': 8}, {'schedule': [3, 2, 1, 0], 'leaves': [4, 5, 6, 7], 'levels': [[0, 0], [1, 2], [3, 6], [7, 7]], 'unpaired_parent': 3, 'dependencies': [[1, 0], [2, 0], [3, 1]], 'internal_count': 4}), ({'size': 15}, {'schedule': [6, 5, 4, 3, 2, 1, 0], 'leaves': [7, 8, 9, 10, 11, 12, 13, 14], 'levels': [[0, 0], [1, 2], [3, 6], [7, 14]], 'unpaired_parent': None, 'dependencies': [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2]], 'internal_count': 7}), ({'size': 20}, {'schedule': [9, 8, 7, 6, 5, 4, 3, 2, 1, 0], 'leaves': [10, 11, 12, 13, 14, 15, 16, 17, 18, 19], 'levels': [[0, 0], [1, 2], [3, 6], [7, 14], [15, 19]], 'unpaired_parent': 9, 'dependencies': [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2], [7, 3], [8, 3], [9, 4]], 'internal_count': 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":"d6aabcd0fdd83a6201b0bf1f41342a438c9551d278b577e22bd564a9198d092e","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(d):\n    n=d['size']; internal=list(range(n//2-1,-1,-1)); levels=[]; start=0; width=1\n    while start<n:\n        levels.append([start,min(n-1,start+width-1)]); start+=width; width*=2\n    return {'schedule': internal,\n    'leaves': list(range(n//2,n)),\n    'levels': levels,\n    'unpaired_parent': n//2-1 if n>0 and n%2==0 else None,\n    'dependencies': [[i,(i-1)//2] for i in range(1,n//2)],\n    'internal_count': n//2}\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncases = [[({'size': 0}, {'schedule': [], 'leaves': [], 'levels': [], 'unpaired_parent': None, 'dependencies': [], 'internal_count': 0}), ({'size': 1}, {'schedule': [], 'leaves': [0], 'levels': [[0, 0]], 'unpaired_parent': None, 'dependencies': [], 'internal_count': 0}), ({'size': 2}, {'schedule': [0], 'leaves': [1], 'levels': [[0, 0], [1, 1]], 'unpaired_parent': 0, 'dependencies': [], 'internal_count': 1}), ({'size': 5}, {'schedule': [1, 0], 'leaves': [2, 3, 4], 'levels': [[0, 0], [1, 2], [3, 4]], 'unpaired_parent': None, 'dependencies': [[1, 0]], 'internal_count': 2}), ({'size': 8}, {'schedule': [3, 2, 1, 0], 'leaves': [4, 5, 6, 7], 'levels': [[0, 0], [1, 2], [3, 6], [7, 7]], 'unpaired_parent': 3, 'dependencies': [[1, 0], [2, 0], [3, 1]], 'internal_count': 4}), ({'size': 15}, {'schedule': [6, 5, 4, 3, 2, 1, 0], 'leaves': [7, 8, 9, 10, 11, 12, 13, 14], 'levels': [[0, 0], [1, 2], [3, 6], [7, 14]], 'unpaired_parent': None, 'dependencies': [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2]], 'internal_count': 7}), ({'size': 16}, {'schedule': [7, 6, 5, 4, 3, 2, 1, 0], 'leaves': [8, 9, 10, 11, 12, 13, 14, 15], 'levels': [[0, 0], [1, 2], [3, 6], [7, 14], [15, 15]], 'unpaired_parent': 7, 'dependencies': [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2], [7, 3]], 'internal_count': 8})], [({'size': 0}, {'schedule': [], 'leaves': [], 'levels': [], 'unpaired_parent': None, 'dependencies': [], 'internal_count': 0}), ({'size': 1}, {'schedule': [], 'leaves': [0], 'levels': [[0, 0]], 'unpaired_parent': None, 'dependencies': [], 'internal_count': 0}), ({'size': 2}, {'schedule': [0], 'leaves': [1], 'levels': [[0, 0], [1, 1]], 'unpaired_parent': 0, 'dependencies': [], 'internal_count': 1}), ({'size': 5}, {'schedule': [1, 0], 'leaves': [2, 3, 4], 'levels': [[0, 0], [1, 2], [3, 4]], 'unpaired_parent': None, 'dependencies': [[1, 0]], 'internal_count': 2}), ({'size': 8}, {'schedule': [3, 2, 1, 0], 'leaves': [4, 5, 6, 7], 'levels': [[0, 0], [1, 2], [3, 6], [7, 7]], 'unpaired_parent': 3, 'dependencies': [[1, 0], [2, 0], [3, 1]], 'internal_count': 4}), ({'size': 15}, {'schedule': [6, 5, 4, 3, 2, 1, 0], 'leaves': [7, 8, 9, 10, 11, 12, 13, 14], 'levels': [[0, 0], [1, 2], [3, 6], [7, 14]], 'unpaired_parent': None, 'dependencies': [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2]], 'internal_count': 7}), ({'size': 17}, {'schedule': [7, 6, 5, 4, 3, 2, 1, 0], 'leaves': [8, 9, 10, 11, 12, 13, 14, 15, 16], 'levels': [[0, 0], [1, 2], [3, 6], [7, 14], [15, 16]], 'unpaired_parent': None, 'dependencies': [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2], [7, 3]], 'internal_count': 8})], [({'size': 0}, {'schedule': [], 'leaves': [], 'levels': [], 'unpaired_parent': None, 'dependencies': [], 'internal_count': 0}), ({'size': 1}, {'schedule': [], 'leaves': [0], 'levels': [[0, 0]], 'unpaired_parent': None, 'dependencies': [], 'internal_count': 0}), ({'size': 2}, {'schedule': [0], 'leaves': [1], 'levels': [[0, 0], [1, 1]], 'unpaired_parent': 0, 'dependencies': [], 'internal_count': 1}), ({'size': 5}, {'schedule': [1, 0], 'leaves': [2, 3, 4], 'levels': [[0, 0], [1, 2], [3, 4]], 'unpaired_parent': None, 'dependencies': [[1, 0]], 'internal_count': 2}), ({'size': 8}, {'schedule': [3, 2, 1, 0], 'leaves': [4, 5, 6, 7], 'levels': [[0, 0], [1, 2], [3, 6], [7, 7]], 'unpaired_parent': 3, 'dependencies': [[1, 0], [2, 0], [3, 1]], 'internal_count': 4}), ({'size': 15}, {'schedule': [6, 5, 4, 3, 2, 1, 0], 'leaves': [7, 8, 9, 10, 11, 12, 13, 14], 'levels': [[0, 0], [1, 2], [3, 6], [7, 14]], 'unpaired_parent': None, 'dependencies': [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2]], 'internal_count': 7}), ({'size': 18}, {'schedule': [8, 7, 6, 5, 4, 3, 2, 1, 0], 'leaves': [9, 10, 11, 12, 13, 14, 15, 16, 17], 'levels': [[0, 0], [1, 2], [3, 6], [7, 14], [15, 17]], 'unpaired_parent': 8, 'dependencies': [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2], [7, 3], [8, 3]], 'internal_count': 9})], [({'size': 0}, {'schedule': [], 'leaves': [], 'levels': [], 'unpaired_parent': None, 'dependencies': [], 'internal_count': 0}), ({'size': 1}, {'schedule': [], 'leaves': [0], 'levels': [[0, 0]], 'unpaired_parent': None, 'dependencies': [], 'internal_count': 0}), ({'size': 2}, {'schedule': [0], 'leaves': [1], 'levels': [[0, 0], [1, 1]], 'unpaired_parent': 0, 'dependencies': [], 'internal_count': 1}), ({'size': 5}, {'schedule': [1, 0], 'leaves': [2, 3, 4], 'levels': [[0, 0], [1, 2], [3, 4]], 'unpaired_parent': None, 'dependencies': [[1, 0]], 'internal_count': 2}), ({'size': 8}, {'schedule': [3, 2, 1, 0], 'leaves': [4, 5, 6, 7], 'levels': [[0, 0], [1, 2], [3, 6], [7, 7]], 'unpaired_parent': 3, 'dependencies': [[1, 0], [2, 0], [3, 1]], 'internal_count': 4}), ({'size': 15}, {'schedule': [6, 5, 4, 3, 2, 1, 0], 'leaves': [7, 8, 9, 10, 11, 12, 13, 14], 'levels': [[0, 0], [1, 2], [3, 6], [7, 14]], 'unpaired_parent': None, 'dependencies': [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2]], 'internal_count': 7}), ({'size': 19}, {'schedule': [8, 7, 6, 5, 4, 3, 2, 1, 0], 'leaves': [9, 10, 11, 12, 13, 14, 15, 16, 17, 18], 'levels': [[0, 0], [1, 2], [3, 6], [7, 14], [15, 18]], 'unpaired_parent': None, 'dependencies': [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2], [7, 3], [8, 3]], 'internal_count': 9})], [({'size': 0}, {'schedule': [], 'leaves': [], 'levels': [], 'unpaired_parent': None, 'dependencies': [], 'internal_count': 0}), ({'size': 1}, {'schedule': [], 'leaves': [0], 'levels': [[0, 0]], 'unpaired_parent': None, 'dependencies': [], 'internal_count': 0}), ({'size': 2}, {'schedule': [0], 'leaves': [1], 'levels': [[0, 0], [1, 1]], 'unpaired_parent': 0, 'dependencies': [], 'internal_count': 1}), ({'size': 5}, {'schedule': [1, 0], 'leaves': [2, 3, 4], 'levels': [[0, 0], [1, 2], [3, 4]], 'unpaired_parent': None, 'dependencies': [[1, 0]], 'internal_count': 2}), ({'size': 8}, {'schedule': [3, 2, 1, 0], 'leaves': [4, 5, 6, 7], 'levels': [[0, 0], [1, 2], [3, 6], [7, 7]], 'unpaired_parent': 3, 'dependencies': [[1, 0], [2, 0], [3, 1]], 'internal_count': 4}), ({'size': 15}, {'schedule': [6, 5, 4, 3, 2, 1, 0], 'leaves': [7, 8, 9, 10, 11, 12, 13, 14], 'levels': [[0, 0], [1, 2], [3, 6], [7, 14]], 'unpaired_parent': None, 'dependencies': [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2]], 'internal_count': 7}), ({'size': 20}, {'schedule': [9, 8, 7, 6, 5, 4, 3, 2, 1, 0], 'leaves': [10, 11, 12, 13, 14, 15, 16, 17, 18, 19], 'levels': [[0, 0], [1, 2], [3, 6], [7, 14], [15, 19]], 'unpaired_parent': 9, 'dependencies': [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2], [7, 3], [8, 3], [9, 4]], 'internal_count': 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-bottomup-schedule-leaves","generated_at":"2026-09-29T14:43:32.620736+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 leaves using list(range(n//2,n)) under the stated bounded certificate contract.","root_cause":"Complete heap leaf boundary includes the middle node in an odd-size tree.","sha256":"da7eab3c95c0f8433a7612251a1b37221dfa1c8150631555314030c000217bee","title":"Complete heap leaf boundary includes the middle node in an odd-size tree · 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":39.966,"exit_code":1,"observations":[{"actual":{"dependencies":[],"internal_count":0,"leaves":[],"levels":[],"schedule":[],"unpaired_parent":null},"check":"regression certificate 1","expected":{"dependencies":[],"internal_count":0,"leaves":[],"levels":[],"schedule":[],"unpaired_parent":null},"passed":true},{"actual":{"dependencies":[],"internal_count":0,"leaves":[],"levels":[[0,0]],"schedule":[],"unpaired_parent":null},"check":"regression certificate 2","expected":{"dependencies":[],"internal_count":0,"leaves":[0],"levels":[[0,0]],"schedule":[],"unpaired_parent":null},"passed":false},{"actual":{"dependencies":[],"internal_count":1,"leaves":[1],"levels":[[0,0],[1,1]],"schedule":[0],"unpaired_parent":0},"check":"regression certificate 3","expected":{"dependencies":[],"internal_count":1,"leaves":[1],"levels":[[0,0],[1,1]],"schedule":[0],"unpaired_parent":0},"passed":true},{"actual":{"dependencies":[[1,0]],"internal_count":2,"leaves":[3,4],"levels":[[0,0],[1,2],[3,4]],"schedule":[1,0],"unpaired_parent":null},"check":"regression certificate 4","expected":{"dependencies":[[1,0]],"internal_count":2,"leaves":[2,3,4],"levels":[[0,0],[1,2],[3,4]],"schedule":[1,0],"unpaired_parent":null},"passed":false},{"actual":{"dependencies":[[1,0],[2,0],[3,1]],"internal_count":4,"leaves":[4,5,6,7],"levels":[[0,0],[1,2],[3,6],[7,7]],"schedule":[3,2,1,0],"unpaired_parent":3},"check":"regression certificate 5","expected":{"dependencies":[[1,0],[2,0],[3,1]],"internal_count":4,"leaves":[4,5,6,7],"levels":[[0,0],[1,2],[3,6],[7,7]],"schedule":[3,2,1,0],"unpaired_parent":3},"passed":true},{"actual":{"dependencies":[[1,0],[2,0],[3,1],[4,1],[5,2],[6,2]],"internal_count":7,"leaves":[8,9,10,11,12,13,14],"levels":[[0,0],[1,2],[3,6],[7,14]],"schedule":[6,5,4,3,2,1,0],"unpaired_parent":null},"check":"regression certificate 6","expected":{"dependencies":[[1,0],[2,0],[3,1],[4,1],[5,2],[6,2]],"internal_count":7,"leaves":[7,8,9,10,11,12,13,14],"levels":[[0,0],[1,2],[3,6],[7,14]],"schedule":[6,5,4,3,2,1,0],"unpaired_parent":null},"passed":false},{"actual":{"dependencies":[[1,0],[2,0],[3,1],[4,1],[5,2],[6,2],[7,3]],"internal_count":8,"leaves":[8,9,10,11,12,13,14,15],"levels":[[0,0],[1,2],[3,6],[7,14],[15,15]],"schedule":[7,6,5,4,3,2,1,0],"unpaired_parent":7},"check":"variant-dependent certificate","expected":{"dependencies":[[1,0],[2,0],[3,1],[4,1],[5,2],[6,2],[7,3]],"internal_count":8,"leaves":[8,9,10,11,12,13,14,15],"levels":[[0,0],[1,2],[3,6],[7,14],[15,15]],"schedule":[7,6,5,4,3,2,1,0],"unpaired_parent":7},"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression certificate 1\", \"actual\": {\"schedule\": [], \"leaves\": [], \"levels\": [], \"unpaired_parent\": null, \"dependencies\": [], \"internal_count\": 0}, \"expected\": {\"schedule\": [], \"leaves\": [], \"levels\": [], \"unpaired_parent\": null, \"dependencies\": [], \"internal_count\": 0}, \"passed\": true}, {\"check\": \"regression certificate 2\", \"actual\": {\"schedule\": [], \"leaves\": [], \"levels\": [[0, 0]], \"unpaired_parent\": null, \"dependencies\": [], \"internal_count\": 0}, \"expected\": {\"schedule\": [], \"leaves\": [0], \"levels\": [[0, 0]], \"unpaired_parent\": null, \"dependencies\": [], \"internal_count\": 0}, \"passed\": false}, {\"check\": \"regression certificate 3\", \"actual\": {\"schedule\": [0], \"leaves\": [1], \"levels\": [[0, 0], [1, 1]], \"unpaired_parent\": 0, \"dependencies\": [], \"internal_count\": 1}, \"expected\": {\"schedule\": [0], \"leaves\": [1], \"levels\": [[0, 0], [1, 1]], \"unpaired_parent\": 0, \"dependencies\": [], \"internal_count\": 1}, \"passed\": true}, {\"check\": \"regression certificate 4\", \"actual\": {\"schedule\": [1, 0], \"leaves\": [3, 4], \"levels\": [[0, 0], [1, 2], [3, 4]], \"unpaired_parent\": null, \"dependencies\": [[1, 0]], \"internal_count\": 2}, \"expected\": {\"schedule\": [1, 0], \"leaves\": [2, 3, 4], \"levels\": [[0, 0], [1, 2], [3, 4]], \"unpaired_parent\": null, \"dependencies\": [[1, 0]], \"internal_count\": 2}, \"passed\": false}, {\"check\": \"regression certificate 5\", \"actual\": {\"schedule\": [3, 2, 1, 0], \"leaves\": [4, 5, 6, 7], \"levels\": [[0, 0], [1, 2], [3, 6], [7, 7]], \"unpaired_parent\": 3, \"dependencies\": [[1, 0], [2, 0], [3, 1]], \"internal_count\": 4}, \"expected\": {\"schedule\": [3, 2, 1, 0], \"leaves\": [4, 5, 6, 7], \"levels\": [[0, 0], [1, 2], [3, 6], [7, 7]], \"unpaired_parent\": 3, \"dependencies\": [[1, 0], [2, 0], [3, 1]], \"internal_count\": 4}, \"passed\": true}, {\"check\": \"regression certificate 6\", \"actual\": {\"schedule\": [6, 5, 4, 3, 2, 1, 0], \"leaves\": [8, 9, 10, 11, 12, 13, 14], \"levels\": [[0, 0], [1, 2], [3, 6], [7, 14]], \"unpaired_parent\": null, \"dependencies\": [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2]], \"internal_count\": 7}, \"expected\": {\"schedule\": [6, 5, 4, 3, 2, 1, 0], \"leaves\": [7, 8, 9, 10, 11, 12, 13, 14], \"levels\": [[0, 0], [1, 2], [3, 6], [7, 14]], \"unpaired_parent\": null, \"dependencies\": [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2]], \"internal_count\": 7}, \"passed\": false}, {\"check\": \"variant-dependent certificate\", \"actual\": {\"schedule\": [7, 6, 5, 4, 3, 2, 1, 0], \"leaves\": [8, 9, 10, 11, 12, 13, 14, 15], \"levels\": [[0, 0], [1, 2], [3, 6], [7, 14], [15, 15]], \"unpaired_parent\": 7, \"dependencies\": [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2], [7, 3]], \"internal_count\": 8}, \"expected\": {\"schedule\": [7, 6, 5, 4, 3, 2, 1, 0], \"leaves\": [8, 9, 10, 11, 12, 13, 14, 15], \"levels\": [[0, 0], [1, 2], [3, 6], [7, 14], [15, 15]], \"unpaired_parent\": 7, \"dependencies\": [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2], [7, 3]], \"internal_count\": 8}, \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":47.807,"exit_code":1,"observations":[{"actual":{"dependencies":[],"internal_count":0,"leaves":[],"levels":[],"schedule":[],"unpaired_parent":null},"check":"regression certificate 1","expected":{"dependencies":[],"internal_count":0,"leaves":[],"levels":[],"schedule":[],"unpaired_parent":null},"passed":true},{"actual":{"dependencies":[],"internal_count":0,"leaves":[],"levels":[[0,0]],"schedule":[],"unpaired_parent":null},"check":"regression certificate 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\"regression certificate 3\", \"actual\": {\"schedule\": [0], \"leaves\": [], \"levels\": [[0, 0], [1, 1]], \"unpaired_parent\": 0, \"dependencies\": [], \"internal_count\": 1}, \"expected\": {\"schedule\": [0], \"leaves\": [1], \"levels\": [[0, 0], [1, 1]], \"unpaired_parent\": 0, \"dependencies\": [], \"internal_count\": 1}, \"passed\": false}, {\"check\": \"regression certificate 4\", \"actual\": {\"schedule\": [1, 0], \"leaves\": [3, 4], \"levels\": [[0, 0], [1, 2], [3, 4]], \"unpaired_parent\": null, \"dependencies\": [[1, 0]], \"internal_count\": 2}, \"expected\": {\"schedule\": [1, 0], \"leaves\": [2, 3, 4], \"levels\": [[0, 0], [1, 2], [3, 4]], \"unpaired_parent\": null, \"dependencies\": [[1, 0]], \"internal_count\": 2}, \"passed\": false}, {\"check\": \"regression certificate 5\", \"actual\": {\"schedule\": [3, 2, 1, 0], \"leaves\": [5, 6, 7], \"levels\": [[0, 0], [1, 2], [3, 6], [7, 7]], \"unpaired_parent\": 3, \"dependencies\": [[1, 0], [2, 0], [3, 1]], \"internal_count\": 4}, \"expected\": {\"schedule\": [3, 2, 1, 0], \"leaves\": [4, 5, 6, 7], \"levels\": [[0, 0], [1, 2], [3, 6], [7, 7]], \"unpaired_parent\": 3, \"dependencies\": [[1, 0], [2, 0], [3, 1]], \"internal_count\": 4}, \"passed\": false}, {\"check\": \"regression certificate 6\", \"actual\": {\"schedule\": [6, 5, 4, 3, 2, 1, 0], \"leaves\": [8, 9, 10, 11, 12, 13, 14], \"levels\": [[0, 0], [1, 2], [3, 6], [7, 14]], \"unpaired_parent\": null, \"dependencies\": [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2]], \"internal_count\": 7}, \"expected\": {\"schedule\": [6, 5, 4, 3, 2, 1, 0], \"leaves\": [7, 8, 9, 10, 11, 12, 13, 14], \"levels\": [[0, 0], [1, 2], [3, 6], [7, 14]], \"unpaired_parent\": null, \"dependencies\": [[1, 0], [2, 0], [3, 1], [4, 1], [5, 2], [6, 2]], \"internal_count\": 7}, \"passed\": false}, {\"check\": \"variant-dependent certificate\", \"actual\": {\"schedule\": [7, 6, 5, 4, 3, 2, 1, 0], \"leaves\": [9, 10, 11, 12, 13, 14, 15], \"levels\": [[0, 0], [1, 2], [3, 6], [7, 14], 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