{"abstract":"The bounded leftist ranks certificate reports an incorrect heap edges.","category":"Heap invariants","checks":7,"contract":"A leftist-tree certificate has nodes [key,left,right,stored_npl] with missing child=-1 and valid references. Null-path length of null is -1. Report local heap-edge violations, rank recurrence violations, leftist orientation violations, leaves, unary-right nodes, and root-to-right-spine length; spine traversal stops on repeated node.","evaluation_group":"s3-heap-model-leftist-ranks","failed_approach":"The local patch uses [[i,j] for i,x in enumerate(a) for j in x[1:3] if j!=-1 and a[j][0]<=x[0]] and still violates the stated relation.","family":"s3-heap-leftist-ranks-heap_edges","id":"FA-39901","implementations":{"attempt":{"sha256":"457bcf3174182104345b51a646d459c4a8d59f67faa84b18fb60fc83b41fa35c","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(d):\n    a=d['nodes']; root=d['root']\n    def rank(i): return -1 if i==-1 else a[i][3]\n    spine=[]; q=root\n    while q!=-1 and q not in spine:\n        spine.append(q); q=a[q][2]\n    return {'heap_edges': [[i,j] for i,x in enumerate(a) for j in x[1:3] if j!=-1 and a[j][0]<=x[0]],\n    'rank_recurrence': [i for i,x in enumerate(a) if x[3]!=1+min(rank(x[1]),rank(x[2]))],\n    'orientation': [i for i,x in enumerate(a) if rank(x[1])<rank(x[2])],\n    'leaves': [i for i,x in enumerate(a) if x[1]==-1 and x[2]==-1],\n    'right_orphans': [i for i,x in enumerate(a) if x[1]==-1 and x[2]!=-1],\n    'spine_length': len(spine)}\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncases = [[({'nodes': [], 'root': -1}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [], 'right_orphans': [], 'spine_length': 0}), ({'nodes': [[4, -1, -1, 0]], 'root': 0}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [0], 'right_orphans': [], 'spine_length': 1}), ({'nodes': [[1, 1, 2, 1], [5, -1, -1, 0], [7, -1, -1, 0]], 'root': 0}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [1, 2], 'right_orphans': [], 'spine_length': 2}), ({'nodes': [[5, 1, -1, 0], [5, -1, -1, 0]], 'root': 0}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [1], 'right_orphans': [], 'spine_length': 1}), ({'nodes': [[8, -1, 1, 1], [2, -1, -1, 0]], 'root': 0}, {'heap_edges': [[0, 1]], 'rank_recurrence': [0], 'orientation': [0], 'leaves': [1], 'right_orphans': [0], 'spine_length': 2}), ({'nodes': [[2, 1, 2, 2], [9, -1, -1, 0], [1, 3, 4, 1], [4, -1, -1, 0], [5, -1, -1, 0]], 'root': 0}, {'heap_edges': [[0, 2]], 'rank_recurrence': [0], 'orientation': [0], 'leaves': [1, 3, 4], 'right_orphans': [], 'spine_length': 3}), ({'nodes': [[3, 1, 2, 2], [9, -1, -1, 0], [1, 3, 4, 1], [4, -1, -1, 0], [5, -1, -1, 0]], 'root': 0}, {'heap_edges': [[0, 2]], 'rank_recurrence': [0], 'orientation': [0], 'leaves': [1, 3, 4], 'right_orphans': [], 'spine_length': 3})], [({'nodes': [], 'root': -1}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [], 'right_orphans': [], 'spine_length': 0}), ({'nodes': [[4, -1, -1, 0]], 'root': 0}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [0], 'right_orphans': [], 'spine_length': 1}), ({'nodes': [[1, 1, 2, 1], [5, -1, -1, 0], [7, -1, -1, 0]], 'root': 0}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [1, 2], 'right_orphans': [], 'spine_length': 2}), ({'nodes': [[5, 1, -1, 0], [5, -1, -1, 0]], 'root': 0}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [1], 'right_orphans': [], 'spine_length': 1}), ({'nodes': [[8, -1, 1, 1], [2, -1, -1, 0]], 'root': 0}, {'heap_edges': [[0, 1]], 'rank_recurrence': [0], 'orientation': [0], 'leaves': [1], 'right_orphans': [0], 'spine_length': 2}), ({'nodes': [[2, 1, 2, 2], [9, -1, -1, 0], [1, 3, 4, 1], [4, -1, -1, 0], [5, -1, -1, 0]], 'root': 0}, {'heap_edges': [[0, 2]], 'rank_recurrence': [0], 'orientation': [0], 'leaves': [1, 3, 4], 'right_orphans': [], 'spine_length': 3}), ({'nodes': [[4, 1, 2, 2], [9, -1, -1, 0], [1, 3, 4, 1], [4, -1, -1, 0], [5, -1, -1, 0]], 'root': 0}, {'heap_edges': [[0, 2]], 'rank_recurrence': [0], 'orientation': [0], 'leaves': [1, 3, 4], 'right_orphans': [], 'spine_length': 3})], [({'nodes': [], 'root': -1}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [], 'right_orphans': [], 'spine_length': 0}), ({'nodes': [[4, -1, -1, 0]], 'root': 0}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [0], 'right_orphans': [], 'spine_length': 1}), ({'nodes': [[1, 1, 2, 1], [5, -1, -1, 0], [7, -1, -1, 0]], 'root': 0}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [1, 2], 'right_orphans': [], 'spine_length': 2}), ({'nodes': [[5, 1, -1, 0], [5, -1, -1, 0]], 'root': 0}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [1], 'right_orphans': [], 'spine_length': 1}), ({'nodes': [[8, -1, 1, 1], [2, -1, -1, 0]], 'root': 0}, {'heap_edges': [[0, 1]], 'rank_recurrence': [0], 'orientation': [0], 'leaves': [1], 'right_orphans': [0], 'spine_length': 2}), ({'nodes': [[2, 1, 2, 2], [9, -1, -1, 0], [1, 3, 4, 1], [4, -1, -1, 0], [5, -1, -1, 0]], 'root': 0}, {'heap_edges': [[0, 2]], 'rank_recurrence': [0], 'orientation': [0], 'leaves': [1, 3, 4], 'right_orphans': [], 'spine_length': 3}), ({'nodes': [[5, 1, 2, 2], [9, -1, -1, 0], [1, 3, 4, 1], [4, -1, -1, 0], [5, -1, -1, 0]], 'root': 0}, {'heap_edges': [[0, 2]], 'rank_recurrence': [0], 'orientation': [0], 'leaves': [1, 3, 4], 'right_orphans': [], 'spine_length': 3})], [({'nodes': [], 'root': -1}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [], 'right_orphans': [], 'spine_length': 0}), ({'nodes': [[4, -1, -1, 0]], 'root': 0}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [0], 'right_orphans': [], 'spine_length': 1}), ({'nodes': [[1, 1, 2, 1], [5, -1, -1, 0], [7, -1, -1, 0]], 'root': 0}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [1, 2], 'right_orphans': [], 'spine_length': 2}), ({'nodes': [[5, 1, -1, 0], [5, -1, -1, 0]], 'root': 0}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [1], 'right_orphans': [], 'spine_length': 1}), ({'nodes': [[8, -1, 1, 1], [2, -1, -1, 0]], 'root': 0}, {'heap_edges': [[0, 1]], 'rank_recurrence': [0], 'orientation': [0], 'leaves': [1], 'right_orphans': [0], 'spine_length': 2}), ({'nodes': [[2, 1, 2, 2], [9, -1, -1, 0], [1, 3, 4, 1], [4, -1, -1, 0], [5, -1, -1, 0]], 'root': 0}, {'heap_edges': [[0, 2]], 'rank_recurrence': [0], 'orientation': [0], 'leaves': [1, 3, 4], 'right_orphans': [], 'spine_length': 3}), ({'nodes': [[6, 1, 2, 2], [9, -1, -1, 0], [1, 3, 4, 1], [4, -1, -1, 0], [5, -1, -1, 0]], 'root': 0}, {'heap_edges': [[0, 2]], 'rank_recurrence': [0], 'orientation': [0], 'leaves': [1, 3, 4], 'right_orphans': [], 'spine_length': 3})], [({'nodes': [], 'root': -1}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [], 'right_orphans': [], 'spine_length': 0}), ({'nodes': [[4, -1, -1, 0]], 'root': 0}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [0], 'right_orphans': [], 'spine_length': 1}), ({'nodes': [[1, 1, 2, 1], [5, -1, -1, 0], [7, -1, -1, 0]], 'root': 0}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [1, 2], 'right_orphans': [], 'spine_length': 2}), ({'nodes': [[5, 1, -1, 0], [5, -1, -1, 0]], 'root': 0}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [1], 'right_orphans': [], 'spine_length': 1}), ({'nodes': [[8, -1, 1, 1], [2, -1, -1, 0]], 'root': 0}, {'heap_edges': [[0, 1]], 'rank_recurrence': [0], 'orientation': [0], 'leaves': [1], 'right_orphans': [0], 'spine_length': 2}), ({'nodes': [[2, 1, 2, 2], [9, -1, -1, 0], [1, 3, 4, 1], [4, -1, -1, 0], [5, -1, -1, 0]], 'root': 0}, {'heap_edges': [[0, 2]], 'rank_recurrence': [0], 'orientation': [0], 'leaves': [1, 3, 4], 'right_orphans': [], 'spine_length': 3}), ({'nodes': [[7, 1, 2, 2], [9, -1, -1, 0], [1, 3, 4, 1], [4, -1, -1, 0], [5, -1, -1, 0]], 'root': 0}, {'heap_edges': [[0, 2]], 'rank_recurrence': [0], 'orientation': [0], 'leaves': [1, 3, 4], 'right_orphans': [], 'spine_length': 3})]][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":"e72398f2302e84dfd1172015314d3962a3f668e56fe72c31cb5b847898bd330d","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(d):\n    a=d['nodes']; root=d['root']\n    def rank(i): return -1 if i==-1 else a[i][3]\n    spine=[]; q=root\n    while q!=-1 and q not in spine:\n        spine.append(q); q=a[q][2]\n    return {'heap_edges': [[i,x[1]] for i,x in enumerate(a) if x[1]!=-1 and a[x[1]][0]<x[0]],\n    'rank_recurrence': [i for i,x in enumerate(a) if x[3]!=1+min(rank(x[1]),rank(x[2]))],\n    'orientation': [i for i,x in enumerate(a) if rank(x[1])<rank(x[2])],\n    'leaves': [i for i,x in enumerate(a) if x[1]==-1 and x[2]==-1],\n    'right_orphans': [i for i,x in enumerate(a) if x[1]==-1 and x[2]!=-1],\n    'spine_length': len(spine)}\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncases = [[({'nodes': [], 'root': -1}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [], 'right_orphans': [], 'spine_length': 0}), ({'nodes': [[4, -1, -1, 0]], 'root': 0}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [0], 'right_orphans': [], 'spine_length': 1}), ({'nodes': [[1, 1, 2, 1], [5, -1, -1, 0], [7, -1, -1, 0]], 'root': 0}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [1, 2], 'right_orphans': [], 'spine_length': 2}), ({'nodes': [[5, 1, -1, 0], [5, -1, -1, 0]], 'root': 0}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [1], 'right_orphans': [], 'spine_length': 1}), ({'nodes': [[8, -1, 1, 1], [2, -1, -1, 0]], 'root': 0}, {'heap_edges': [[0, 1]], 'rank_recurrence': [0], 'orientation': [0], 'leaves': [1], 'right_orphans': [0], 'spine_length': 2}), ({'nodes': [[2, 1, 2, 2], [9, -1, -1, 0], [1, 3, 4, 1], [4, -1, -1, 0], [5, -1, -1, 0]], 'root': 0}, {'heap_edges': [[0, 2]], 'rank_recurrence': [0], 'orientation': [0], 'leaves': [1, 3, 4], 'right_orphans': [], 'spine_length': 3}), ({'nodes': [[3, 1, 2, 2], [9, -1, -1, 0], [1, 3, 4, 1], [4, -1, -1, 0], [5, -1, -1, 0]], 'root': 0}, {'heap_edges': [[0, 2]], 'rank_recurrence': [0], 'orientation': [0], 'leaves': [1, 3, 4], 'right_orphans': [], 'spine_length': 3})], [({'nodes': [], 'root': -1}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [], 'right_orphans': [], 'spine_length': 0}), ({'nodes': [[4, -1, -1, 0]], 'root': 0}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [0], 'right_orphans': [], 'spine_length': 1}), ({'nodes': [[1, 1, 2, 1], [5, -1, -1, 0], [7, -1, -1, 0]], 'root': 0}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [1, 2], 'right_orphans': [], 'spine_length': 2}), ({'nodes': [[5, 1, -1, 0], [5, -1, -1, 0]], 'root': 0}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [1], 'right_orphans': [], 'spine_length': 1}), ({'nodes': [[8, -1, 1, 1], [2, -1, -1, 0]], 'root': 0}, {'heap_edges': [[0, 1]], 'rank_recurrence': [0], 'orientation': [0], 'leaves': [1], 'right_orphans': [0], 'spine_length': 2}), ({'nodes': [[2, 1, 2, 2], [9, -1, -1, 0], [1, 3, 4, 1], [4, -1, -1, 0], [5, -1, -1, 0]], 'root': 0}, {'heap_edges': [[0, 2]], 'rank_recurrence': [0], 'orientation': [0], 'leaves': [1, 3, 4], 'right_orphans': [], 'spine_length': 3}), ({'nodes': [[4, 1, 2, 2], [9, -1, -1, 0], [1, 3, 4, 1], [4, -1, -1, 0], [5, -1, -1, 0]], 'root': 0}, {'heap_edges': [[0, 2]], 'rank_recurrence': [0], 'orientation': [0], 'leaves': [1, 3, 4], 'right_orphans': [], 'spine_length': 3})], [({'nodes': [], 'root': -1}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [], 'right_orphans': [], 'spine_length': 0}), ({'nodes': [[4, -1, -1, 0]], 'root': 0}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [0], 'right_orphans': [], 'spine_length': 1}), ({'nodes': [[1, 1, 2, 1], [5, -1, -1, 0], [7, -1, -1, 0]], 'root': 0}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [1, 2], 'right_orphans': [], 'spine_length': 2}), ({'nodes': [[5, 1, -1, 0], [5, -1, -1, 0]], 'root': 0}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [1], 'right_orphans': [], 'spine_length': 1}), ({'nodes': [[8, -1, 1, 1], [2, -1, -1, 0]], 'root': 0}, {'heap_edges': [[0, 1]], 'rank_recurrence': [0], 'orientation': [0], 'leaves': [1], 'right_orphans': [0], 'spine_length': 2}), ({'nodes': [[2, 1, 2, 2], [9, -1, -1, 0], [1, 3, 4, 1], [4, -1, -1, 0], [5, -1, -1, 0]], 'root': 0}, {'heap_edges': [[0, 2]], 'rank_recurrence': [0], 'orientation': [0], 'leaves': [1, 3, 4], 'right_orphans': [], 'spine_length': 3}), ({'nodes': [[5, 1, 2, 2], [9, -1, -1, 0], [1, 3, 4, 1], [4, -1, -1, 0], [5, -1, -1, 0]], 'root': 0}, {'heap_edges': [[0, 2]], 'rank_recurrence': [0], 'orientation': [0], 'leaves': [1, 3, 4], 'right_orphans': [], 'spine_length': 3})], [({'nodes': [], 'root': -1}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [], 'right_orphans': [], 'spine_length': 0}), ({'nodes': [[4, -1, -1, 0]], 'root': 0}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [0], 'right_orphans': [], 'spine_length': 1}), ({'nodes': [[1, 1, 2, 1], [5, -1, -1, 0], [7, -1, -1, 0]], 'root': 0}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [1, 2], 'right_orphans': [], 'spine_length': 2}), ({'nodes': [[5, 1, -1, 0], [5, -1, -1, 0]], 'root': 0}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [1], 'right_orphans': [], 'spine_length': 1}), ({'nodes': [[8, -1, 1, 1], [2, -1, -1, 0]], 'root': 0}, {'heap_edges': [[0, 1]], 'rank_recurrence': [0], 'orientation': [0], 'leaves': [1], 'right_orphans': [0], 'spine_length': 2}), ({'nodes': [[2, 1, 2, 2], [9, -1, -1, 0], [1, 3, 4, 1], [4, -1, -1, 0], [5, -1, -1, 0]], 'root': 0}, {'heap_edges': [[0, 2]], 'rank_recurrence': [0], 'orientation': [0], 'leaves': [1, 3, 4], 'right_orphans': [], 'spine_length': 3}), ({'nodes': [[6, 1, 2, 2], [9, -1, -1, 0], [1, 3, 4, 1], [4, -1, -1, 0], [5, -1, -1, 0]], 'root': 0}, {'heap_edges': [[0, 2]], 'rank_recurrence': [0], 'orientation': [0], 'leaves': [1, 3, 4], 'right_orphans': [], 'spine_length': 3})], [({'nodes': [], 'root': -1}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [], 'right_orphans': [], 'spine_length': 0}), ({'nodes': [[4, -1, -1, 0]], 'root': 0}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [0], 'right_orphans': [], 'spine_length': 1}), ({'nodes': [[1, 1, 2, 1], [5, -1, -1, 0], [7, -1, -1, 0]], 'root': 0}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [1, 2], 'right_orphans': [], 'spine_length': 2}), ({'nodes': [[5, 1, -1, 0], [5, -1, -1, 0]], 'root': 0}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [1], 'right_orphans': [], 'spine_length': 1}), ({'nodes': [[8, -1, 1, 1], [2, -1, -1, 0]], 'root': 0}, {'heap_edges': [[0, 1]], 'rank_recurrence': [0], 'orientation': [0], 'leaves': [1], 'right_orphans': [0], 'spine_length': 2}), ({'nodes': [[2, 1, 2, 2], [9, -1, -1, 0], [1, 3, 4, 1], [4, -1, -1, 0], [5, -1, -1, 0]], 'root': 0}, {'heap_edges': [[0, 2]], 'rank_recurrence': [0], 'orientation': [0], 'leaves': [1, 3, 4], 'right_orphans': [], 'spine_length': 3}), ({'nodes': [[7, 1, 2, 2], [9, -1, -1, 0], [1, 3, 4, 1], [4, -1, -1, 0], [5, -1, -1, 0]], 'root': 0}, {'heap_edges': [[0, 2]], 'rank_recurrence': [0], 'orientation': [0], 'leaves': [1, 3, 4], 'right_orphans': [], 'spine_length': 3})]][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":"afb1ea1ed9648f06c0ecbcc1d8c3192066cc48d1472c5b9793221119551217c1","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(d):\n    a=d['nodes']; root=d['root']\n    def rank(i): return -1 if i==-1 else a[i][3]\n    spine=[]; q=root\n    while q!=-1 and q not in spine:\n        spine.append(q); q=a[q][2]\n    return {'heap_edges': [[i,j] for i,x in enumerate(a) for j in x[1:3] if j!=-1 and a[j][0]<x[0]],\n    'rank_recurrence': [i for i,x in enumerate(a) if x[3]!=1+min(rank(x[1]),rank(x[2]))],\n    'orientation': [i for i,x in enumerate(a) if rank(x[1])<rank(x[2])],\n    'leaves': [i for i,x in enumerate(a) if x[1]==-1 and x[2]==-1],\n    'right_orphans': [i for i,x in enumerate(a) if x[1]==-1 and x[2]!=-1],\n    'spine_length': len(spine)}\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncases = [[({'nodes': [], 'root': -1}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [], 'right_orphans': [], 'spine_length': 0}), ({'nodes': [[4, -1, -1, 0]], 'root': 0}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [0], 'right_orphans': [], 'spine_length': 1}), ({'nodes': [[1, 1, 2, 1], [5, -1, -1, 0], [7, -1, -1, 0]], 'root': 0}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [1, 2], 'right_orphans': [], 'spine_length': 2}), ({'nodes': [[5, 1, -1, 0], [5, -1, -1, 0]], 'root': 0}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [1], 'right_orphans': [], 'spine_length': 1}), ({'nodes': [[8, -1, 1, 1], [2, -1, -1, 0]], 'root': 0}, {'heap_edges': [[0, 1]], 'rank_recurrence': [0], 'orientation': [0], 'leaves': [1], 'right_orphans': [0], 'spine_length': 2}), ({'nodes': [[2, 1, 2, 2], [9, -1, -1, 0], [1, 3, 4, 1], [4, -1, -1, 0], [5, -1, -1, 0]], 'root': 0}, {'heap_edges': [[0, 2]], 'rank_recurrence': [0], 'orientation': [0], 'leaves': [1, 3, 4], 'right_orphans': [], 'spine_length': 3}), ({'nodes': [[3, 1, 2, 2], [9, -1, -1, 0], [1, 3, 4, 1], [4, -1, -1, 0], [5, -1, -1, 0]], 'root': 0}, {'heap_edges': [[0, 2]], 'rank_recurrence': [0], 'orientation': [0], 'leaves': [1, 3, 4], 'right_orphans': [], 'spine_length': 3})], [({'nodes': [], 'root': -1}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [], 'right_orphans': [], 'spine_length': 0}), ({'nodes': [[4, -1, -1, 0]], 'root': 0}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [0], 'right_orphans': [], 'spine_length': 1}), ({'nodes': [[1, 1, 2, 1], [5, -1, -1, 0], [7, -1, -1, 0]], 'root': 0}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [1, 2], 'right_orphans': [], 'spine_length': 2}), ({'nodes': [[5, 1, -1, 0], [5, -1, -1, 0]], 'root': 0}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [1], 'right_orphans': [], 'spine_length': 1}), ({'nodes': [[8, -1, 1, 1], [2, -1, -1, 0]], 'root': 0}, {'heap_edges': [[0, 1]], 'rank_recurrence': [0], 'orientation': [0], 'leaves': [1], 'right_orphans': [0], 'spine_length': 2}), ({'nodes': [[2, 1, 2, 2], [9, -1, -1, 0], [1, 3, 4, 1], [4, -1, -1, 0], [5, -1, -1, 0]], 'root': 0}, {'heap_edges': [[0, 2]], 'rank_recurrence': [0], 'orientation': [0], 'leaves': [1, 3, 4], 'right_orphans': [], 'spine_length': 3}), ({'nodes': [[4, 1, 2, 2], [9, -1, -1, 0], [1, 3, 4, 1], [4, -1, -1, 0], [5, -1, -1, 0]], 'root': 0}, {'heap_edges': [[0, 2]], 'rank_recurrence': [0], 'orientation': [0], 'leaves': [1, 3, 4], 'right_orphans': [], 'spine_length': 3})], [({'nodes': [], 'root': -1}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [], 'right_orphans': [], 'spine_length': 0}), ({'nodes': [[4, -1, -1, 0]], 'root': 0}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [0], 'right_orphans': [], 'spine_length': 1}), ({'nodes': [[1, 1, 2, 1], [5, -1, -1, 0], [7, -1, -1, 0]], 'root': 0}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [1, 2], 'right_orphans': [], 'spine_length': 2}), ({'nodes': [[5, 1, -1, 0], [5, -1, -1, 0]], 'root': 0}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [1], 'right_orphans': [], 'spine_length': 1}), ({'nodes': [[8, -1, 1, 1], [2, -1, -1, 0]], 'root': 0}, {'heap_edges': [[0, 1]], 'rank_recurrence': [0], 'orientation': [0], 'leaves': [1], 'right_orphans': [0], 'spine_length': 2}), ({'nodes': [[2, 1, 2, 2], [9, -1, -1, 0], [1, 3, 4, 1], [4, -1, -1, 0], [5, -1, -1, 0]], 'root': 0}, {'heap_edges': [[0, 2]], 'rank_recurrence': [0], 'orientation': [0], 'leaves': [1, 3, 4], 'right_orphans': [], 'spine_length': 3}), ({'nodes': [[5, 1, 2, 2], [9, -1, -1, 0], [1, 3, 4, 1], [4, -1, -1, 0], [5, -1, -1, 0]], 'root': 0}, {'heap_edges': [[0, 2]], 'rank_recurrence': [0], 'orientation': [0], 'leaves': [1, 3, 4], 'right_orphans': [], 'spine_length': 3})], [({'nodes': [], 'root': -1}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [], 'right_orphans': [], 'spine_length': 0}), ({'nodes': [[4, -1, -1, 0]], 'root': 0}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [0], 'right_orphans': [], 'spine_length': 1}), ({'nodes': [[1, 1, 2, 1], [5, -1, -1, 0], [7, -1, -1, 0]], 'root': 0}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [1, 2], 'right_orphans': [], 'spine_length': 2}), ({'nodes': [[5, 1, -1, 0], [5, -1, -1, 0]], 'root': 0}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [1], 'right_orphans': [], 'spine_length': 1}), ({'nodes': [[8, -1, 1, 1], [2, -1, -1, 0]], 'root': 0}, {'heap_edges': [[0, 1]], 'rank_recurrence': [0], 'orientation': [0], 'leaves': [1], 'right_orphans': [0], 'spine_length': 2}), ({'nodes': [[2, 1, 2, 2], [9, -1, -1, 0], [1, 3, 4, 1], [4, -1, -1, 0], [5, -1, -1, 0]], 'root': 0}, {'heap_edges': [[0, 2]], 'rank_recurrence': [0], 'orientation': [0], 'leaves': [1, 3, 4], 'right_orphans': [], 'spine_length': 3}), ({'nodes': [[6, 1, 2, 2], [9, -1, -1, 0], [1, 3, 4, 1], [4, -1, -1, 0], [5, -1, -1, 0]], 'root': 0}, {'heap_edges': [[0, 2]], 'rank_recurrence': [0], 'orientation': [0], 'leaves': [1, 3, 4], 'right_orphans': [], 'spine_length': 3})], [({'nodes': [], 'root': -1}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [], 'right_orphans': [], 'spine_length': 0}), ({'nodes': [[4, -1, -1, 0]], 'root': 0}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [0], 'right_orphans': [], 'spine_length': 1}), ({'nodes': [[1, 1, 2, 1], [5, -1, -1, 0], [7, -1, -1, 0]], 'root': 0}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [1, 2], 'right_orphans': [], 'spine_length': 2}), ({'nodes': [[5, 1, -1, 0], [5, -1, -1, 0]], 'root': 0}, {'heap_edges': [], 'rank_recurrence': [], 'orientation': [], 'leaves': [1], 'right_orphans': [], 'spine_length': 1}), ({'nodes': [[8, -1, 1, 1], [2, -1, -1, 0]], 'root': 0}, {'heap_edges': [[0, 1]], 'rank_recurrence': [0], 'orientation': [0], 'leaves': [1], 'right_orphans': [0], 'spine_length': 2}), ({'nodes': [[2, 1, 2, 2], [9, -1, -1, 0], [1, 3, 4, 1], [4, -1, -1, 0], [5, -1, -1, 0]], 'root': 0}, {'heap_edges': [[0, 2]], 'rank_recurrence': [0], 'orientation': [0], 'leaves': [1, 3, 4], 'right_orphans': [], 'spine_length': 3}), ({'nodes': [[7, 1, 2, 2], [9, -1, -1, 0], [1, 3, 4, 1], [4, -1, -1, 0], [5, -1, -1, 0]], 'root': 0}, {'heap_edges': [[0, 2]], 'rank_recurrence': [0], 'orientation': [0], 'leaves': [1, 3, 4], 'right_orphans': [], 'spine_length': 3})]][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-leftist-ranks-heap_edges","generated_at":"2026-09-29T14:43:25.928794+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 heap edges using [[i,j] for i,x in enumerate(a) for j in x[1:3] if j!=-1 and a[j][0]<x[0]] under the stated bounded certificate contract.","root_cause":"Heap order covers both links and permits equal priorities.","sha256":"48313f3f351a0b5a1ad14f88a0cdb0d5a122edba828fb7dacd7887bbf5a16f70","title":"Leftist verifier compares children only with the left child · case 01","variant":1,"variant_policy":"Six explicit regression certificates are retained; a seventh changes structural size, position, priority, or bounds with N.","verification":{"attempt":{"elapsed_ms":46.657,"exit_code":1,"observations":[{"actual":{"heap_edges":[],"leaves":[],"orientation":[],"rank_recurrence":[],"right_orphans":[],"spine_length":0},"check":"regression certificate 1","expected":{"heap_edges":[],"leaves":[],"orientation":[],"rank_recurrence":[],"right_orphans":[],"spine_length":0},"passed":true},{"actual":{"heap_edges":[],"leaves":[0],"orientation":[],"rank_recurrence":[],"right_orphans":[],"spine_length":1},"check":"regression certificate 2","expected":{"heap_edges":[],"leaves":[0],"orientation":[],"rank_recurrence":[],"right_orphans":[],"spine_length":1},"passed":true},{"actual":{"heap_edges":[],"leaves":[1,2],"orientation":[],"rank_recurrence":[],"right_orphans":[],"spine_length":2},"check":"regression certificate 3","expected":{"heap_edges":[],"leaves":[1,2],"orientation":[],"rank_recurrence":[],"right_orphans":[],"spine_length":2},"passed":true},{"actual":{"heap_edges":[[0,1]],"leaves":[1],"orientation":[],"rank_recurrence":[],"right_orphans":[],"spine_length":1},"check":"regression certificate 4","expected":{"heap_edges":[],"leaves":[1],"orientation":[],"rank_recurrence":[],"right_orphans":[],"spine_length":1},"passed":false},{"actual":{"heap_edges":[[0,1]],"leaves":[1],"orientation":[0],"rank_recurrence":[0],"right_orphans":[0],"spine_length":2},"check":"regression certificate 5","expected":{"heap_edges":[[0,1]],"leaves":[1],"orientation":[0],"rank_recurrence":[0],"right_orphans":[0],"spine_length":2},"passed":true},{"actual":{"heap_edges":[[0,2]],"leaves":[1,3,4],"orientation":[0],"rank_recurrence":[0],"right_orphans":[],"spine_length":3},"check":"regression certificate 6","expected":{"heap_edges":[[0,2]],"leaves":[1,3,4],"orientation":[0],"rank_recurrence":[0],"right_orphans":[],"spine_length":3},"passed":true},{"actual":{"heap_edges":[[0,2]],"leaves":[1,3,4],"orientation":[0],"rank_recurrence":[0],"right_orphans":[],"spine_length":3},"check":"variant-dependent certificate","expected":{"heap_edges":[[0,2]],"leaves":[1,3,4],"orientation":[0],"rank_recurrence":[0],"right_orphans":[],"spine_length":3},"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression certificate 1\", \"actual\": {\"heap_edges\": [], \"rank_recurrence\": [], \"orientation\": [], \"leaves\": [], \"right_orphans\": [], \"spine_length\": 0}, \"expected\": {\"heap_edges\": [], \"rank_recurrence\": [], \"orientation\": [], \"leaves\": [], \"right_orphans\": [], \"spine_length\": 0}, \"passed\": true}, {\"check\": \"regression certificate 2\", \"actual\": {\"heap_edges\": [], \"rank_recurrence\": [], \"orientation\": [], \"leaves\": [0], \"right_orphans\": [], \"spine_length\": 1}, \"expected\": {\"heap_edges\": [], \"rank_recurrence\": [], \"orientation\": [], \"leaves\": [0], \"right_orphans\": [], \"spine_length\": 1}, \"passed\": true}, {\"check\": \"regression certificate 3\", \"actual\": {\"heap_edges\": [], \"rank_recurrence\": [], \"orientation\": [], \"leaves\": [1, 2], \"right_orphans\": [], \"spine_length\": 2}, \"expected\": {\"heap_edges\": [], \"rank_recurrence\": [], \"orientation\": [], \"leaves\": [1, 2], \"right_orphans\": [], \"spine_length\": 2}, \"passed\": true}, {\"check\": \"regression certificate 4\", \"actual\": {\"heap_edges\": [[0, 1]], \"rank_recurrence\": [], \"orientation\": [], \"leaves\": [1], \"right_orphans\": [], \"spine_length\": 1}, \"expected\": {\"heap_edges\": [], \"rank_recurrence\": [], \"orientation\": [], \"leaves\": [1], \"right_orphans\": [], \"spine_length\": 1}, \"passed\": false}, {\"check\": \"regression certificate 5\", \"actual\": {\"heap_edges\": [[0, 1]], \"rank_recurrence\": [0], \"orientation\": [0], \"leaves\": [1], \"right_orphans\": [0], \"spine_length\": 2}, \"expected\": {\"heap_edges\": [[0, 1]], \"rank_recurrence\": [0], \"orientation\": [0], \"leaves\": [1], \"right_orphans\": [0], \"spine_length\": 2}, \"passed\": true}, {\"check\": \"regression certificate 6\", \"actual\": {\"heap_edges\": [[0, 2]], \"rank_recurrence\": [0], \"orientation\": [0], \"leaves\": [1, 3, 4], \"right_orphans\": [], \"spine_length\": 3}, \"expected\": {\"heap_edges\": [[0, 2]], \"rank_recurrence\": [0], \"orientation\": [0], \"leaves\": [1, 3, 4], \"right_orphans\": [], \"spine_length\": 3}, \"passed\": true}, {\"check\": \"variant-dependent certificate\", \"actual\": {\"heap_edges\": [[0, 2]], \"rank_recurrence\": [0], \"orientation\": [0], \"leaves\": [1, 3, 4], \"right_orphans\": [], \"spine_length\": 3}, \"expected\": {\"heap_edges\": [[0, 2]], \"rank_recurrence\": [0], \"orientation\": [0], \"leaves\": [1, 3, 4], \"right_orphans\": [], \"spine_length\": 3}, \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":44.228,"exit_code":1,"observations":[{"actual":{"heap_edges":[],"leaves":[],"orientation":[],"rank_recurrence":[],"right_orphans":[],"spine_length":0},"check":"regression certificate 1","expected":{"heap_edges":[],"leaves":[],"orientation":[],"rank_recurrence":[],"right_orphans":[],"spine_length":0},"passed":true},{"actual":{"heap_edges":[],"leaves":[0],"orientation":[],"rank_recurrence":[],"right_orphans":[],"spine_length":1},"check":"regression certificate 2","expected":{"heap_edges":[],"leaves":[0],"orientation":[],"rank_recurrence":[],"right_orphans":[],"spine_length":1},"passed":true},{"actual":{"heap_edges":[],"leaves":[1,2],"orientation":[],"rank_recurrence":[],"right_orphans":[],"spine_length":2},"check":"regression certificate 3","expected":{"heap_edges":[],"leaves":[1,2],"orientation":[],"rank_recurrence":[],"right_orphans":[],"spine_length":2},"passed":true},{"actual":{"heap_edges":[],"leaves":[1],"orientation":[],"rank_recurrence":[],"right_orphans":[],"spine_length":1},"check":"regression certificate 4","expected":{"heap_edges":[],"leaves":[1],"orientation":[],"rank_recurrence":[],"right_orphans":[],"spine_length":1},"passed":true},{"actual":{"heap_edges":[],"leaves":[1],"orientation":[0],"rank_recurrence":[0],"right_orphans":[0],"spine_length":2},"check":"regression certificate 5","expected":{"heap_edges":[[0,1]],"leaves":[1],"orientation":[0],"rank_recurrence":[0],"right_orphans":[0],"spine_length":2},"passed":false},{"actual":{"heap_edges":[],"leaves":[1,3,4],"orientation":[0],"rank_recurrence":[0],"right_orphans":[],"spine_length":3},"check":"regression certificate 6","expected":{"heap_edges":[[0,2]],"leaves":[1,3,4],"orientation":[0],"rank_recurrence":[0],"right_orphans":[],"spine_length":3},"passed":false},{"actual":{"heap_edges":[],"leaves":[1,3,4],"orientation":[0],"rank_recurrence":[0],"right_orphans":[],"spine_length":3},"check":"variant-dependent certificate","expected":{"heap_edges":[[0,2]],"leaves":[1,3,4],"orientation":[0],"rank_recurrence":[0],"right_orphans":[],"spine_length":3},"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression certificate 1\", \"actual\": {\"heap_edges\": [], \"rank_recurrence\": [], \"orientation\": [], \"leaves\": [], \"right_orphans\": [], \"spine_length\": 0}, \"expected\": {\"heap_edges\": [], \"rank_recurrence\": [], \"orientation\": [], \"leaves\": [], \"right_orphans\": [], \"spine_length\": 0}, \"passed\": true}, {\"check\": \"regression certificate 2\", \"actual\": {\"heap_edges\": [], \"rank_recurrence\": [], \"orientation\": [], \"leaves\": [0], \"right_orphans\": [], \"spine_length\": 1}, \"expected\": {\"heap_edges\": [], \"rank_recurrence\": [], \"orientation\": [], \"leaves\": [0], \"right_orphans\": [], \"spine_length\": 1}, \"passed\": true}, {\"check\": \"regression certificate 3\", \"actual\": {\"heap_edges\": [], \"rank_recurrence\": [], \"orientation\": [], \"leaves\": [1, 2], \"right_orphans\": [], \"spine_length\": 2}, \"expected\": {\"heap_edges\": [], \"rank_recurrence\": [], \"orientation\": [], \"leaves\": [1, 2], \"right_orphans\": [], \"spine_length\": 2}, \"passed\": true}, {\"check\": \"regression certificate 4\", \"actual\": {\"heap_edges\": [], \"rank_recurrence\": [], \"orientation\": [], \"leaves\": [1], \"right_orphans\": [], \"spine_length\": 1}, \"expected\": {\"heap_edges\": [], \"rank_recurrence\": [], \"orientation\": [], \"leaves\": [1], \"right_orphans\": [], \"spine_length\": 1}, \"passed\": true}, {\"check\": \"regression certificate 5\", \"actual\": {\"heap_edges\": [], \"rank_recurrence\": [0], \"orientation\": [0], \"leaves\": [1], \"right_orphans\": [0], \"spine_length\": 2}, \"expected\": {\"heap_edges\": [[0, 1]], \"rank_recurrence\": [0], \"orientation\": [0], \"leaves\": [1], \"right_orphans\": [0], \"spine_length\": 2}, \"passed\": false}, {\"check\": \"regression certificate 6\", \"actual\": {\"heap_edges\": [], \"rank_recurrence\": [0], \"orientation\": [0], \"leaves\": [1, 3, 4], \"right_orphans\": [], \"spine_length\": 3}, \"expected\": {\"heap_edges\": [[0, 2]], \"rank_recurrence\": [0], \"orientation\": [0], \"leaves\": [1, 3, 4], \"right_orphans\": [], \"spine_length\": 3}, \"passed\": false}, {\"check\": \"variant-dependent certificate\", \"actual\": {\"heap_edges\": [], \"rank_recurrence\": [0], \"orientation\": [0], \"leaves\": [1, 3, 4], \"right_orphans\": [], \"spine_length\": 3}, \"expected\": {\"heap_edges\": [[0, 2]], \"rank_recurrence\": [0], \"orientation\": [0], \"leaves\": [1, 3, 4], \"right_orphans\": [], \"spine_length\": 3}, \"passed\": false}], \"passed\": false}\n"},"fixed":{"elapsed_ms":42.242,"exit_code":0,"observations":[{"actual":{"heap_edges":[],"leaves":[],"orientation":[],"rank_recurrence":[],"right_orphans":[],"spine_length":0},"check":"regression certificate 1","expected":{"heap_edges":[],"leaves":[],"orientation":[],"rank_recurrence":[],"right_orphans":[],"spine_length":0},"passed":true},{"actual":{"heap_edges":[],"leaves":[0],"orientation":[],"rank_recurrence":[],"right_orphans":[],"spine_length":1},"check":"regression certificate 2","expected":{"heap_edges":[],"leaves":[0],"orientation":[],"rank_recurrence":[],"right_orphans":[],"spine_length":1},"passed":true},{"actual":{"heap_edges":[],"leaves":[1,2],"orientation":[],"rank_recurrence":[],"right_orphans":[],"spine_length":2},"check":"regression certificate 3","expected":{"heap_edges":[],"leaves":[1,2],"orientation":[],"rank_recurrence":[],"right_orphans":[],"spine_length":2},"passed":true},{"actual":{"heap_edges":[],"leaves":[1],"orientation":[],"rank_recurrence":[],"right_orphans":[],"spine_length":1},"check":"regression certificate 4","expected":{"heap_edges":[],"leaves":[1],"orientation":[],"rank_recurrence":[],"right_orphans":[],"spine_length":1},"passed":true},{"actual":{"heap_edges":[[0,1]],"leaves":[1],"orientation":[0],"rank_recurrence":[0],"right_orphans":[0],"spine_length":2},"check":"regression certificate 5","expected":{"heap_edges":[[0,1]],"leaves":[1],"orientation":[0],"rank_recurrence":[0],"right_orphans":[0],"spine_length":2},"passed":true},{"actual":{"heap_edges":[[0,2]],"leaves":[1,3,4],"orientation":[0],"rank_recurrence":[0],"right_orphans":[],"spine_length":3},"check":"regression certificate 6","expected":{"heap_edges":[[0,2]],"leaves":[1,3,4],"orientation":[0],"rank_recurrence":[0],"right_orphans":[],"spine_length":3},"passed":true},{"actual":{"heap_edges":[[0,2]],"leaves":[1,3,4],"orientation":[0],"rank_recurrence":[0],"right_orphans":[],"spine_length":3},"check":"variant-dependent certificate","expected":{"heap_edges":[[0,2]],"leaves":[1,3,4],"orientation":[0],"rank_recurrence":[0],"right_orphans":[],"spine_length":3},"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression certificate 1\", \"actual\": {\"heap_edges\": [], \"rank_recurrence\": [], \"orientation\": [], \"leaves\": [], \"right_orphans\": [], \"spine_length\": 0}, \"expected\": {\"heap_edges\": [], \"rank_recurrence\": [], \"orientation\": [], \"leaves\": [], \"right_orphans\": [], \"spine_length\": 0}, \"passed\": true}, {\"check\": \"regression certificate 2\", \"actual\": {\"heap_edges\": [], \"rank_recurrence\": [], \"orientation\": [], \"leaves\": [0], \"right_orphans\": [], \"spine_length\": 1}, \"expected\": {\"heap_edges\": [], \"rank_recurrence\": [], \"orientation\": [], \"leaves\": [0], \"right_orphans\": [], \"spine_length\": 1}, \"passed\": true}, {\"check\": \"regression certificate 3\", \"actual\": {\"heap_edges\": [], \"rank_recurrence\": [], \"orientation\": [], \"leaves\": [1, 2], \"right_orphans\": [], \"spine_length\": 2}, \"expected\": {\"heap_edges\": [], \"rank_recurrence\": [], \"orientation\": [], \"leaves\": [1, 2], \"right_orphans\": [], \"spine_length\": 2}, \"passed\": true}, {\"check\": \"regression certificate 4\", \"actual\": {\"heap_edges\": [], \"rank_recurrence\": [], \"orientation\": [], \"leaves\": [1], \"right_orphans\": [], \"spine_length\": 1}, \"expected\": {\"heap_edges\": [], \"rank_recurrence\": [], \"orientation\": [], \"leaves\": [1], \"right_orphans\": [], \"spine_length\": 1}, \"passed\": true}, {\"check\": \"regression certificate 5\", \"actual\": {\"heap_edges\": [[0, 1]], \"rank_recurrence\": [0], \"orientation\": [0], \"leaves\": [1], \"right_orphans\": [0], \"spine_length\": 2}, \"expected\": {\"heap_edges\": [[0, 1]], \"rank_recurrence\": [0], \"orientation\": [0], \"leaves\": [1], \"right_orphans\": [0], \"spine_length\": 2}, \"passed\": true}, {\"check\": \"regression certificate 6\", \"actual\": {\"heap_edges\": [[0, 2]], \"rank_recurrence\": [0], \"orientation\": [0], \"leaves\": [1, 3, 4], \"right_orphans\": [], \"spine_length\": 3}, \"expected\": {\"heap_edges\": [[0, 2]], \"rank_recurrence\": [0], \"orientation\": [0], \"leaves\": [1, 3, 4], \"right_orphans\": [], \"spine_length\": 3}, \"passed\": true}, {\"check\": \"variant-dependent certificate\", \"actual\": {\"heap_edges\": [[0, 2]], \"rank_recurrence\": [0], \"orientation\": [0], \"leaves\": [1, 3, 4], \"right_orphans\": [], \"spine_length\": 3}, \"expected\": {\"heap_edges\": [[0, 2]], \"rank_recurrence\": [0], \"orientation\": [0], \"leaves\": [1, 3, 4], \"right_orphans\": [], \"spine_length\": 3}, \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}