{"abstract":"The bounded binomial forest certificate reports an incorrect children.","category":"Heap invariants","checks":7,"contract":"For a binomial-forest certificate, roots is a list of [rank,key,node_count,child_ranks]. Report canonical rank order, duplicate ranks, root minimum, size, tree-cardinality failures, and descending child-rank failures. No implicit tree nodes are present.","evaluation_group":"s3-heap-model-binomial-forest","failed_approach":"The local patch uses [i for i,x in enumerate(r) if len(x[3]) != x[0]] and still violates the stated relation.","family":"s3-heap-binomial-forest-children","id":"FA-39866","implementations":{"attempt":{"sha256":"be7cf85e64e68c20309b8b8f7640dbdbd1317cb30142165595cd26cd687152b2","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(d):\n    r = d['roots']\n    return {'canonical': sorted([x[0] for x in r]),\n    'collisions': sorted({x[0] for x in r if sum(y[0]==x[0] for y in r)>1}),\n    'minimum': min([x[1] for x in r],default=None),\n    'population': sum(x[2] for x in r),\n    'cardinality': [i for i,x in enumerate(r) if x[2] != 2**x[0]],\n    'children': [i for i,x in enumerate(r) if len(x[3]) != x[0]]}\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncases = [[({'roots': []}, {'canonical': [], 'collisions': [], 'minimum': None, 'population': 0, 'cardinality': [], 'children': []}), ({'roots': [[0, 8, 1, []]]}, {'canonical': [0], 'collisions': [], 'minimum': 8, 'population': 1, 'cardinality': [], 'children': []}), ({'roots': [[2, 9, 4, [1, 0]], [0, 3, 1, []], [2, 2, 4, [1, 0]]]}, {'canonical': [0, 2, 2], 'collisions': [2], 'minimum': 2, 'population': 9, 'cardinality': [], 'children': []}), ({'roots': [[3, 1, 8, [2, 1, 0]], [1, 5, 2, [0]]]}, {'canonical': [1, 3], 'collisions': [], 'minimum': 1, 'population': 10, 'cardinality': [], 'children': []}), ({'roots': [[2, 4, 5, [0, 1]], [1, 4, 1, [0]]]}, {'canonical': [1, 2], 'collisions': [], 'minimum': 4, 'population': 6, 'cardinality': [0, 1], 'children': [0]}), ({'roots': [[1, 7, 2, []], [3, 0, 7, [2, 0, 1]], [1, 2, 2, [0]]]}, {'canonical': [1, 1, 3], 'collisions': [1], 'minimum': 0, 'population': 11, 'cardinality': [1], 'children': [0, 1]}), ({'roots': [[1, 8, 2, []], [3, 0, 7, [2, 0, 1]], [1, 2, 2, [0]]]}, {'canonical': [1, 1, 3], 'collisions': [1], 'minimum': 0, 'population': 11, 'cardinality': [1], 'children': [0, 1]})], [({'roots': []}, {'canonical': [], 'collisions': [], 'minimum': None, 'population': 0, 'cardinality': [], 'children': []}), ({'roots': [[0, 8, 1, []]]}, {'canonical': [0], 'collisions': [], 'minimum': 8, 'population': 1, 'cardinality': [], 'children': []}), ({'roots': [[2, 9, 4, [1, 0]], [0, 3, 1, []], [2, 2, 4, [1, 0]]]}, {'canonical': [0, 2, 2], 'collisions': [2], 'minimum': 2, 'population': 9, 'cardinality': [], 'children': []}), ({'roots': [[3, 1, 8, [2, 1, 0]], [1, 5, 2, [0]]]}, {'canonical': [1, 3], 'collisions': [], 'minimum': 1, 'population': 10, 'cardinality': [], 'children': []}), ({'roots': [[2, 4, 5, [0, 1]], [1, 4, 1, [0]]]}, {'canonical': [1, 2], 'collisions': [], 'minimum': 4, 'population': 6, 'cardinality': [0, 1], 'children': [0]}), ({'roots': [[1, 7, 2, []], [3, 0, 7, [2, 0, 1]], [1, 2, 2, [0]]]}, {'canonical': [1, 1, 3], 'collisions': [1], 'minimum': 0, 'population': 11, 'cardinality': [1], 'children': [0, 1]}), ({'roots': [[1, 9, 2, []], [3, 0, 7, [2, 0, 1]], [1, 2, 2, [0]]]}, {'canonical': [1, 1, 3], 'collisions': [1], 'minimum': 0, 'population': 11, 'cardinality': [1], 'children': [0, 1]})], [({'roots': []}, {'canonical': [], 'collisions': [], 'minimum': None, 'population': 0, 'cardinality': [], 'children': []}), ({'roots': [[0, 8, 1, []]]}, {'canonical': [0], 'collisions': [], 'minimum': 8, 'population': 1, 'cardinality': [], 'children': []}), ({'roots': [[2, 9, 4, [1, 0]], [0, 3, 1, []], [2, 2, 4, [1, 0]]]}, {'canonical': [0, 2, 2], 'collisions': [2], 'minimum': 2, 'population': 9, 'cardinality': [], 'children': []}), ({'roots': [[3, 1, 8, [2, 1, 0]], [1, 5, 2, [0]]]}, {'canonical': [1, 3], 'collisions': [], 'minimum': 1, 'population': 10, 'cardinality': [], 'children': []}), ({'roots': [[2, 4, 5, [0, 1]], [1, 4, 1, [0]]]}, {'canonical': [1, 2], 'collisions': [], 'minimum': 4, 'population': 6, 'cardinality': [0, 1], 'children': [0]}), ({'roots': [[1, 7, 2, []], [3, 0, 7, [2, 0, 1]], [1, 2, 2, [0]]]}, {'canonical': [1, 1, 3], 'collisions': [1], 'minimum': 0, 'population': 11, 'cardinality': [1], 'children': [0, 1]}), ({'roots': [[1, 10, 2, []], [3, 0, 7, [2, 0, 1]], [1, 2, 2, [0]]]}, {'canonical': [1, 1, 3], 'collisions': [1], 'minimum': 0, 'population': 11, 'cardinality': [1], 'children': [0, 1]})], [({'roots': []}, {'canonical': [], 'collisions': [], 'minimum': None, 'population': 0, 'cardinality': [], 'children': []}), ({'roots': [[0, 8, 1, []]]}, {'canonical': [0], 'collisions': [], 'minimum': 8, 'population': 1, 'cardinality': [], 'children': []}), ({'roots': [[2, 9, 4, [1, 0]], [0, 3, 1, []], [2, 2, 4, [1, 0]]]}, {'canonical': [0, 2, 2], 'collisions': [2], 'minimum': 2, 'population': 9, 'cardinality': [], 'children': []}), ({'roots': [[3, 1, 8, [2, 1, 0]], [1, 5, 2, [0]]]}, {'canonical': [1, 3], 'collisions': [], 'minimum': 1, 'population': 10, 'cardinality': [], 'children': []}), ({'roots': [[2, 4, 5, [0, 1]], [1, 4, 1, [0]]]}, {'canonical': [1, 2], 'collisions': [], 'minimum': 4, 'population': 6, 'cardinality': [0, 1], 'children': [0]}), ({'roots': [[1, 7, 2, []], [3, 0, 7, [2, 0, 1]], [1, 2, 2, [0]]]}, {'canonical': [1, 1, 3], 'collisions': [1], 'minimum': 0, 'population': 11, 'cardinality': [1], 'children': [0, 1]}), ({'roots': [[1, 11, 2, []], [3, 0, 7, [2, 0, 1]], [1, 2, 2, [0]]]}, {'canonical': [1, 1, 3], 'collisions': [1], 'minimum': 0, 'population': 11, 'cardinality': [1], 'children': [0, 1]})], [({'roots': []}, {'canonical': [], 'collisions': [], 'minimum': None, 'population': 0, 'cardinality': [], 'children': []}), ({'roots': [[0, 8, 1, []]]}, {'canonical': [0], 'collisions': [], 'minimum': 8, 'population': 1, 'cardinality': [], 'children': []}), ({'roots': [[2, 9, 4, [1, 0]], [0, 3, 1, []], [2, 2, 4, [1, 0]]]}, {'canonical': [0, 2, 2], 'collisions': [2], 'minimum': 2, 'population': 9, 'cardinality': [], 'children': []}), ({'roots': [[3, 1, 8, [2, 1, 0]], [1, 5, 2, [0]]]}, {'canonical': [1, 3], 'collisions': [], 'minimum': 1, 'population': 10, 'cardinality': [], 'children': []}), ({'roots': [[2, 4, 5, [0, 1]], [1, 4, 1, [0]]]}, {'canonical': [1, 2], 'collisions': [], 'minimum': 4, 'population': 6, 'cardinality': [0, 1], 'children': [0]}), ({'roots': [[1, 7, 2, []], [3, 0, 7, [2, 0, 1]], [1, 2, 2, [0]]]}, {'canonical': [1, 1, 3], 'collisions': [1], 'minimum': 0, 'population': 11, 'cardinality': [1], 'children': [0, 1]}), ({'roots': [[1, 12, 2, []], [3, 0, 7, [2, 0, 1]], [1, 2, 2, [0]]]}, {'canonical': [1, 1, 3], 'collisions': [1], 'minimum': 0, 'population': 11, 'cardinality': [1], 'children': [0, 1]})]][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":"ce773bd8d73c6790f482282f2b8cc4e6d6648dc710118b57bac0c04129c0d662","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(d):\n    r = d['roots']\n    return {'canonical': sorted([x[0] for x in r]),\n    'collisions': sorted({x[0] for x in r if sum(y[0]==x[0] for y in r)>1}),\n    'minimum': min([x[1] for x in r],default=None),\n    'population': sum(x[2] for x in r),\n    'cardinality': [i for i,x in enumerate(r) if x[2] != 2**x[0]],\n    'children': [i for i,x in enumerate(r) if sorted(x[3]) != list(range(x[0]))]}\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncases = [[({'roots': []}, {'canonical': [], 'collisions': [], 'minimum': None, 'population': 0, 'cardinality': [], 'children': []}), ({'roots': [[0, 8, 1, []]]}, {'canonical': [0], 'collisions': [], 'minimum': 8, 'population': 1, 'cardinality': [], 'children': []}), ({'roots': [[2, 9, 4, [1, 0]], [0, 3, 1, []], [2, 2, 4, [1, 0]]]}, {'canonical': [0, 2, 2], 'collisions': [2], 'minimum': 2, 'population': 9, 'cardinality': [], 'children': []}), ({'roots': [[3, 1, 8, [2, 1, 0]], [1, 5, 2, [0]]]}, {'canonical': [1, 3], 'collisions': [], 'minimum': 1, 'population': 10, 'cardinality': [], 'children': []}), ({'roots': [[2, 4, 5, [0, 1]], [1, 4, 1, [0]]]}, {'canonical': [1, 2], 'collisions': [], 'minimum': 4, 'population': 6, 'cardinality': [0, 1], 'children': [0]}), ({'roots': [[1, 7, 2, []], [3, 0, 7, [2, 0, 1]], [1, 2, 2, [0]]]}, {'canonical': [1, 1, 3], 'collisions': [1], 'minimum': 0, 'population': 11, 'cardinality': [1], 'children': [0, 1]}), ({'roots': [[1, 8, 2, []], [3, 0, 7, [2, 0, 1]], [1, 2, 2, [0]]]}, {'canonical': [1, 1, 3], 'collisions': [1], 'minimum': 0, 'population': 11, 'cardinality': [1], 'children': [0, 1]})], [({'roots': []}, {'canonical': [], 'collisions': [], 'minimum': None, 'population': 0, 'cardinality': [], 'children': []}), ({'roots': [[0, 8, 1, []]]}, {'canonical': [0], 'collisions': [], 'minimum': 8, 'population': 1, 'cardinality': [], 'children': []}), ({'roots': [[2, 9, 4, [1, 0]], [0, 3, 1, []], [2, 2, 4, [1, 0]]]}, {'canonical': [0, 2, 2], 'collisions': [2], 'minimum': 2, 'population': 9, 'cardinality': [], 'children': []}), ({'roots': [[3, 1, 8, [2, 1, 0]], [1, 5, 2, [0]]]}, {'canonical': [1, 3], 'collisions': [], 'minimum': 1, 'population': 10, 'cardinality': [], 'children': []}), ({'roots': [[2, 4, 5, [0, 1]], [1, 4, 1, [0]]]}, {'canonical': [1, 2], 'collisions': [], 'minimum': 4, 'population': 6, 'cardinality': [0, 1], 'children': [0]}), ({'roots': [[1, 7, 2, []], [3, 0, 7, [2, 0, 1]], [1, 2, 2, [0]]]}, {'canonical': [1, 1, 3], 'collisions': [1], 'minimum': 0, 'population': 11, 'cardinality': [1], 'children': [0, 1]}), ({'roots': [[1, 9, 2, []], [3, 0, 7, [2, 0, 1]], [1, 2, 2, [0]]]}, {'canonical': [1, 1, 3], 'collisions': [1], 'minimum': 0, 'population': 11, 'cardinality': [1], 'children': [0, 1]})], [({'roots': []}, {'canonical': [], 'collisions': [], 'minimum': None, 'population': 0, 'cardinality': [], 'children': []}), ({'roots': [[0, 8, 1, []]]}, {'canonical': [0], 'collisions': [], 'minimum': 8, 'population': 1, 'cardinality': [], 'children': []}), ({'roots': [[2, 9, 4, [1, 0]], [0, 3, 1, []], [2, 2, 4, [1, 0]]]}, {'canonical': [0, 2, 2], 'collisions': [2], 'minimum': 2, 'population': 9, 'cardinality': [], 'children': []}), ({'roots': [[3, 1, 8, [2, 1, 0]], [1, 5, 2, [0]]]}, {'canonical': [1, 3], 'collisions': [], 'minimum': 1, 'population': 10, 'cardinality': [], 'children': []}), ({'roots': [[2, 4, 5, [0, 1]], [1, 4, 1, [0]]]}, {'canonical': [1, 2], 'collisions': [], 'minimum': 4, 'population': 6, 'cardinality': [0, 1], 'children': [0]}), ({'roots': [[1, 7, 2, []], [3, 0, 7, [2, 0, 1]], [1, 2, 2, [0]]]}, {'canonical': [1, 1, 3], 'collisions': [1], 'minimum': 0, 'population': 11, 'cardinality': [1], 'children': [0, 1]}), ({'roots': [[1, 10, 2, []], [3, 0, 7, [2, 0, 1]], [1, 2, 2, [0]]]}, {'canonical': [1, 1, 3], 'collisions': [1], 'minimum': 0, 'population': 11, 'cardinality': [1], 'children': [0, 1]})], [({'roots': []}, {'canonical': [], 'collisions': [], 'minimum': None, 'population': 0, 'cardinality': [], 'children': []}), ({'roots': [[0, 8, 1, []]]}, {'canonical': [0], 'collisions': [], 'minimum': 8, 'population': 1, 'cardinality': [], 'children': []}), ({'roots': [[2, 9, 4, [1, 0]], [0, 3, 1, []], [2, 2, 4, [1, 0]]]}, {'canonical': [0, 2, 2], 'collisions': [2], 'minimum': 2, 'population': 9, 'cardinality': [], 'children': []}), ({'roots': [[3, 1, 8, [2, 1, 0]], [1, 5, 2, [0]]]}, {'canonical': [1, 3], 'collisions': [], 'minimum': 1, 'population': 10, 'cardinality': [], 'children': []}), ({'roots': [[2, 4, 5, [0, 1]], [1, 4, 1, [0]]]}, {'canonical': [1, 2], 'collisions': [], 'minimum': 4, 'population': 6, 'cardinality': [0, 1], 'children': [0]}), ({'roots': [[1, 7, 2, []], [3, 0, 7, [2, 0, 1]], [1, 2, 2, [0]]]}, {'canonical': [1, 1, 3], 'collisions': [1], 'minimum': 0, 'population': 11, 'cardinality': [1], 'children': [0, 1]}), ({'roots': [[1, 11, 2, []], [3, 0, 7, [2, 0, 1]], [1, 2, 2, [0]]]}, {'canonical': [1, 1, 3], 'collisions': [1], 'minimum': 0, 'population': 11, 'cardinality': [1], 'children': [0, 1]})], [({'roots': []}, {'canonical': [], 'collisions': [], 'minimum': None, 'population': 0, 'cardinality': [], 'children': []}), ({'roots': [[0, 8, 1, []]]}, {'canonical': [0], 'collisions': [], 'minimum': 8, 'population': 1, 'cardinality': [], 'children': []}), ({'roots': [[2, 9, 4, [1, 0]], [0, 3, 1, []], [2, 2, 4, [1, 0]]]}, {'canonical': [0, 2, 2], 'collisions': [2], 'minimum': 2, 'population': 9, 'cardinality': [], 'children': []}), ({'roots': [[3, 1, 8, [2, 1, 0]], [1, 5, 2, [0]]]}, {'canonical': [1, 3], 'collisions': [], 'minimum': 1, 'population': 10, 'cardinality': [], 'children': []}), ({'roots': [[2, 4, 5, [0, 1]], [1, 4, 1, [0]]]}, {'canonical': [1, 2], 'collisions': [], 'minimum': 4, 'population': 6, 'cardinality': [0, 1], 'children': [0]}), ({'roots': [[1, 7, 2, []], [3, 0, 7, [2, 0, 1]], [1, 2, 2, [0]]]}, {'canonical': [1, 1, 3], 'collisions': [1], 'minimum': 0, 'population': 11, 'cardinality': [1], 'children': [0, 1]}), ({'roots': [[1, 12, 2, []], [3, 0, 7, [2, 0, 1]], [1, 2, 2, [0]]]}, {'canonical': [1, 1, 3], 'collisions': [1], 'minimum': 0, 'population': 11, 'cardinality': [1], 'children': [0, 1]})]][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":"7801cf55b67d2ae1bafcf85034e3d253b8c6a27a75ba40d6413404288499ad49","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(d):\n    r = d['roots']\n    return {'canonical': sorted([x[0] for x in r]),\n    'collisions': sorted({x[0] for x in r if sum(y[0]==x[0] for y in r)>1}),\n    'minimum': min([x[1] for x in r],default=None),\n    'population': sum(x[2] for x in r),\n    'cardinality': [i for i,x in enumerate(r) if x[2] != 2**x[0]],\n    'children': [i for i,x in enumerate(r) if x[3] != list(range(x[0]-1,-1,-1))]}\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncases = [[({'roots': []}, {'canonical': [], 'collisions': [], 'minimum': None, 'population': 0, 'cardinality': [], 'children': []}), ({'roots': [[0, 8, 1, []]]}, {'canonical': [0], 'collisions': [], 'minimum': 8, 'population': 1, 'cardinality': [], 'children': []}), ({'roots': [[2, 9, 4, [1, 0]], [0, 3, 1, []], [2, 2, 4, [1, 0]]]}, {'canonical': [0, 2, 2], 'collisions': [2], 'minimum': 2, 'population': 9, 'cardinality': [], 'children': []}), ({'roots': [[3, 1, 8, [2, 1, 0]], [1, 5, 2, [0]]]}, {'canonical': [1, 3], 'collisions': [], 'minimum': 1, 'population': 10, 'cardinality': [], 'children': []}), ({'roots': [[2, 4, 5, [0, 1]], [1, 4, 1, [0]]]}, {'canonical': [1, 2], 'collisions': [], 'minimum': 4, 'population': 6, 'cardinality': [0, 1], 'children': [0]}), ({'roots': [[1, 7, 2, []], [3, 0, 7, [2, 0, 1]], [1, 2, 2, [0]]]}, {'canonical': [1, 1, 3], 'collisions': [1], 'minimum': 0, 'population': 11, 'cardinality': [1], 'children': [0, 1]}), ({'roots': [[1, 8, 2, []], [3, 0, 7, [2, 0, 1]], [1, 2, 2, [0]]]}, {'canonical': [1, 1, 3], 'collisions': [1], 'minimum': 0, 'population': 11, 'cardinality': [1], 'children': [0, 1]})], [({'roots': []}, {'canonical': [], 'collisions': [], 'minimum': None, 'population': 0, 'cardinality': [], 'children': []}), ({'roots': [[0, 8, 1, []]]}, {'canonical': [0], 'collisions': [], 'minimum': 8, 'population': 1, 'cardinality': [], 'children': []}), ({'roots': [[2, 9, 4, [1, 0]], [0, 3, 1, []], [2, 2, 4, [1, 0]]]}, {'canonical': [0, 2, 2], 'collisions': [2], 'minimum': 2, 'population': 9, 'cardinality': [], 'children': []}), ({'roots': [[3, 1, 8, [2, 1, 0]], [1, 5, 2, [0]]]}, {'canonical': [1, 3], 'collisions': [], 'minimum': 1, 'population': 10, 'cardinality': [], 'children': []}), ({'roots': [[2, 4, 5, [0, 1]], [1, 4, 1, [0]]]}, {'canonical': [1, 2], 'collisions': [], 'minimum': 4, 'population': 6, 'cardinality': [0, 1], 'children': [0]}), ({'roots': [[1, 7, 2, []], [3, 0, 7, [2, 0, 1]], [1, 2, 2, [0]]]}, {'canonical': [1, 1, 3], 'collisions': [1], 'minimum': 0, 'population': 11, 'cardinality': [1], 'children': [0, 1]}), ({'roots': [[1, 9, 2, []], [3, 0, 7, [2, 0, 1]], [1, 2, 2, [0]]]}, {'canonical': [1, 1, 3], 'collisions': [1], 'minimum': 0, 'population': 11, 'cardinality': [1], 'children': [0, 1]})], [({'roots': []}, {'canonical': [], 'collisions': [], 'minimum': None, 'population': 0, 'cardinality': [], 'children': []}), ({'roots': [[0, 8, 1, []]]}, {'canonical': [0], 'collisions': [], 'minimum': 8, 'population': 1, 'cardinality': [], 'children': []}), ({'roots': [[2, 9, 4, [1, 0]], [0, 3, 1, []], [2, 2, 4, [1, 0]]]}, {'canonical': [0, 2, 2], 'collisions': [2], 'minimum': 2, 'population': 9, 'cardinality': [], 'children': []}), ({'roots': [[3, 1, 8, [2, 1, 0]], [1, 5, 2, [0]]]}, {'canonical': [1, 3], 'collisions': [], 'minimum': 1, 'population': 10, 'cardinality': [], 'children': []}), ({'roots': [[2, 4, 5, [0, 1]], [1, 4, 1, [0]]]}, {'canonical': [1, 2], 'collisions': [], 'minimum': 4, 'population': 6, 'cardinality': [0, 1], 'children': [0]}), ({'roots': [[1, 7, 2, []], [3, 0, 7, [2, 0, 1]], [1, 2, 2, [0]]]}, {'canonical': [1, 1, 3], 'collisions': [1], 'minimum': 0, 'population': 11, 'cardinality': [1], 'children': [0, 1]}), ({'roots': [[1, 10, 2, []], [3, 0, 7, [2, 0, 1]], [1, 2, 2, [0]]]}, {'canonical': [1, 1, 3], 'collisions': [1], 'minimum': 0, 'population': 11, 'cardinality': [1], 'children': [0, 1]})], [({'roots': []}, {'canonical': [], 'collisions': [], 'minimum': None, 'population': 0, 'cardinality': [], 'children': []}), ({'roots': [[0, 8, 1, []]]}, {'canonical': [0], 'collisions': [], 'minimum': 8, 'population': 1, 'cardinality': [], 'children': []}), ({'roots': [[2, 9, 4, [1, 0]], [0, 3, 1, []], [2, 2, 4, [1, 0]]]}, {'canonical': [0, 2, 2], 'collisions': [2], 'minimum': 2, 'population': 9, 'cardinality': [], 'children': []}), ({'roots': [[3, 1, 8, [2, 1, 0]], [1, 5, 2, [0]]]}, {'canonical': [1, 3], 'collisions': [], 'minimum': 1, 'population': 10, 'cardinality': [], 'children': []}), ({'roots': [[2, 4, 5, [0, 1]], [1, 4, 1, [0]]]}, {'canonical': [1, 2], 'collisions': [], 'minimum': 4, 'population': 6, 'cardinality': [0, 1], 'children': [0]}), ({'roots': [[1, 7, 2, []], [3, 0, 7, [2, 0, 1]], [1, 2, 2, [0]]]}, {'canonical': [1, 1, 3], 'collisions': [1], 'minimum': 0, 'population': 11, 'cardinality': [1], 'children': [0, 1]}), ({'roots': [[1, 11, 2, []], [3, 0, 7, [2, 0, 1]], [1, 2, 2, [0]]]}, {'canonical': [1, 1, 3], 'collisions': [1], 'minimum': 0, 'population': 11, 'cardinality': [1], 'children': [0, 1]})], [({'roots': []}, {'canonical': [], 'collisions': [], 'minimum': None, 'population': 0, 'cardinality': [], 'children': []}), ({'roots': [[0, 8, 1, []]]}, {'canonical': [0], 'collisions': [], 'minimum': 8, 'population': 1, 'cardinality': [], 'children': []}), ({'roots': [[2, 9, 4, [1, 0]], [0, 3, 1, []], [2, 2, 4, [1, 0]]]}, {'canonical': [0, 2, 2], 'collisions': [2], 'minimum': 2, 'population': 9, 'cardinality': [], 'children': []}), ({'roots': [[3, 1, 8, [2, 1, 0]], [1, 5, 2, [0]]]}, {'canonical': [1, 3], 'collisions': [], 'minimum': 1, 'population': 10, 'cardinality': [], 'children': []}), ({'roots': [[2, 4, 5, [0, 1]], [1, 4, 1, [0]]]}, {'canonical': [1, 2], 'collisions': [], 'minimum': 4, 'population': 6, 'cardinality': [0, 1], 'children': [0]}), ({'roots': [[1, 7, 2, []], [3, 0, 7, [2, 0, 1]], [1, 2, 2, [0]]]}, {'canonical': [1, 1, 3], 'collisions': [1], 'minimum': 0, 'population': 11, 'cardinality': [1], 'children': [0, 1]}), ({'roots': [[1, 12, 2, []], [3, 0, 7, [2, 0, 1]], [1, 2, 2, [0]]]}, {'canonical': [1, 1, 3], 'collisions': [1], 'minimum': 0, 'population': 11, 'cardinality': [1], 'children': [0, 1]})]][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-binomial-forest-children","generated_at":"2026-09-29T14:43:25.496784+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 children using [i for i,x in enumerate(r) if x[3] != list(range(x[0]-1,-1,-1))] under the stated bounded certificate contract.","root_cause":"The stipulated representation stores a descending child-rank chain; cardinality alone is insufficient.","sha256":"3f66c4603839eaed3bee09267a717f2a9caf907e947d103d3f1029cc77446ff2","title":"Binomial child rank chain accepts ascending children · 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":41.682,"exit_code":1,"observations":[{"actual":{"canonical":[],"cardinality":[],"children":[],"collisions":[],"minimum":null,"population":0},"check":"regression certificate 1","expected":{"canonical":[],"cardinality":[],"children":[],"collisions":[],"minimum":null,"population":0},"passed":true},{"actual":{"canonical":[0],"cardinality":[],"children":[],"collisions":[],"minimum":8,"population":1},"check":"regression certificate 2","expected":{"canonical":[0],"cardinality":[],"children":[],"collisions":[],"minimum":8,"population":1},"passed":true},{"actual":{"canonical":[0,2,2],"cardinality":[],"children":[],"collisions":[2],"minimum":2,"population":9},"check":"regression certificate 3","expected":{"canonical":[0,2,2],"cardinality":[],"children":[],"collisions":[2],"minimum":2,"population":9},"passed":true},{"actual":{"canonical":[1,3],"cardinality":[],"children":[],"collisions":[],"minimum":1,"population":10},"check":"regression certificate 4","expected":{"canonical":[1,3],"cardinality":[],"children":[],"collisions":[],"minimum":1,"population":10},"passed":true},{"actual":{"canonical":[1,2],"cardinality":[0,1],"children":[],"collisions":[],"minimum":4,"population":6},"check":"regression certificate 5","expected":{"canonical":[1,2],"cardinality":[0,1],"children":[0],"collisions":[],"minimum":4,"population":6},"passed":false},{"actual":{"canonical":[1,1,3],"cardinality":[1],"children":[0],"collisions":[1],"minimum":0,"population":11},"check":"regression certificate 6","expected":{"canonical":[1,1,3],"cardinality":[1],"children":[0,1],"collisions":[1],"minimum":0,"population":11},"passed":false},{"actual":{"canonical":[1,1,3],"cardinality":[1],"children":[0],"collisions":[1],"minimum":0,"population":11},"check":"variant-dependent certificate","expected":{"canonical":[1,1,3],"cardinality":[1],"children":[0,1],"collisions":[1],"minimum":0,"population":11},"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression certificate 1\", \"actual\": {\"canonical\": [], \"collisions\": [], \"minimum\": null, \"population\": 0, \"cardinality\": [], \"children\": []}, \"expected\": {\"canonical\": [], \"collisions\": [], \"minimum\": null, \"population\": 0, \"cardinality\": [], \"children\": []}, \"passed\": true}, {\"check\": \"regression certificate 2\", \"actual\": {\"canonical\": [0], \"collisions\": [], \"minimum\": 8, \"population\": 1, \"cardinality\": [], \"children\": []}, \"expected\": {\"canonical\": [0], \"collisions\": [], \"minimum\": 8, \"population\": 1, \"cardinality\": [], \"children\": []}, \"passed\": true}, {\"check\": \"regression certificate 3\", \"actual\": {\"canonical\": [0, 2, 2], \"collisions\": [2], \"minimum\": 2, \"population\": 9, \"cardinality\": [], \"children\": []}, \"expected\": {\"canonical\": [0, 2, 2], \"collisions\": [2], \"minimum\": 2, \"population\": 9, \"cardinality\": [], \"children\": []}, \"passed\": true}, {\"check\": \"regression certificate 4\", \"actual\": {\"canonical\": [1, 3], \"collisions\": [], \"minimum\": 1, \"population\": 10, \"cardinality\": [], \"children\": []}, \"expected\": {\"canonical\": [1, 3], \"collisions\": [], \"minimum\": 1, \"population\": 10, \"cardinality\": [], \"children\": []}, \"passed\": true}, {\"check\": \"regression certificate 5\", \"actual\": {\"canonical\": [1, 2], \"collisions\": [], \"minimum\": 4, \"population\": 6, \"cardinality\": [0, 1], \"children\": []}, \"expected\": {\"canonical\": [1, 2], \"collisions\": [], \"minimum\": 4, \"population\": 6, \"cardinality\": [0, 1], \"children\": [0]}, \"passed\": false}, {\"check\": \"regression certificate 6\", \"actual\": {\"canonical\": [1, 1, 3], \"collisions\": [1], \"minimum\": 0, \"population\": 11, \"cardinality\": [1], \"children\": [0]}, \"expected\": {\"canonical\": [1, 1, 3], \"collisions\": [1], \"minimum\": 0, \"population\": 11, \"cardinality\": [1], \"children\": [0, 1]}, \"passed\": false}, {\"check\": \"variant-dependent certificate\", \"actual\": {\"canonical\": [1, 1, 3], \"collisions\": [1], \"minimum\": 0, \"population\": 11, \"cardinality\": [1], \"children\": [0]}, \"expected\": {\"canonical\": [1, 1, 3], \"collisions\": [1], \"minimum\": 0, \"population\": 11, \"cardinality\": [1], \"children\": [0, 1]}, \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":41.455,"exit_code":1,"observations":[{"actual":{"canonical":[],"cardinality":[],"children":[],"collisions":[],"minimum":null,"population":0},"check":"regression certificate 1","expected":{"canonical":[],"cardinality":[],"children":[],"collisions":[],"minimum":null,"population":0},"passed":true},{"actual":{"canonical":[0],"cardinality":[],"children":[],"collisions":[],"minimum":8,"population":1},"check":"regression certificate 2","expected":{"canonical":[0],"cardinality":[],"children":[],"collisions":[],"minimum":8,"population":1},"passed":true},{"actual":{"canonical":[0,2,2],"cardinality":[],"children":[],"collisions":[2],"minimum":2,"population":9},"check":"regression certificate 3","expected":{"canonical":[0,2,2],"cardinality":[],"children":[],"collisions":[2],"minimum":2,"population":9},"passed":true},{"actual":{"canonical":[1,3],"cardinality":[],"children":[],"collisions":[],"minimum":1,"population":10},"check":"regression certificate 4","expected":{"canonical":[1,3],"cardinality":[],"children":[],"collisions":[],"minimum":1,"population":10},"passed":true},{"actual":{"canonical":[1,2],"cardinality":[0,1],"children":[],"collisions":[],"minimum":4,"population":6},"check":"regression certificate 5","expected":{"canonical":[1,2],"cardinality":[0,1],"children":[0],"collisions":[],"minimum":4,"population":6},"passed":false},{"actual":{"canonical":[1,1,3],"cardinality":[1],"children":[0],"collisions":[1],"minimum":0,"population":11},"check":"regression certificate 6","expected":{"canonical":[1,1,3],"cardinality":[1],"children":[0,1],"collisions":[1],"minimum":0,"population":11},"passed":false},{"actual":{"canonical":[1,1,3],"cardinality":[1],"children":[0],"collisions":[1],"minimum":0,"population":11},"check":"variant-dependent certificate","expected":{"canonical":[1,1,3],"cardinality":[1],"children":[0,1],"collisions":[1],"minimum":0,"population":11},"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression certificate 1\", \"actual\": {\"canonical\": [], \"collisions\": [], \"minimum\": null, \"population\": 0, \"cardinality\": [], \"children\": []}, \"expected\": {\"canonical\": [], \"collisions\": [], \"minimum\": null, \"population\": 0, \"cardinality\": [], \"children\": []}, \"passed\": true}, {\"check\": \"regression certificate 2\", \"actual\": {\"canonical\": [0], \"collisions\": [], \"minimum\": 8, \"population\": 1, \"cardinality\": [], \"children\": []}, \"expected\": {\"canonical\": [0], \"collisions\": [], \"minimum\": 8, \"population\": 1, \"cardinality\": [], \"children\": []}, \"passed\": true}, {\"check\": \"regression certificate 3\", \"actual\": {\"canonical\": [0, 2, 2], \"collisions\": [2], \"minimum\": 2, \"population\": 9, \"cardinality\": [], \"children\": []}, \"expected\": {\"canonical\": [0, 2, 2], \"collisions\": [2], \"minimum\": 2, \"population\": 9, \"cardinality\": [], \"children\": []}, \"passed\": true}, {\"check\": \"regression certificate 4\", \"actual\": {\"canonical\": [1, 3], \"collisions\": [], \"minimum\": 1, \"population\": 10, \"cardinality\": [], \"children\": []}, \"expected\": {\"canonical\": [1, 3], \"collisions\": [], \"minimum\": 1, \"population\": 10, \"cardinality\": [], \"children\": []}, \"passed\": true}, {\"check\": \"regression certificate 5\", \"actual\": {\"canonical\": [1, 2], \"collisions\": [], \"minimum\": 4, \"population\": 6, \"cardinality\": [0, 1], \"children\": []}, \"expected\": {\"canonical\": [1, 2], \"collisions\": [], \"minimum\": 4, \"population\": 6, \"cardinality\": [0, 1], \"children\": [0]}, \"passed\": false}, {\"check\": \"regression certificate 6\", \"actual\": {\"canonical\": [1, 1, 3], \"collisions\": [1], \"minimum\": 0, \"population\": 11, \"cardinality\": [1], \"children\": [0]}, \"expected\": {\"canonical\": [1, 1, 3], \"collisions\": [1], \"minimum\": 0, \"population\": 11, \"cardinality\": [1], \"children\": [0, 1]}, \"passed\": false}, {\"check\": \"variant-dependent certificate\", \"actual\": {\"canonical\": [1, 1, 3], \"collisions\": [1], \"minimum\": 0, \"population\": 11, \"cardinality\": [1], \"children\": [0]}, \"expected\": {\"canonical\": [1, 1, 3], \"collisions\": [1], \"minimum\": 0, \"population\": 11, \"cardinality\": [1], \"children\": [0, 1]}, \"passed\": false}], \"passed\": false}\n"},"fixed":{"elapsed_ms":42.634,"exit_code":0,"observations":[{"actual":{"canonical":[],"cardinality":[],"children":[],"collisions":[],"minimum":null,"population":0},"check":"regression certificate 1","expected":{"canonical":[],"cardinality":[],"children":[],"collisions":[],"minimum":null,"population":0},"passed":true},{"actual":{"canonical":[0],"cardinality":[],"children":[],"collisions":[],"minimum":8,"population":1},"check":"regression certificate 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0, \"cardinality\": [], \"children\": []}, \"passed\": true}, {\"check\": \"regression certificate 2\", \"actual\": {\"canonical\": [0], \"collisions\": [], \"minimum\": 8, \"population\": 1, \"cardinality\": [], \"children\": []}, \"expected\": {\"canonical\": [0], \"collisions\": [], \"minimum\": 8, \"population\": 1, \"cardinality\": [], \"children\": []}, \"passed\": true}, {\"check\": \"regression certificate 3\", \"actual\": {\"canonical\": [0, 2, 2], \"collisions\": [2], \"minimum\": 2, \"population\": 9, \"cardinality\": [], \"children\": []}, \"expected\": {\"canonical\": [0, 2, 2], \"collisions\": [2], \"minimum\": 2, \"population\": 9, \"cardinality\": [], \"children\": []}, \"passed\": true}, {\"check\": \"regression certificate 4\", \"actual\": {\"canonical\": [1, 3], \"collisions\": [], \"minimum\": 1, \"population\": 10, \"cardinality\": [], \"children\": []}, \"expected\": {\"canonical\": [1, 3], \"collisions\": [], \"minimum\": 1, \"population\": 10, \"cardinality\": [], \"children\": []}, \"passed\": true}, {\"check\": \"regression certificate 5\", \"actual\": {\"canonical\": [1, 2], \"collisions\": [], \"minimum\": 4, \"population\": 6, \"cardinality\": [0, 1], \"children\": [0]}, \"expected\": {\"canonical\": [1, 2], \"collisions\": [], \"minimum\": 4, \"population\": 6, \"cardinality\": [0, 1], \"children\": [0]}, \"passed\": true}, {\"check\": \"regression certificate 6\", \"actual\": {\"canonical\": [1, 1, 3], \"collisions\": [1], \"minimum\": 0, \"population\": 11, \"cardinality\": [1], \"children\": [0, 1]}, \"expected\": {\"canonical\": [1, 1, 3], \"collisions\": [1], \"minimum\": 0, \"population\": 11, \"cardinality\": [1], \"children\": [0, 1]}, \"passed\": true}, {\"check\": \"variant-dependent certificate\", \"actual\": {\"canonical\": [1, 1, 3], \"collisions\": [1], \"minimum\": 0, \"population\": 11, \"cardinality\": [1], \"children\": [0, 1]}, \"expected\": {\"canonical\": [1, 1, 3], \"collisions\": [1], \"minimum\": 0, \"population\": 11, \"cardinality\": [1], \"children\": [0, 1]}, \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}