{"abstract":"The bounded skew meld step certificate reports an incorrect size.","category":"Heap invariants","checks":7,"contract":"A skew meld unwind chooses the smaller root, recursively melds its old right subtree with the other heap, and unconditionally swaps children. Record supplies winner, old_left, recursive_result and sizes. Missing subtrees are None. No rank-based swap condition is part of this model.","evaluation_group":"s3-heap-model-skew-meld-step","failed_approach":"The local patch uses sum(sizes) and still violates the stated relation.","family":"s3-heap-skew-meld-step-size","id":"FA-40211","implementations":{"attempt":{"sha256":"7c4ffe5f57cc25c8d7be86ab0150f9aa24b5d800fa0f01343783e2ce5e8a2537","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(d):\n    old=d['old_left']; result=d['result']; sizes=d['sizes']\n    return {'new_left': result,\n    'new_right': old,\n    'size': sum(sizes),\n    'rewrites': [[x,d[\"winner\"]] for x in (result,old) if x is not None],\n    'preorder_children': [x for x in (result,old) if x is not None],\n    'leaf': old is None and result is None}\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncases = [[({'winner': 9, 'old_left': None, 'result': None, 'sizes': [0, 0]}, {'new_left': None, 'new_right': None, 'size': 1, 'rewrites': [], 'preorder_children': [], 'leaf': True}), ({'winner': 9, 'old_left': 1, 'result': None, 'sizes': [2, 0]}, {'new_left': None, 'new_right': 1, 'size': 3, 'rewrites': [[1, 9]], 'preorder_children': [1], 'leaf': False}), ({'winner': 9, 'old_left': None, 'result': 3, 'sizes': [0, 4]}, {'new_left': 3, 'new_right': None, 'size': 5, 'rewrites': [[3, 9]], 'preorder_children': [3], 'leaf': False}), ({'winner': 9, 'old_left': 1, 'result': 2, 'sizes': [5, 3]}, {'new_left': 2, 'new_right': 1, 'size': 9, 'rewrites': [[2, 9], [1, 9]], 'preorder_children': [2, 1], 'leaf': False}), ({'winner': 9, 'old_left': 7, 'result': 2, 'sizes': [1, 2]}, {'new_left': 2, 'new_right': 7, 'size': 4, 'rewrites': [[2, 9], [7, 9]], 'preorder_children': [2, 7], 'leaf': False}), ({'winner': 9, 'old_left': 4, 'result': 8, 'sizes': [7, 9]}, {'new_left': 8, 'new_right': 4, 'size': 17, 'rewrites': [[8, 9], [4, 9]], 'preorder_children': [8, 4], 'leaf': False}), ({'winner': 9, 'old_left': 4, 'result': 8, 'sizes': [8, 10]}, {'new_left': 8, 'new_right': 4, 'size': 19, 'rewrites': [[8, 9], [4, 9]], 'preorder_children': [8, 4], 'leaf': False})], [({'winner': 9, 'old_left': None, 'result': None, 'sizes': [0, 0]}, {'new_left': None, 'new_right': None, 'size': 1, 'rewrites': [], 'preorder_children': [], 'leaf': True}), ({'winner': 9, 'old_left': 1, 'result': None, 'sizes': [2, 0]}, {'new_left': None, 'new_right': 1, 'size': 3, 'rewrites': [[1, 9]], 'preorder_children': [1], 'leaf': False}), ({'winner': 9, 'old_left': None, 'result': 3, 'sizes': [0, 4]}, {'new_left': 3, 'new_right': None, 'size': 5, 'rewrites': [[3, 9]], 'preorder_children': [3], 'leaf': False}), ({'winner': 9, 'old_left': 1, 'result': 2, 'sizes': [5, 3]}, {'new_left': 2, 'new_right': 1, 'size': 9, 'rewrites': [[2, 9], [1, 9]], 'preorder_children': [2, 1], 'leaf': False}), ({'winner': 9, 'old_left': 7, 'result': 2, 'sizes': [1, 2]}, {'new_left': 2, 'new_right': 7, 'size': 4, 'rewrites': [[2, 9], [7, 9]], 'preorder_children': [2, 7], 'leaf': False}), ({'winner': 9, 'old_left': 4, 'result': 8, 'sizes': [7, 9]}, {'new_left': 8, 'new_right': 4, 'size': 17, 'rewrites': [[8, 9], [4, 9]], 'preorder_children': [8, 4], 'leaf': False}), ({'winner': 9, 'old_left': 4, 'result': 8, 'sizes': [9, 11]}, {'new_left': 8, 'new_right': 4, 'size': 21, 'rewrites': [[8, 9], [4, 9]], 'preorder_children': [8, 4], 'leaf': False})], [({'winner': 9, 'old_left': None, 'result': None, 'sizes': [0, 0]}, {'new_left': None, 'new_right': None, 'size': 1, 'rewrites': [], 'preorder_children': [], 'leaf': True}), ({'winner': 9, 'old_left': 1, 'result': None, 'sizes': [2, 0]}, {'new_left': None, 'new_right': 1, 'size': 3, 'rewrites': [[1, 9]], 'preorder_children': [1], 'leaf': False}), ({'winner': 9, 'old_left': None, 'result': 3, 'sizes': [0, 4]}, {'new_left': 3, 'new_right': None, 'size': 5, 'rewrites': [[3, 9]], 'preorder_children': [3], 'leaf': False}), ({'winner': 9, 'old_left': 1, 'result': 2, 'sizes': [5, 3]}, {'new_left': 2, 'new_right': 1, 'size': 9, 'rewrites': [[2, 9], [1, 9]], 'preorder_children': [2, 1], 'leaf': False}), ({'winner': 9, 'old_left': 7, 'result': 2, 'sizes': [1, 2]}, {'new_left': 2, 'new_right': 7, 'size': 4, 'rewrites': [[2, 9], [7, 9]], 'preorder_children': [2, 7], 'leaf': False}), ({'winner': 9, 'old_left': 4, 'result': 8, 'sizes': [7, 9]}, {'new_left': 8, 'new_right': 4, 'size': 17, 'rewrites': [[8, 9], [4, 9]], 'preorder_children': [8, 4], 'leaf': False}), ({'winner': 9, 'old_left': 4, 'result': 8, 'sizes': [10, 12]}, {'new_left': 8, 'new_right': 4, 'size': 23, 'rewrites': [[8, 9], [4, 9]], 'preorder_children': [8, 4], 'leaf': False})], [({'winner': 9, 'old_left': None, 'result': None, 'sizes': [0, 0]}, {'new_left': None, 'new_right': None, 'size': 1, 'rewrites': [], 'preorder_children': [], 'leaf': True}), ({'winner': 9, 'old_left': 1, 'result': None, 'sizes': [2, 0]}, {'new_left': None, 'new_right': 1, 'size': 3, 'rewrites': [[1, 9]], 'preorder_children': [1], 'leaf': False}), ({'winner': 9, 'old_left': None, 'result': 3, 'sizes': [0, 4]}, {'new_left': 3, 'new_right': None, 'size': 5, 'rewrites': [[3, 9]], 'preorder_children': [3], 'leaf': False}), ({'winner': 9, 'old_left': 1, 'result': 2, 'sizes': [5, 3]}, {'new_left': 2, 'new_right': 1, 'size': 9, 'rewrites': [[2, 9], [1, 9]], 'preorder_children': [2, 1], 'leaf': False}), ({'winner': 9, 'old_left': 7, 'result': 2, 'sizes': [1, 2]}, {'new_left': 2, 'new_right': 7, 'size': 4, 'rewrites': [[2, 9], [7, 9]], 'preorder_children': [2, 7], 'leaf': False}), ({'winner': 9, 'old_left': 4, 'result': 8, 'sizes': [7, 9]}, {'new_left': 8, 'new_right': 4, 'size': 17, 'rewrites': [[8, 9], [4, 9]], 'preorder_children': [8, 4], 'leaf': False}), ({'winner': 9, 'old_left': 4, 'result': 8, 'sizes': [11, 13]}, {'new_left': 8, 'new_right': 4, 'size': 25, 'rewrites': [[8, 9], [4, 9]], 'preorder_children': [8, 4], 'leaf': False})], [({'winner': 9, 'old_left': None, 'result': None, 'sizes': [0, 0]}, {'new_left': None, 'new_right': None, 'size': 1, 'rewrites': [], 'preorder_children': [], 'leaf': True}), ({'winner': 9, 'old_left': 1, 'result': None, 'sizes': [2, 0]}, {'new_left': None, 'new_right': 1, 'size': 3, 'rewrites': [[1, 9]], 'preorder_children': [1], 'leaf': False}), ({'winner': 9, 'old_left': None, 'result': 3, 'sizes': [0, 4]}, {'new_left': 3, 'new_right': None, 'size': 5, 'rewrites': [[3, 9]], 'preorder_children': [3], 'leaf': False}), ({'winner': 9, 'old_left': 1, 'result': 2, 'sizes': [5, 3]}, {'new_left': 2, 'new_right': 1, 'size': 9, 'rewrites': [[2, 9], [1, 9]], 'preorder_children': [2, 1], 'leaf': False}), ({'winner': 9, 'old_left': 7, 'result': 2, 'sizes': [1, 2]}, {'new_left': 2, 'new_right': 7, 'size': 4, 'rewrites': [[2, 9], [7, 9]], 'preorder_children': [2, 7], 'leaf': False}), ({'winner': 9, 'old_left': 4, 'result': 8, 'sizes': [7, 9]}, {'new_left': 8, 'new_right': 4, 'size': 17, 'rewrites': [[8, 9], [4, 9]], 'preorder_children': [8, 4], 'leaf': False}), ({'winner': 9, 'old_left': 4, 'result': 8, 'sizes': [12, 14]}, {'new_left': 8, 'new_right': 4, 'size': 27, 'rewrites': [[8, 9], [4, 9]], 'preorder_children': [8, 4], 'leaf': False})]][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":"1975149b392942c8318e984097e2c29b824202a5b9113f2b7468e8974fdf5778","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(d):\n    old=d['old_left']; result=d['result']; sizes=d['sizes']\n    return {'new_left': result,\n    'new_right': old,\n    'size': max(sizes,default=0)+1,\n    'rewrites': [[x,d[\"winner\"]] for x in (result,old) if x is not None],\n    'preorder_children': [x for x in (result,old) if x is not None],\n    'leaf': old is None and result is None}\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncases = [[({'winner': 9, 'old_left': None, 'result': None, 'sizes': [0, 0]}, {'new_left': None, 'new_right': None, 'size': 1, 'rewrites': [], 'preorder_children': [], 'leaf': True}), ({'winner': 9, 'old_left': 1, 'result': None, 'sizes': [2, 0]}, {'new_left': None, 'new_right': 1, 'size': 3, 'rewrites': [[1, 9]], 'preorder_children': [1], 'leaf': False}), ({'winner': 9, 'old_left': None, 'result': 3, 'sizes': [0, 4]}, {'new_left': 3, 'new_right': None, 'size': 5, 'rewrites': [[3, 9]], 'preorder_children': [3], 'leaf': False}), ({'winner': 9, 'old_left': 1, 'result': 2, 'sizes': [5, 3]}, {'new_left': 2, 'new_right': 1, 'size': 9, 'rewrites': [[2, 9], [1, 9]], 'preorder_children': [2, 1], 'leaf': False}), ({'winner': 9, 'old_left': 7, 'result': 2, 'sizes': [1, 2]}, {'new_left': 2, 'new_right': 7, 'size': 4, 'rewrites': [[2, 9], [7, 9]], 'preorder_children': [2, 7], 'leaf': False}), ({'winner': 9, 'old_left': 4, 'result': 8, 'sizes': [7, 9]}, {'new_left': 8, 'new_right': 4, 'size': 17, 'rewrites': [[8, 9], [4, 9]], 'preorder_children': [8, 4], 'leaf': False}), ({'winner': 9, 'old_left': 4, 'result': 8, 'sizes': [8, 10]}, {'new_left': 8, 'new_right': 4, 'size': 19, 'rewrites': [[8, 9], [4, 9]], 'preorder_children': [8, 4], 'leaf': False})], [({'winner': 9, 'old_left': None, 'result': None, 'sizes': [0, 0]}, {'new_left': None, 'new_right': None, 'size': 1, 'rewrites': [], 'preorder_children': [], 'leaf': True}), ({'winner': 9, 'old_left': 1, 'result': None, 'sizes': [2, 0]}, {'new_left': None, 'new_right': 1, 'size': 3, 'rewrites': [[1, 9]], 'preorder_children': [1], 'leaf': False}), ({'winner': 9, 'old_left': None, 'result': 3, 'sizes': [0, 4]}, {'new_left': 3, 'new_right': None, 'size': 5, 'rewrites': [[3, 9]], 'preorder_children': [3], 'leaf': False}), ({'winner': 9, 'old_left': 1, 'result': 2, 'sizes': [5, 3]}, {'new_left': 2, 'new_right': 1, 'size': 9, 'rewrites': [[2, 9], [1, 9]], 'preorder_children': [2, 1], 'leaf': False}), ({'winner': 9, 'old_left': 7, 'result': 2, 'sizes': [1, 2]}, {'new_left': 2, 'new_right': 7, 'size': 4, 'rewrites': [[2, 9], [7, 9]], 'preorder_children': [2, 7], 'leaf': False}), ({'winner': 9, 'old_left': 4, 'result': 8, 'sizes': [7, 9]}, {'new_left': 8, 'new_right': 4, 'size': 17, 'rewrites': [[8, 9], [4, 9]], 'preorder_children': [8, 4], 'leaf': False}), ({'winner': 9, 'old_left': 4, 'result': 8, 'sizes': [9, 11]}, {'new_left': 8, 'new_right': 4, 'size': 21, 'rewrites': [[8, 9], [4, 9]], 'preorder_children': [8, 4], 'leaf': False})], [({'winner': 9, 'old_left': None, 'result': None, 'sizes': [0, 0]}, {'new_left': None, 'new_right': None, 'size': 1, 'rewrites': [], 'preorder_children': [], 'leaf': True}), ({'winner': 9, 'old_left': 1, 'result': None, 'sizes': [2, 0]}, {'new_left': None, 'new_right': 1, 'size': 3, 'rewrites': [[1, 9]], 'preorder_children': [1], 'leaf': False}), ({'winner': 9, 'old_left': None, 'result': 3, 'sizes': [0, 4]}, {'new_left': 3, 'new_right': None, 'size': 5, 'rewrites': [[3, 9]], 'preorder_children': [3], 'leaf': False}), ({'winner': 9, 'old_left': 1, 'result': 2, 'sizes': [5, 3]}, {'new_left': 2, 'new_right': 1, 'size': 9, 'rewrites': [[2, 9], [1, 9]], 'preorder_children': [2, 1], 'leaf': False}), ({'winner': 9, 'old_left': 7, 'result': 2, 'sizes': [1, 2]}, {'new_left': 2, 'new_right': 7, 'size': 4, 'rewrites': [[2, 9], [7, 9]], 'preorder_children': [2, 7], 'leaf': False}), ({'winner': 9, 'old_left': 4, 'result': 8, 'sizes': [7, 9]}, {'new_left': 8, 'new_right': 4, 'size': 17, 'rewrites': [[8, 9], [4, 9]], 'preorder_children': [8, 4], 'leaf': False}), ({'winner': 9, 'old_left': 4, 'result': 8, 'sizes': [10, 12]}, {'new_left': 8, 'new_right': 4, 'size': 23, 'rewrites': [[8, 9], [4, 9]], 'preorder_children': [8, 4], 'leaf': False})], [({'winner': 9, 'old_left': None, 'result': None, 'sizes': [0, 0]}, {'new_left': None, 'new_right': None, 'size': 1, 'rewrites': [], 'preorder_children': [], 'leaf': True}), ({'winner': 9, 'old_left': 1, 'result': None, 'sizes': [2, 0]}, {'new_left': None, 'new_right': 1, 'size': 3, 'rewrites': [[1, 9]], 'preorder_children': [1], 'leaf': False}), ({'winner': 9, 'old_left': None, 'result': 3, 'sizes': [0, 4]}, {'new_left': 3, 'new_right': None, 'size': 5, 'rewrites': [[3, 9]], 'preorder_children': [3], 'leaf': False}), ({'winner': 9, 'old_left': 1, 'result': 2, 'sizes': [5, 3]}, {'new_left': 2, 'new_right': 1, 'size': 9, 'rewrites': [[2, 9], [1, 9]], 'preorder_children': [2, 1], 'leaf': False}), ({'winner': 9, 'old_left': 7, 'result': 2, 'sizes': [1, 2]}, {'new_left': 2, 'new_right': 7, 'size': 4, 'rewrites': [[2, 9], [7, 9]], 'preorder_children': [2, 7], 'leaf': False}), ({'winner': 9, 'old_left': 4, 'result': 8, 'sizes': [7, 9]}, {'new_left': 8, 'new_right': 4, 'size': 17, 'rewrites': [[8, 9], [4, 9]], 'preorder_children': [8, 4], 'leaf': False}), ({'winner': 9, 'old_left': 4, 'result': 8, 'sizes': [11, 13]}, {'new_left': 8, 'new_right': 4, 'size': 25, 'rewrites': [[8, 9], [4, 9]], 'preorder_children': [8, 4], 'leaf': False})], [({'winner': 9, 'old_left': None, 'result': None, 'sizes': [0, 0]}, {'new_left': None, 'new_right': None, 'size': 1, 'rewrites': [], 'preorder_children': [], 'leaf': True}), ({'winner': 9, 'old_left': 1, 'result': None, 'sizes': [2, 0]}, {'new_left': None, 'new_right': 1, 'size': 3, 'rewrites': [[1, 9]], 'preorder_children': [1], 'leaf': False}), ({'winner': 9, 'old_left': None, 'result': 3, 'sizes': [0, 4]}, {'new_left': 3, 'new_right': None, 'size': 5, 'rewrites': [[3, 9]], 'preorder_children': [3], 'leaf': False}), ({'winner': 9, 'old_left': 1, 'result': 2, 'sizes': [5, 3]}, {'new_left': 2, 'new_right': 1, 'size': 9, 'rewrites': [[2, 9], [1, 9]], 'preorder_children': [2, 1], 'leaf': False}), ({'winner': 9, 'old_left': 7, 'result': 2, 'sizes': [1, 2]}, {'new_left': 2, 'new_right': 7, 'size': 4, 'rewrites': [[2, 9], [7, 9]], 'preorder_children': [2, 7], 'leaf': False}), ({'winner': 9, 'old_left': 4, 'result': 8, 'sizes': [7, 9]}, {'new_left': 8, 'new_right': 4, 'size': 17, 'rewrites': [[8, 9], [4, 9]], 'preorder_children': [8, 4], 'leaf': False}), ({'winner': 9, 'old_left': 4, 'result': 8, 'sizes': [12, 14]}, {'new_left': 8, 'new_right': 4, 'size': 27, 'rewrites': [[8, 9], [4, 9]], 'preorder_children': [8, 4], 'leaf': False})]][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":"04de77e3580155d55e2f1fad03479510df3fe6a16dd22973c1ebfcdc99eae9b6","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(d):\n    old=d['old_left']; result=d['result']; sizes=d['sizes']\n    return {'new_left': result,\n    'new_right': old,\n    'size': 1+sum(sizes),\n    'rewrites': [[x,d[\"winner\"]] for x in (result,old) if x is not None],\n    'preorder_children': [x for x in (result,old) if x is not None],\n    'leaf': old is None and result is None}\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncases = [[({'winner': 9, 'old_left': None, 'result': None, 'sizes': [0, 0]}, {'new_left': None, 'new_right': None, 'size': 1, 'rewrites': [], 'preorder_children': [], 'leaf': True}), ({'winner': 9, 'old_left': 1, 'result': None, 'sizes': [2, 0]}, {'new_left': None, 'new_right': 1, 'size': 3, 'rewrites': [[1, 9]], 'preorder_children': [1], 'leaf': False}), ({'winner': 9, 'old_left': None, 'result': 3, 'sizes': [0, 4]}, {'new_left': 3, 'new_right': None, 'size': 5, 'rewrites': [[3, 9]], 'preorder_children': [3], 'leaf': False}), ({'winner': 9, 'old_left': 1, 'result': 2, 'sizes': [5, 3]}, {'new_left': 2, 'new_right': 1, 'size': 9, 'rewrites': [[2, 9], [1, 9]], 'preorder_children': [2, 1], 'leaf': False}), ({'winner': 9, 'old_left': 7, 'result': 2, 'sizes': [1, 2]}, {'new_left': 2, 'new_right': 7, 'size': 4, 'rewrites': [[2, 9], [7, 9]], 'preorder_children': [2, 7], 'leaf': False}), ({'winner': 9, 'old_left': 4, 'result': 8, 'sizes': [7, 9]}, {'new_left': 8, 'new_right': 4, 'size': 17, 'rewrites': [[8, 9], [4, 9]], 'preorder_children': [8, 4], 'leaf': False}), ({'winner': 9, 'old_left': 4, 'result': 8, 'sizes': [8, 10]}, {'new_left': 8, 'new_right': 4, 'size': 19, 'rewrites': [[8, 9], [4, 9]], 'preorder_children': [8, 4], 'leaf': False})], [({'winner': 9, 'old_left': None, 'result': None, 'sizes': [0, 0]}, {'new_left': None, 'new_right': None, 'size': 1, 'rewrites': [], 'preorder_children': [], 'leaf': True}), ({'winner': 9, 'old_left': 1, 'result': None, 'sizes': [2, 0]}, {'new_left': None, 'new_right': 1, 'size': 3, 'rewrites': [[1, 9]], 'preorder_children': [1], 'leaf': False}), ({'winner': 9, 'old_left': None, 'result': 3, 'sizes': [0, 4]}, {'new_left': 3, 'new_right': None, 'size': 5, 'rewrites': [[3, 9]], 'preorder_children': [3], 'leaf': False}), ({'winner': 9, 'old_left': 1, 'result': 2, 'sizes': [5, 3]}, {'new_left': 2, 'new_right': 1, 'size': 9, 'rewrites': [[2, 9], [1, 9]], 'preorder_children': [2, 1], 'leaf': False}), ({'winner': 9, 'old_left': 7, 'result': 2, 'sizes': [1, 2]}, {'new_left': 2, 'new_right': 7, 'size': 4, 'rewrites': [[2, 9], [7, 9]], 'preorder_children': [2, 7], 'leaf': False}), ({'winner': 9, 'old_left': 4, 'result': 8, 'sizes': [7, 9]}, {'new_left': 8, 'new_right': 4, 'size': 17, 'rewrites': [[8, 9], [4, 9]], 'preorder_children': [8, 4], 'leaf': False}), ({'winner': 9, 'old_left': 4, 'result': 8, 'sizes': [9, 11]}, {'new_left': 8, 'new_right': 4, 'size': 21, 'rewrites': [[8, 9], [4, 9]], 'preorder_children': [8, 4], 'leaf': False})], [({'winner': 9, 'old_left': None, 'result': None, 'sizes': [0, 0]}, {'new_left': None, 'new_right': None, 'size': 1, 'rewrites': [], 'preorder_children': [], 'leaf': True}), ({'winner': 9, 'old_left': 1, 'result': None, 'sizes': [2, 0]}, {'new_left': None, 'new_right': 1, 'size': 3, 'rewrites': [[1, 9]], 'preorder_children': [1], 'leaf': False}), ({'winner': 9, 'old_left': None, 'result': 3, 'sizes': [0, 4]}, {'new_left': 3, 'new_right': None, 'size': 5, 'rewrites': [[3, 9]], 'preorder_children': [3], 'leaf': False}), ({'winner': 9, 'old_left': 1, 'result': 2, 'sizes': [5, 3]}, {'new_left': 2, 'new_right': 1, 'size': 9, 'rewrites': [[2, 9], [1, 9]], 'preorder_children': [2, 1], 'leaf': False}), ({'winner': 9, 'old_left': 7, 'result': 2, 'sizes': [1, 2]}, {'new_left': 2, 'new_right': 7, 'size': 4, 'rewrites': [[2, 9], [7, 9]], 'preorder_children': [2, 7], 'leaf': False}), ({'winner': 9, 'old_left': 4, 'result': 8, 'sizes': [7, 9]}, {'new_left': 8, 'new_right': 4, 'size': 17, 'rewrites': [[8, 9], [4, 9]], 'preorder_children': [8, 4], 'leaf': False}), ({'winner': 9, 'old_left': 4, 'result': 8, 'sizes': [10, 12]}, {'new_left': 8, 'new_right': 4, 'size': 23, 'rewrites': [[8, 9], [4, 9]], 'preorder_children': [8, 4], 'leaf': False})], [({'winner': 9, 'old_left': None, 'result': None, 'sizes': [0, 0]}, {'new_left': None, 'new_right': None, 'size': 1, 'rewrites': [], 'preorder_children': [], 'leaf': True}), ({'winner': 9, 'old_left': 1, 'result': None, 'sizes': [2, 0]}, {'new_left': None, 'new_right': 1, 'size': 3, 'rewrites': [[1, 9]], 'preorder_children': [1], 'leaf': False}), ({'winner': 9, 'old_left': None, 'result': 3, 'sizes': [0, 4]}, {'new_left': 3, 'new_right': None, 'size': 5, 'rewrites': [[3, 9]], 'preorder_children': [3], 'leaf': False}), ({'winner': 9, 'old_left': 1, 'result': 2, 'sizes': [5, 3]}, {'new_left': 2, 'new_right': 1, 'size': 9, 'rewrites': [[2, 9], [1, 9]], 'preorder_children': [2, 1], 'leaf': False}), ({'winner': 9, 'old_left': 7, 'result': 2, 'sizes': [1, 2]}, {'new_left': 2, 'new_right': 7, 'size': 4, 'rewrites': [[2, 9], [7, 9]], 'preorder_children': [2, 7], 'leaf': False}), ({'winner': 9, 'old_left': 4, 'result': 8, 'sizes': [7, 9]}, {'new_left': 8, 'new_right': 4, 'size': 17, 'rewrites': [[8, 9], [4, 9]], 'preorder_children': [8, 4], 'leaf': False}), ({'winner': 9, 'old_left': 4, 'result': 8, 'sizes': [11, 13]}, {'new_left': 8, 'new_right': 4, 'size': 25, 'rewrites': [[8, 9], [4, 9]], 'preorder_children': [8, 4], 'leaf': False})], [({'winner': 9, 'old_left': None, 'result': None, 'sizes': [0, 0]}, {'new_left': None, 'new_right': None, 'size': 1, 'rewrites': [], 'preorder_children': [], 'leaf': True}), ({'winner': 9, 'old_left': 1, 'result': None, 'sizes': [2, 0]}, {'new_left': None, 'new_right': 1, 'size': 3, 'rewrites': [[1, 9]], 'preorder_children': [1], 'leaf': False}), ({'winner': 9, 'old_left': None, 'result': 3, 'sizes': [0, 4]}, {'new_left': 3, 'new_right': None, 'size': 5, 'rewrites': [[3, 9]], 'preorder_children': [3], 'leaf': False}), ({'winner': 9, 'old_left': 1, 'result': 2, 'sizes': [5, 3]}, {'new_left': 2, 'new_right': 1, 'size': 9, 'rewrites': [[2, 9], [1, 9]], 'preorder_children': [2, 1], 'leaf': False}), ({'winner': 9, 'old_left': 7, 'result': 2, 'sizes': [1, 2]}, {'new_left': 2, 'new_right': 7, 'size': 4, 'rewrites': [[2, 9], [7, 9]], 'preorder_children': [2, 7], 'leaf': False}), ({'winner': 9, 'old_left': 4, 'result': 8, 'sizes': [7, 9]}, {'new_left': 8, 'new_right': 4, 'size': 17, 'rewrites': [[8, 9], [4, 9]], 'preorder_children': [8, 4], 'leaf': False}), ({'winner': 9, 'old_left': 4, 'result': 8, 'sizes': [12, 14]}, {'new_left': 8, 'new_right': 4, 'size': 27, 'rewrites': [[8, 9], [4, 9]], 'preorder_children': [8, 4], 'leaf': False})]][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-skew-meld-step-size","generated_at":"2026-09-29T14:43:28.840856+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 size using 1+sum(sizes) under the stated bounded certificate contract.","root_cause":"Skew meld size includes both disjoint recursive inputs and the chosen root.","sha256":"15a4eaaeb16cb182617e65626e4a9195759307b0261c12be0a1508a07c54c79a","title":"Skew meld size includes both disjoint recursive inputs and the chosen root · 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":47.363,"exit_code":1,"observations":[{"actual":{"leaf":true,"new_left":null,"new_right":null,"preorder_children":[],"rewrites":[],"size":0},"check":"regression certificate 1","expected":{"leaf":true,"new_left":null,"new_right":null,"preorder_children":[],"rewrites":[],"size":1},"passed":false},{"actual":{"leaf":false,"new_left":null,"new_right":1,"preorder_children":[1],"rewrites":[[1,9]],"size":2},"check":"regression certificate 2","expected":{"leaf":false,"new_left":null,"new_right":1,"preorder_children":[1],"rewrites":[[1,9]],"size":3},"passed":false},{"actual":{"leaf":false,"new_left":3,"new_right":null,"preorder_children":[3],"rewrites":[[3,9]],"size":4},"check":"regression certificate 3","expected":{"leaf":false,"new_left":3,"new_right":null,"preorder_children":[3],"rewrites":[[3,9]],"size":5},"passed":false},{"actual":{"leaf":false,"new_left":2,"new_right":1,"preorder_children":[2,1],"rewrites":[[2,9],[1,9]],"size":8},"check":"regression certificate 4","expected":{"leaf":false,"new_left":2,"new_right":1,"preorder_children":[2,1],"rewrites":[[2,9],[1,9]],"size":9},"passed":false},{"actual":{"leaf":false,"new_left":2,"new_right":7,"preorder_children":[2,7],"rewrites":[[2,9],[7,9]],"size":3},"check":"regression certificate 5","expected":{"leaf":false,"new_left":2,"new_right":7,"preorder_children":[2,7],"rewrites":[[2,9],[7,9]],"size":4},"passed":false},{"actual":{"leaf":false,"new_left":8,"new_right":4,"preorder_children":[8,4],"rewrites":[[8,9],[4,9]],"size":16},"check":"regression certificate 6","expected":{"leaf":false,"new_left":8,"new_right":4,"preorder_children":[8,4],"rewrites":[[8,9],[4,9]],"size":17},"passed":false},{"actual":{"leaf":false,"new_left":8,"new_right":4,"preorder_children":[8,4],"rewrites":[[8,9],[4,9]],"size":18},"check":"variant-dependent certificate","expected":{"leaf":false,"new_left":8,"new_right":4,"preorder_children":[8,4],"rewrites":[[8,9],[4,9]],"size":19},"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression certificate 1\", \"actual\": {\"new_left\": null, \"new_right\": null, \"size\": 0, \"rewrites\": [], \"preorder_children\": [], \"leaf\": true}, \"expected\": {\"new_left\": null, \"new_right\": null, \"size\": 1, \"rewrites\": [], \"preorder_children\": [], \"leaf\": true}, \"passed\": false}, {\"check\": \"regression certificate 2\", \"actual\": {\"new_left\": null, \"new_right\": 1, \"size\": 2, \"rewrites\": [[1, 9]], \"preorder_children\": [1], \"leaf\": false}, \"expected\": {\"new_left\": null, \"new_right\": 1, \"size\": 3, \"rewrites\": [[1, 9]], \"preorder_children\": [1], \"leaf\": false}, \"passed\": false}, {\"check\": \"regression certificate 3\", \"actual\": {\"new_left\": 3, \"new_right\": null, \"size\": 4, \"rewrites\": [[3, 9]], \"preorder_children\": [3], \"leaf\": false}, \"expected\": {\"new_left\": 3, \"new_right\": null, \"size\": 5, \"rewrites\": [[3, 9]], \"preorder_children\": [3], \"leaf\": false}, \"passed\": false}, {\"check\": \"regression certificate 4\", \"actual\": {\"new_left\": 2, \"new_right\": 1, \"size\": 8, \"rewrites\": [[2, 9], [1, 9]], \"preorder_children\": [2, 1], \"leaf\": false}, \"expected\": {\"new_left\": 2, \"new_right\": 1, \"size\": 9, \"rewrites\": [[2, 9], [1, 9]], \"preorder_children\": [2, 1], \"leaf\": false}, \"passed\": false}, {\"check\": \"regression certificate 5\", \"actual\": {\"new_left\": 2, \"new_right\": 7, \"size\": 3, \"rewrites\": [[2, 9], [7, 9]], \"preorder_children\": [2, 7], \"leaf\": false}, \"expected\": {\"new_left\": 2, \"new_right\": 7, \"size\": 4, \"rewrites\": [[2, 9], [7, 9]], \"preorder_children\": [2, 7], \"leaf\": false}, \"passed\": false}, {\"check\": \"regression certificate 6\", \"actual\": {\"new_left\": 8, \"new_right\": 4, \"size\": 16, \"rewrites\": [[8, 9], [4, 9]], \"preorder_children\": [8, 4], \"leaf\": false}, \"expected\": {\"new_left\": 8, \"new_right\": 4, \"size\": 17, \"rewrites\": [[8, 9], [4, 9]], \"preorder_children\": [8, 4], \"leaf\": false}, \"passed\": false}, {\"check\": \"variant-dependent certificate\", \"actual\": {\"new_left\": 8, \"new_right\": 4, \"size\": 18, \"rewrites\": [[8, 9], [4, 9]], \"preorder_children\": [8, 4], \"leaf\": false}, \"expected\": {\"new_left\": 8, \"new_right\": 4, \"size\": 19, \"rewrites\": [[8, 9], [4, 9]], \"preorder_children\": [8, 4], \"leaf\": false}, \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":50.522,"exit_code":1,"observations":[{"actual":{"leaf":true,"new_left":null,"new_right":null,"preorder_children":[],"rewrites":[],"size":1},"check":"regression certificate 1","expected":{"leaf":true,"new_left":null,"new_right":null,"preorder_children":[],"rewrites":[],"size":1},"passed":true},{"actual":{"leaf":false,"new_left":null,"new_right":1,"preorder_children":[1],"rewrites":[[1,9]],"size":3},"check":"regression certificate 2","expected":{"leaf":false,"new_left":null,"new_right":1,"preorder_children":[1],"rewrites":[[1,9]],"size":3},"passed":true},{"actual":{"leaf":false,"new_left":3,"new_right":null,"preorder_children":[3],"rewrites":[[3,9]],"size":5},"check":"regression certificate 3","expected":{"leaf":false,"new_left":3,"new_right":null,"preorder_children":[3],"rewrites":[[3,9]],"size":5},"passed":true},{"actual":{"leaf":false,"new_left":2,"new_right":1,"preorder_children":[2,1],"rewrites":[[2,9],[1,9]],"size":6},"check":"regression certificate 4","expected":{"leaf":false,"new_left":2,"new_right":1,"preorder_children":[2,1],"rewrites":[[2,9],[1,9]],"size":9},"passed":false},{"actual":{"leaf":false,"new_left":2,"new_right":7,"preorder_children":[2,7],"rewrites":[[2,9],[7,9]],"size":3},"check":"regression certificate 5","expected":{"leaf":false,"new_left":2,"new_right":7,"preorder_children":[2,7],"rewrites":[[2,9],[7,9]],"size":4},"passed":false},{"actual":{"leaf":false,"new_left":8,"new_right":4,"preorder_children":[8,4],"rewrites":[[8,9],[4,9]],"size":10},"check":"regression certificate 6","expected":{"leaf":false,"new_left":8,"new_right":4,"preorder_children":[8,4],"rewrites":[[8,9],[4,9]],"size":17},"passed":false},{"actual":{"leaf":false,"new_left":8,"new_right":4,"preorder_children":[8,4],"rewrites":[[8,9],[4,9]],"size":11},"check":"variant-dependent certificate","expected":{"leaf":false,"new_left":8,"new_right":4,"preorder_children":[8,4],"rewrites":[[8,9],[4,9]],"size":19},"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression certificate 1\", \"actual\": {\"new_left\": null, \"new_right\": null, \"size\": 1, \"rewrites\": [], \"preorder_children\": [], \"leaf\": true}, \"expected\": {\"new_left\": null, \"new_right\": null, \"size\": 1, \"rewrites\": [], \"preorder_children\": [], \"leaf\": true}, \"passed\": true}, {\"check\": \"regression certificate 2\", \"actual\": {\"new_left\": null, \"new_right\": 1, \"size\": 3, \"rewrites\": [[1, 9]], \"preorder_children\": [1], \"leaf\": false}, \"expected\": {\"new_left\": null, \"new_right\": 1, \"size\": 3, \"rewrites\": [[1, 9]], \"preorder_children\": [1], \"leaf\": false}, \"passed\": true}, {\"check\": \"regression certificate 3\", \"actual\": {\"new_left\": 3, \"new_right\": null, \"size\": 5, \"rewrites\": [[3, 9]], \"preorder_children\": [3], \"leaf\": false}, \"expected\": {\"new_left\": 3, \"new_right\": null, \"size\": 5, \"rewrites\": [[3, 9]], \"preorder_children\": [3], \"leaf\": false}, \"passed\": true}, {\"check\": \"regression certificate 4\", \"actual\": {\"new_left\": 2, \"new_right\": 1, \"size\": 6, \"rewrites\": [[2, 9], [1, 9]], \"preorder_children\": [2, 1], \"leaf\": false}, \"expected\": {\"new_left\": 2, \"new_right\": 1, \"size\": 9, \"rewrites\": [[2, 9], [1, 9]], \"preorder_children\": [2, 1], \"leaf\": false}, \"passed\": false}, {\"check\": \"regression certificate 5\", \"actual\": {\"new_left\": 2, \"new_right\": 7, \"size\": 3, \"rewrites\": [[2, 9], [7, 9]], \"preorder_children\": [2, 7], \"leaf\": false}, \"expected\": {\"new_left\": 2, \"new_right\": 7, \"size\": 4, \"rewrites\": [[2, 9], [7, 9]], \"preorder_children\": [2, 7], \"leaf\": false}, \"passed\": false}, {\"check\": \"regression certificate 6\", \"actual\": {\"new_left\": 8, \"new_right\": 4, \"size\": 10, \"rewrites\": [[8, 9], [4, 9]], \"preorder_children\": [8, 4], \"leaf\": false}, \"expected\": {\"new_left\": 8, \"new_right\": 4, \"size\": 17, \"rewrites\": [[8, 9], [4, 9]], \"preorder_children\": [8, 4], \"leaf\": false}, \"passed\": false}, {\"check\": \"variant-dependent certificate\", \"actual\": {\"new_left\": 8, \"new_right\": 4, \"size\": 11, \"rewrites\": [[8, 9], [4, 9]], \"preorder_children\": [8, 4], \"leaf\": false}, \"expected\": {\"new_left\": 8, \"new_right\": 4, \"size\": 19, \"rewrites\": [[8, 9], [4, 9]], \"preorder_children\": [8, 4], \"leaf\": false}, \"passed\": false}], \"passed\": false}\n"},"fixed":{"elapsed_ms":44.009,"exit_code":0,"observations":[{"actual":{"leaf":true,"new_left":null,"new_right":null,"preorder_children":[],"rewrites":[],"size":1},"check":"regression certificate 1","expected":{"leaf":true,"new_left":null,"new_right":null,"preorder_children":[],"rewrites":[],"size":1},"passed":true},{"actual":{"leaf":false,"new_left":null,"new_right":1,"preorder_children":[1],"rewrites":[[1,9]],"size":3},"check":"regression certificate 2","expected":{"leaf":false,"new_left":null,"new_right":1,"preorder_children":[1],"rewrites":[[1,9]],"size":3},"passed":true},{"actual":{"leaf":false,"new_left":3,"new_right":null,"preorder_children":[3],"rewrites":[[3,9]],"size":5},"check":"regression certificate 3","expected":{"leaf":false,"new_left":3,"new_right":null,"preorder_children":[3],"rewrites":[[3,9]],"size":5},"passed":true},{"actual":{"leaf":false,"new_left":2,"new_right":1,"preorder_children":[2,1],"rewrites":[[2,9],[1,9]],"size":9},"check":"regression certificate 4","expected":{"leaf":false,"new_left":2,"new_right":1,"preorder_children":[2,1],"rewrites":[[2,9],[1,9]],"size":9},"passed":true},{"actual":{"leaf":false,"new_left":2,"new_right":7,"preorder_children":[2,7],"rewrites":[[2,9],[7,9]],"size":4},"check":"regression certificate 5","expected":{"leaf":false,"new_left":2,"new_right":7,"preorder_children":[2,7],"rewrites":[[2,9],[7,9]],"size":4},"passed":true},{"actual":{"leaf":false,"new_left":8,"new_right":4,"preorder_children":[8,4],"rewrites":[[8,9],[4,9]],"size":17},"check":"regression certificate 6","expected":{"leaf":false,"new_left":8,"new_right":4,"preorder_children":[8,4],"rewrites":[[8,9],[4,9]],"size":17},"passed":true},{"actual":{"leaf":false,"new_left":8,"new_right":4,"preorder_children":[8,4],"rewrites":[[8,9],[4,9]],"size":19},"check":"variant-dependent certificate","expected":{"leaf":false,"new_left":8,"new_right":4,"preorder_children":[8,4],"rewrites":[[8,9],[4,9]],"size":19},"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression certificate 1\", \"actual\": {\"new_left\": null, \"new_right\": null, \"size\": 1, \"rewrites\": [], \"preorder_children\": [], \"leaf\": true}, \"expected\": {\"new_left\": null, \"new_right\": null, \"size\": 1, \"rewrites\": [], \"preorder_children\": [], \"leaf\": true}, \"passed\": true}, {\"check\": \"regression certificate 2\", \"actual\": {\"new_left\": null, \"new_right\": 1, \"size\": 3, \"rewrites\": [[1, 9]], \"preorder_children\": [1], \"leaf\": false}, \"expected\": {\"new_left\": null, \"new_right\": 1, \"size\": 3, \"rewrites\": [[1, 9]], \"preorder_children\": [1], \"leaf\": false}, \"passed\": true}, {\"check\": \"regression certificate 3\", \"actual\": {\"new_left\": 3, \"new_right\": null, \"size\": 5, \"rewrites\": [[3, 9]], \"preorder_children\": [3], \"leaf\": false}, \"expected\": {\"new_left\": 3, \"new_right\": null, \"size\": 5, \"rewrites\": [[3, 9]], \"preorder_children\": [3], \"leaf\": false}, \"passed\": true}, {\"check\": \"regression certificate 4\", \"actual\": {\"new_left\": 2, \"new_right\": 1, \"size\": 9, \"rewrites\": [[2, 9], [1, 9]], \"preorder_children\": [2, 1], \"leaf\": false}, \"expected\": {\"new_left\": 2, \"new_right\": 1, \"size\": 9, \"rewrites\": [[2, 9], [1, 9]], \"preorder_children\": [2, 1], \"leaf\": false}, \"passed\": true}, {\"check\": \"regression certificate 5\", \"actual\": {\"new_left\": 2, \"new_right\": 7, \"size\": 4, \"rewrites\": [[2, 9], [7, 9]], \"preorder_children\": [2, 7], \"leaf\": false}, \"expected\": {\"new_left\": 2, \"new_right\": 7, \"size\": 4, \"rewrites\": [[2, 9], [7, 9]], \"preorder_children\": [2, 7], \"leaf\": false}, \"passed\": true}, {\"check\": \"regression certificate 6\", \"actual\": {\"new_left\": 8, \"new_right\": 4, \"size\": 17, \"rewrites\": [[8, 9], [4, 9]], \"preorder_children\": [8, 4], \"leaf\": false}, \"expected\": {\"new_left\": 8, \"new_right\": 4, \"size\": 17, \"rewrites\": [[8, 9], [4, 9]], \"preorder_children\": [8, 4], \"leaf\": false}, \"passed\": true}, {\"check\": \"variant-dependent certificate\", \"actual\": {\"new_left\": 8, \"new_right\": 4, \"size\": 19, \"rewrites\": [[8, 9], [4, 9]], \"preorder_children\": [8, 4], \"leaf\": false}, \"expected\": {\"new_left\": 8, \"new_right\": 4, \"size\": 19, \"rewrites\": [[8, 9], [4, 9]], \"preorder_children\": [8, 4], \"leaf\": false}, \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}