{"abstract":"The bounded fibonacci cascade certificate reports an incorrect potential delta.","category":"Heap invariants","checks":7,"contract":"A cascading-cut path runs from the parent of an initially cut node upward as [id,is_root,marked]. Stop at a root or first unmarked nonroot; mark that first unmarked node. Previously marked nonroots are cut and unmarked. Report cut ids, marked stop, cleared ids, visited count, promoted count, and potential change roots+2*marks.","evaluation_group":"s3-heap-model-fibonacci-cascade","failed_approach":"The local patch uses -2*len(cut)+(2 if marked is not None else 0) and still violates the stated relation.","family":"s3-heap-fibonacci-cascade-potential_delta","id":"FA-40136","implementations":{"attempt":{"sha256":"020e2d5b0399c509ec66b2d1f74b5dc71dbc30a7ca38ce5ee8f8e361cb7ec51f","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(d):\n    path=d['path']; cut=[]; marked=None; visited=0\n    for ident,root,mark in path:\n        visited+=1\n        if root: break\n        if not mark:\n            marked=ident; break\n        cut.append(ident)\n    return {'cuts': cut,\n    'new_mark': marked,\n    'cleared': cut,\n    'visits': visited,\n    'promoted_count': len(cut),\n    'potential_delta': -2*len(cut)+(2 if marked is not None else 0)}\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncases = [[({'path': []}, {'cuts': [], 'new_mark': None, 'cleared': [], 'visits': 0, 'promoted_count': 0, 'potential_delta': 0}), ({'path': [[1, True, False]]}, {'cuts': [], 'new_mark': None, 'cleared': [], 'visits': 1, 'promoted_count': 0, 'potential_delta': 0}), ({'path': [[1, False, False], [2, True, False]]}, {'cuts': [], 'new_mark': 1, 'cleared': [], 'visits': 1, 'promoted_count': 0, 'potential_delta': 2}), ({'path': [[1, False, True], [2, False, False], [3, True, False]]}, {'cuts': [1], 'new_mark': 2, 'cleared': [1], 'visits': 2, 'promoted_count': 1, 'potential_delta': 1}), ({'path': [[1, False, True], [2, False, True], [3, True, True]]}, {'cuts': [1, 2], 'new_mark': None, 'cleared': [1, 2], 'visits': 3, 'promoted_count': 2, 'potential_delta': -2}), ({'path': [[1, False, False], [2, False, True], [3, True, False]]}, {'cuts': [], 'new_mark': 1, 'cleared': [], 'visits': 1, 'promoted_count': 0, 'potential_delta': 2}), ({'path': [[100, False, True], [1, False, False], [2, False, True], [3, True, False]]}, {'cuts': [100], 'new_mark': 1, 'cleared': [100], 'visits': 2, 'promoted_count': 1, 'potential_delta': 1})], [({'path': []}, {'cuts': [], 'new_mark': None, 'cleared': [], 'visits': 0, 'promoted_count': 0, 'potential_delta': 0}), ({'path': [[1, True, False]]}, {'cuts': [], 'new_mark': None, 'cleared': [], 'visits': 1, 'promoted_count': 0, 'potential_delta': 0}), ({'path': [[1, False, False], [2, True, False]]}, {'cuts': [], 'new_mark': 1, 'cleared': [], 'visits': 1, 'promoted_count': 0, 'potential_delta': 2}), ({'path': [[1, False, True], [2, False, False], [3, True, False]]}, {'cuts': [1], 'new_mark': 2, 'cleared': [1], 'visits': 2, 'promoted_count': 1, 'potential_delta': 1}), ({'path': [[1, False, True], [2, False, True], [3, True, True]]}, {'cuts': [1, 2], 'new_mark': None, 'cleared': [1, 2], 'visits': 3, 'promoted_count': 2, 'potential_delta': -2}), ({'path': [[1, False, False], [2, False, True], [3, True, False]]}, {'cuts': [], 'new_mark': 1, 'cleared': [], 'visits': 1, 'promoted_count': 0, 'potential_delta': 2}), ({'path': [[100, False, True], [101, False, True], [1, False, False], [2, False, True], [3, True, False]]}, {'cuts': [100, 101], 'new_mark': 1, 'cleared': [100, 101], 'visits': 3, 'promoted_count': 2, 'potential_delta': 0})], [({'path': []}, {'cuts': [], 'new_mark': None, 'cleared': [], 'visits': 0, 'promoted_count': 0, 'potential_delta': 0}), ({'path': [[1, True, False]]}, {'cuts': [], 'new_mark': None, 'cleared': [], 'visits': 1, 'promoted_count': 0, 'potential_delta': 0}), ({'path': [[1, False, False], [2, True, False]]}, {'cuts': [], 'new_mark': 1, 'cleared': [], 'visits': 1, 'promoted_count': 0, 'potential_delta': 2}), ({'path': [[1, False, True], [2, False, False], [3, True, False]]}, {'cuts': [1], 'new_mark': 2, 'cleared': [1], 'visits': 2, 'promoted_count': 1, 'potential_delta': 1}), ({'path': [[1, False, True], [2, False, True], [3, True, True]]}, {'cuts': [1, 2], 'new_mark': None, 'cleared': [1, 2], 'visits': 3, 'promoted_count': 2, 'potential_delta': -2}), ({'path': [[1, False, False], [2, False, True], [3, True, False]]}, {'cuts': [], 'new_mark': 1, 'cleared': [], 'visits': 1, 'promoted_count': 0, 'potential_delta': 2}), ({'path': [[100, False, True], [101, False, True], [102, False, True], [1, False, False], [2, False, True], [3, True, False]]}, {'cuts': [100, 101, 102], 'new_mark': 1, 'cleared': [100, 101, 102], 'visits': 4, 'promoted_count': 3, 'potential_delta': -1})], [({'path': []}, {'cuts': [], 'new_mark': None, 'cleared': [], 'visits': 0, 'promoted_count': 0, 'potential_delta': 0}), ({'path': [[1, True, False]]}, {'cuts': [], 'new_mark': None, 'cleared': [], 'visits': 1, 'promoted_count': 0, 'potential_delta': 0}), ({'path': [[1, False, False], [2, True, False]]}, {'cuts': [], 'new_mark': 1, 'cleared': [], 'visits': 1, 'promoted_count': 0, 'potential_delta': 2}), ({'path': [[1, False, True], [2, False, False], [3, True, False]]}, {'cuts': [1], 'new_mark': 2, 'cleared': [1], 'visits': 2, 'promoted_count': 1, 'potential_delta': 1}), ({'path': [[1, False, True], [2, False, True], [3, True, True]]}, {'cuts': [1, 2], 'new_mark': None, 'cleared': [1, 2], 'visits': 3, 'promoted_count': 2, 'potential_delta': -2}), ({'path': [[1, False, False], [2, False, True], [3, True, False]]}, {'cuts': [], 'new_mark': 1, 'cleared': [], 'visits': 1, 'promoted_count': 0, 'potential_delta': 2}), ({'path': [[100, False, True], [101, False, True], [102, False, True], [103, False, True], [1, False, False], [2, False, True], [3, True, False]]}, {'cuts': [100, 101, 102, 103], 'new_mark': 1, 'cleared': [100, 101, 102, 103], 'visits': 5, 'promoted_count': 4, 'potential_delta': -2})], [({'path': []}, {'cuts': [], 'new_mark': None, 'cleared': [], 'visits': 0, 'promoted_count': 0, 'potential_delta': 0}), ({'path': [[1, True, False]]}, {'cuts': [], 'new_mark': None, 'cleared': [], 'visits': 1, 'promoted_count': 0, 'potential_delta': 0}), ({'path': [[1, False, False], [2, True, False]]}, {'cuts': [], 'new_mark': 1, 'cleared': [], 'visits': 1, 'promoted_count': 0, 'potential_delta': 2}), ({'path': [[1, False, True], [2, False, False], [3, True, False]]}, {'cuts': [1], 'new_mark': 2, 'cleared': [1], 'visits': 2, 'promoted_count': 1, 'potential_delta': 1}), ({'path': [[1, False, True], [2, False, True], [3, True, True]]}, {'cuts': [1, 2], 'new_mark': None, 'cleared': [1, 2], 'visits': 3, 'promoted_count': 2, 'potential_delta': -2}), ({'path': [[1, False, False], [2, False, True], [3, True, False]]}, {'cuts': [], 'new_mark': 1, 'cleared': [], 'visits': 1, 'promoted_count': 0, 'potential_delta': 2}), ({'path': [[100, False, True], [101, False, True], [102, False, True], [103, False, True], [104, False, True], [1, False, False], [2, False, True], [3, True, False]]}, {'cuts': [100, 101, 102, 103, 104], 'new_mark': 1, 'cleared': [100, 101, 102, 103, 104], 'visits': 6, 'promoted_count': 5, 'potential_delta': -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":"6d6baf76b247476c0349310b8e0d1c43ea2e0cd78502e98339dbaec6235bd484","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(d):\n    path=d['path']; cut=[]; marked=None; visited=0\n    for ident,root,mark in path:\n        visited+=1\n        if root: break\n        if not mark:\n            marked=ident; break\n        cut.append(ident)\n    return {'cuts': cut,\n    'new_mark': marked,\n    'cleared': cut,\n    'visits': visited,\n    'promoted_count': len(cut),\n    'potential_delta': len(cut)+(2 if marked is not None else 0)}\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncases = [[({'path': []}, {'cuts': [], 'new_mark': None, 'cleared': [], 'visits': 0, 'promoted_count': 0, 'potential_delta': 0}), ({'path': [[1, True, False]]}, {'cuts': [], 'new_mark': None, 'cleared': [], 'visits': 1, 'promoted_count': 0, 'potential_delta': 0}), ({'path': [[1, False, False], [2, True, False]]}, {'cuts': [], 'new_mark': 1, 'cleared': [], 'visits': 1, 'promoted_count': 0, 'potential_delta': 2}), ({'path': [[1, False, True], [2, False, False], [3, True, False]]}, {'cuts': [1], 'new_mark': 2, 'cleared': [1], 'visits': 2, 'promoted_count': 1, 'potential_delta': 1}), ({'path': [[1, False, True], [2, False, True], [3, True, True]]}, {'cuts': [1, 2], 'new_mark': None, 'cleared': [1, 2], 'visits': 3, 'promoted_count': 2, 'potential_delta': -2}), ({'path': [[1, False, False], [2, False, True], [3, True, False]]}, {'cuts': [], 'new_mark': 1, 'cleared': [], 'visits': 1, 'promoted_count': 0, 'potential_delta': 2}), ({'path': [[100, False, True], [1, False, False], [2, False, True], [3, True, False]]}, {'cuts': [100], 'new_mark': 1, 'cleared': [100], 'visits': 2, 'promoted_count': 1, 'potential_delta': 1})], [({'path': []}, {'cuts': [], 'new_mark': None, 'cleared': [], 'visits': 0, 'promoted_count': 0, 'potential_delta': 0}), ({'path': [[1, True, False]]}, {'cuts': [], 'new_mark': None, 'cleared': [], 'visits': 1, 'promoted_count': 0, 'potential_delta': 0}), ({'path': [[1, False, False], [2, True, False]]}, {'cuts': [], 'new_mark': 1, 'cleared': [], 'visits': 1, 'promoted_count': 0, 'potential_delta': 2}), ({'path': [[1, False, True], [2, False, False], [3, True, False]]}, {'cuts': [1], 'new_mark': 2, 'cleared': [1], 'visits': 2, 'promoted_count': 1, 'potential_delta': 1}), ({'path': [[1, False, True], [2, False, True], [3, True, True]]}, {'cuts': [1, 2], 'new_mark': None, 'cleared': [1, 2], 'visits': 3, 'promoted_count': 2, 'potential_delta': -2}), ({'path': [[1, False, False], [2, False, True], [3, True, False]]}, {'cuts': [], 'new_mark': 1, 'cleared': [], 'visits': 1, 'promoted_count': 0, 'potential_delta': 2}), ({'path': [[100, False, True], [101, False, True], [1, False, False], [2, False, True], [3, True, False]]}, {'cuts': [100, 101], 'new_mark': 1, 'cleared': [100, 101], 'visits': 3, 'promoted_count': 2, 'potential_delta': 0})], [({'path': []}, {'cuts': [], 'new_mark': None, 'cleared': [], 'visits': 0, 'promoted_count': 0, 'potential_delta': 0}), ({'path': [[1, True, False]]}, {'cuts': [], 'new_mark': None, 'cleared': [], 'visits': 1, 'promoted_count': 0, 'potential_delta': 0}), ({'path': [[1, False, False], [2, True, False]]}, {'cuts': [], 'new_mark': 1, 'cleared': [], 'visits': 1, 'promoted_count': 0, 'potential_delta': 2}), ({'path': [[1, False, True], [2, False, False], [3, True, False]]}, {'cuts': [1], 'new_mark': 2, 'cleared': [1], 'visits': 2, 'promoted_count': 1, 'potential_delta': 1}), ({'path': [[1, False, True], [2, False, True], [3, True, True]]}, {'cuts': [1, 2], 'new_mark': None, 'cleared': [1, 2], 'visits': 3, 'promoted_count': 2, 'potential_delta': -2}), ({'path': [[1, False, False], [2, False, True], [3, True, False]]}, {'cuts': [], 'new_mark': 1, 'cleared': [], 'visits': 1, 'promoted_count': 0, 'potential_delta': 2}), ({'path': [[100, False, True], [101, False, True], [102, False, True], [1, False, False], [2, False, True], [3, True, False]]}, {'cuts': [100, 101, 102], 'new_mark': 1, 'cleared': [100, 101, 102], 'visits': 4, 'promoted_count': 3, 'potential_delta': -1})], [({'path': []}, {'cuts': [], 'new_mark': None, 'cleared': [], 'visits': 0, 'promoted_count': 0, 'potential_delta': 0}), ({'path': [[1, True, False]]}, {'cuts': [], 'new_mark': None, 'cleared': [], 'visits': 1, 'promoted_count': 0, 'potential_delta': 0}), ({'path': [[1, False, False], [2, True, False]]}, {'cuts': [], 'new_mark': 1, 'cleared': [], 'visits': 1, 'promoted_count': 0, 'potential_delta': 2}), ({'path': [[1, False, True], [2, False, False], [3, True, False]]}, {'cuts': [1], 'new_mark': 2, 'cleared': [1], 'visits': 2, 'promoted_count': 1, 'potential_delta': 1}), ({'path': [[1, False, True], [2, False, True], [3, True, True]]}, {'cuts': [1, 2], 'new_mark': None, 'cleared': [1, 2], 'visits': 3, 'promoted_count': 2, 'potential_delta': -2}), ({'path': [[1, False, False], [2, False, True], [3, True, False]]}, {'cuts': [], 'new_mark': 1, 'cleared': [], 'visits': 1, 'promoted_count': 0, 'potential_delta': 2}), ({'path': [[100, False, True], [101, False, True], [102, False, True], [103, False, True], [1, False, False], [2, False, True], [3, True, False]]}, {'cuts': [100, 101, 102, 103], 'new_mark': 1, 'cleared': [100, 101, 102, 103], 'visits': 5, 'promoted_count': 4, 'potential_delta': -2})], [({'path': []}, {'cuts': [], 'new_mark': None, 'cleared': [], 'visits': 0, 'promoted_count': 0, 'potential_delta': 0}), ({'path': [[1, True, False]]}, {'cuts': [], 'new_mark': None, 'cleared': [], 'visits': 1, 'promoted_count': 0, 'potential_delta': 0}), ({'path': [[1, False, False], [2, True, False]]}, {'cuts': [], 'new_mark': 1, 'cleared': [], 'visits': 1, 'promoted_count': 0, 'potential_delta': 2}), ({'path': [[1, False, True], [2, False, False], [3, True, False]]}, {'cuts': [1], 'new_mark': 2, 'cleared': [1], 'visits': 2, 'promoted_count': 1, 'potential_delta': 1}), ({'path': [[1, False, True], [2, False, True], [3, True, True]]}, {'cuts': [1, 2], 'new_mark': None, 'cleared': [1, 2], 'visits': 3, 'promoted_count': 2, 'potential_delta': -2}), ({'path': [[1, False, False], [2, False, True], [3, True, False]]}, {'cuts': [], 'new_mark': 1, 'cleared': [], 'visits': 1, 'promoted_count': 0, 'potential_delta': 2}), ({'path': [[100, False, True], [101, False, True], [102, False, True], [103, False, True], [104, False, True], [1, False, False], [2, False, True], [3, True, False]]}, {'cuts': [100, 101, 102, 103, 104], 'new_mark': 1, 'cleared': [100, 101, 102, 103, 104], 'visits': 6, 'promoted_count': 5, 'potential_delta': -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":"15183309fd430843642addc1c99f2c27d3d08ab56e3199c77099b6e7258ca008","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(d):\n    path=d['path']; cut=[]; marked=None; visited=0\n    for ident,root,mark in path:\n        visited+=1\n        if root: break\n        if not mark:\n            marked=ident; break\n        cut.append(ident)\n    return {'cuts': cut,\n    'new_mark': marked,\n    'cleared': cut,\n    'visits': visited,\n    'promoted_count': len(cut),\n    'potential_delta': -len(cut)+(2 if marked is not None else 0)}\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncases = [[({'path': []}, {'cuts': [], 'new_mark': None, 'cleared': [], 'visits': 0, 'promoted_count': 0, 'potential_delta': 0}), ({'path': [[1, True, False]]}, {'cuts': [], 'new_mark': None, 'cleared': [], 'visits': 1, 'promoted_count': 0, 'potential_delta': 0}), ({'path': [[1, False, False], [2, True, False]]}, {'cuts': [], 'new_mark': 1, 'cleared': [], 'visits': 1, 'promoted_count': 0, 'potential_delta': 2}), ({'path': [[1, False, True], [2, False, False], [3, True, False]]}, {'cuts': [1], 'new_mark': 2, 'cleared': [1], 'visits': 2, 'promoted_count': 1, 'potential_delta': 1}), ({'path': [[1, False, True], [2, False, True], [3, True, True]]}, {'cuts': [1, 2], 'new_mark': None, 'cleared': [1, 2], 'visits': 3, 'promoted_count': 2, 'potential_delta': -2}), ({'path': [[1, False, False], [2, False, True], [3, True, False]]}, {'cuts': [], 'new_mark': 1, 'cleared': [], 'visits': 1, 'promoted_count': 0, 'potential_delta': 2}), ({'path': [[100, False, True], [1, False, False], [2, False, True], [3, True, False]]}, {'cuts': [100], 'new_mark': 1, 'cleared': [100], 'visits': 2, 'promoted_count': 1, 'potential_delta': 1})], [({'path': []}, {'cuts': [], 'new_mark': None, 'cleared': [], 'visits': 0, 'promoted_count': 0, 'potential_delta': 0}), ({'path': [[1, True, False]]}, {'cuts': [], 'new_mark': None, 'cleared': [], 'visits': 1, 'promoted_count': 0, 'potential_delta': 0}), ({'path': [[1, False, False], [2, True, False]]}, {'cuts': [], 'new_mark': 1, 'cleared': [], 'visits': 1, 'promoted_count': 0, 'potential_delta': 2}), ({'path': [[1, False, True], [2, False, False], [3, True, False]]}, {'cuts': [1], 'new_mark': 2, 'cleared': [1], 'visits': 2, 'promoted_count': 1, 'potential_delta': 1}), ({'path': [[1, False, True], [2, False, True], [3, True, True]]}, {'cuts': [1, 2], 'new_mark': None, 'cleared': [1, 2], 'visits': 3, 'promoted_count': 2, 'potential_delta': -2}), ({'path': [[1, False, False], [2, False, True], [3, True, False]]}, {'cuts': [], 'new_mark': 1, 'cleared': [], 'visits': 1, 'promoted_count': 0, 'potential_delta': 2}), ({'path': [[100, False, True], [101, False, True], [1, False, False], [2, False, True], [3, True, False]]}, {'cuts': [100, 101], 'new_mark': 1, 'cleared': [100, 101], 'visits': 3, 'promoted_count': 2, 'potential_delta': 0})], [({'path': []}, {'cuts': [], 'new_mark': None, 'cleared': [], 'visits': 0, 'promoted_count': 0, 'potential_delta': 0}), ({'path': [[1, True, False]]}, {'cuts': [], 'new_mark': None, 'cleared': [], 'visits': 1, 'promoted_count': 0, 'potential_delta': 0}), ({'path': [[1, False, False], [2, True, False]]}, {'cuts': [], 'new_mark': 1, 'cleared': [], 'visits': 1, 'promoted_count': 0, 'potential_delta': 2}), ({'path': [[1, False, True], [2, False, False], [3, True, False]]}, {'cuts': [1], 'new_mark': 2, 'cleared': [1], 'visits': 2, 'promoted_count': 1, 'potential_delta': 1}), ({'path': [[1, False, True], [2, False, True], [3, True, True]]}, {'cuts': [1, 2], 'new_mark': None, 'cleared': [1, 2], 'visits': 3, 'promoted_count': 2, 'potential_delta': -2}), ({'path': [[1, False, False], [2, False, True], [3, True, False]]}, {'cuts': [], 'new_mark': 1, 'cleared': [], 'visits': 1, 'promoted_count': 0, 'potential_delta': 2}), ({'path': [[100, False, True], [101, False, True], [102, False, True], [1, False, False], [2, False, True], [3, True, False]]}, {'cuts': [100, 101, 102], 'new_mark': 1, 'cleared': [100, 101, 102], 'visits': 4, 'promoted_count': 3, 'potential_delta': -1})], [({'path': []}, {'cuts': [], 'new_mark': None, 'cleared': [], 'visits': 0, 'promoted_count': 0, 'potential_delta': 0}), ({'path': [[1, True, False]]}, {'cuts': [], 'new_mark': None, 'cleared': [], 'visits': 1, 'promoted_count': 0, 'potential_delta': 0}), ({'path': [[1, False, False], [2, True, False]]}, {'cuts': [], 'new_mark': 1, 'cleared': [], 'visits': 1, 'promoted_count': 0, 'potential_delta': 2}), ({'path': [[1, False, True], [2, False, False], [3, True, False]]}, {'cuts': [1], 'new_mark': 2, 'cleared': [1], 'visits': 2, 'promoted_count': 1, 'potential_delta': 1}), ({'path': [[1, False, True], [2, False, True], [3, True, True]]}, {'cuts': [1, 2], 'new_mark': None, 'cleared': [1, 2], 'visits': 3, 'promoted_count': 2, 'potential_delta': -2}), ({'path': [[1, False, False], [2, False, True], [3, True, False]]}, {'cuts': [], 'new_mark': 1, 'cleared': [], 'visits': 1, 'promoted_count': 0, 'potential_delta': 2}), ({'path': [[100, False, True], [101, False, True], [102, False, True], [103, False, True], [1, False, False], [2, False, True], [3, True, False]]}, {'cuts': [100, 101, 102, 103], 'new_mark': 1, 'cleared': [100, 101, 102, 103], 'visits': 5, 'promoted_count': 4, 'potential_delta': -2})], [({'path': []}, {'cuts': [], 'new_mark': None, 'cleared': [], 'visits': 0, 'promoted_count': 0, 'potential_delta': 0}), ({'path': [[1, True, False]]}, {'cuts': [], 'new_mark': None, 'cleared': [], 'visits': 1, 'promoted_count': 0, 'potential_delta': 0}), ({'path': [[1, False, False], [2, True, False]]}, {'cuts': [], 'new_mark': 1, 'cleared': [], 'visits': 1, 'promoted_count': 0, 'potential_delta': 2}), ({'path': [[1, False, True], [2, False, False], [3, True, False]]}, {'cuts': [1], 'new_mark': 2, 'cleared': [1], 'visits': 2, 'promoted_count': 1, 'potential_delta': 1}), ({'path': [[1, False, True], [2, False, True], [3, True, True]]}, {'cuts': [1, 2], 'new_mark': None, 'cleared': [1, 2], 'visits': 3, 'promoted_count': 2, 'potential_delta': -2}), ({'path': [[1, False, False], [2, False, True], [3, True, False]]}, {'cuts': [], 'new_mark': 1, 'cleared': [], 'visits': 1, 'promoted_count': 0, 'potential_delta': 2}), ({'path': [[100, False, True], [101, False, True], [102, False, True], [103, False, True], [104, False, True], [1, False, False], [2, False, True], [3, True, False]]}, {'cuts': [100, 101, 102, 103, 104], 'new_mark': 1, 'cleared': [100, 101, 102, 103, 104], 'visits': 6, 'promoted_count': 5, 'potential_delta': -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-fibonacci-cascade-potential_delta","generated_at":"2026-09-29T14:43:28.081876+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 potential delta using -len(cut)+(2 if marked is not None else 0) under the stated bounded certificate contract.","root_cause":"Fibonacci cascade potential includes one new root and one cleared mark per cut.","sha256":"a6cde5e47b4b5f242cc7967b4f77de120109f3f1a002ca88bec35791705acec7","title":"Fibonacci cascade potential includes one new root and one cleared mark per cut · case 01","variant":1,"variant_policy":"Six explicit regression certificates are retained; a seventh changes structural size, position, priority, or bounds with N.","verification":{"attempt":{"elapsed_ms":44.971,"exit_code":1,"observations":[{"actual":{"cleared":[],"cuts":[],"new_mark":null,"potential_delta":0,"promoted_count":0,"visits":0},"check":"regression certificate 1","expected":{"cleared":[],"cuts":[],"new_mark":null,"potential_delta":0,"promoted_count":0,"visits":0},"passed":true},{"actual":{"cleared":[],"cuts":[],"new_mark":null,"potential_delta":0,"promoted_count":0,"visits":1},"check":"regression certificate 2","expected":{"cleared":[],"cuts":[],"new_mark":null,"potential_delta":0,"promoted_count":0,"visits":1},"passed":true},{"actual":{"cleared":[],"cuts":[],"new_mark":1,"potential_delta":2,"promoted_count":0,"visits":1},"check":"regression certificate 3","expected":{"cleared":[],"cuts":[],"new_mark":1,"potential_delta":2,"promoted_count":0,"visits":1},"passed":true},{"actual":{"cleared":[1],"cuts":[1],"new_mark":2,"potential_delta":0,"promoted_count":1,"visits":2},"check":"regression certificate 4","expected":{"cleared":[1],"cuts":[1],"new_mark":2,"potential_delta":1,"promoted_count":1,"visits":2},"passed":false},{"actual":{"cleared":[1,2],"cuts":[1,2],"new_mark":null,"potential_delta":-4,"promoted_count":2,"visits":3},"check":"regression certificate 5","expected":{"cleared":[1,2],"cuts":[1,2],"new_mark":null,"potential_delta":-2,"promoted_count":2,"visits":3},"passed":false},{"actual":{"cleared":[],"cuts":[],"new_mark":1,"potential_delta":2,"promoted_count":0,"visits":1},"check":"regression certificate 6","expected":{"cleared":[],"cuts":[],"new_mark":1,"potential_delta":2,"promoted_count":0,"visits":1},"passed":true},{"actual":{"cleared":[100],"cuts":[100],"new_mark":1,"potential_delta":0,"promoted_count":1,"visits":2},"check":"variant-dependent certificate","expected":{"cleared":[100],"cuts":[100],"new_mark":1,"potential_delta":1,"promoted_count":1,"visits":2},"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression certificate 1\", \"actual\": {\"cuts\": [], \"new_mark\": null, \"cleared\": [], \"visits\": 0, \"promoted_count\": 0, \"potential_delta\": 0}, \"expected\": {\"cuts\": [], \"new_mark\": null, \"cleared\": [], \"visits\": 0, \"promoted_count\": 0, \"potential_delta\": 0}, \"passed\": true}, {\"check\": \"regression certificate 2\", \"actual\": {\"cuts\": [], \"new_mark\": null, \"cleared\": [], \"visits\": 1, \"promoted_count\": 0, \"potential_delta\": 0}, \"expected\": {\"cuts\": [], \"new_mark\": null, \"cleared\": [], \"visits\": 1, \"promoted_count\": 0, \"potential_delta\": 0}, \"passed\": true}, {\"check\": \"regression certificate 3\", \"actual\": {\"cuts\": [], \"new_mark\": 1, \"cleared\": [], \"visits\": 1, \"promoted_count\": 0, \"potential_delta\": 2}, \"expected\": {\"cuts\": [], \"new_mark\": 1, \"cleared\": [], \"visits\": 1, \"promoted_count\": 0, \"potential_delta\": 2}, \"passed\": true}, {\"check\": \"regression certificate 4\", \"actual\": {\"cuts\": [1], \"new_mark\": 2, \"cleared\": [1], \"visits\": 2, \"promoted_count\": 1, \"potential_delta\": 0}, \"expected\": {\"cuts\": [1], \"new_mark\": 2, \"cleared\": [1], \"visits\": 2, \"promoted_count\": 1, \"potential_delta\": 1}, \"passed\": false}, {\"check\": \"regression certificate 5\", \"actual\": {\"cuts\": [1, 2], \"new_mark\": null, \"cleared\": [1, 2], \"visits\": 3, \"promoted_count\": 2, \"potential_delta\": -4}, \"expected\": {\"cuts\": [1, 2], \"new_mark\": null, \"cleared\": [1, 2], \"visits\": 3, \"promoted_count\": 2, \"potential_delta\": -2}, \"passed\": false}, {\"check\": \"regression certificate 6\", \"actual\": {\"cuts\": [], \"new_mark\": 1, \"cleared\": [], \"visits\": 1, \"promoted_count\": 0, \"potential_delta\": 2}, \"expected\": {\"cuts\": [], \"new_mark\": 1, \"cleared\": [], \"visits\": 1, \"promoted_count\": 0, \"potential_delta\": 2}, \"passed\": true}, {\"check\": \"variant-dependent certificate\", \"actual\": {\"cuts\": [100], \"new_mark\": 1, \"cleared\": [100], \"visits\": 2, \"promoted_count\": 1, \"potential_delta\": 0}, \"expected\": {\"cuts\": [100], \"new_mark\": 1, \"cleared\": [100], \"visits\": 2, \"promoted_count\": 1, \"potential_delta\": 1}, \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":48.67,"exit_code":1,"observations":[{"actual":{"cleared":[],"cuts":[],"new_mark":null,"potential_delta":0,"promoted_count":0,"visits":0},"check":"regression certificate 1","expected":{"cleared":[],"cuts":[],"new_mark":null,"potential_delta":0,"promoted_count":0,"visits":0},"passed":true},{"actual":{"cleared":[],"cuts":[],"new_mark":null,"potential_delta":0,"promoted_count":0,"visits":1},"check":"regression certificate 2","expected":{"cleared":[],"cuts":[],"new_mark":null,"potential_delta":0,"promoted_count":0,"visits":1},"passed":true},{"actual":{"cleared":[],"cuts":[],"new_mark":1,"potential_delta":2,"promoted_count":0,"visits":1},"check":"regression certificate 3","expected":{"cleared":[],"cuts":[],"new_mark":1,"potential_delta":2,"promoted_count":0,"visits":1},"passed":true},{"actual":{"cleared":[1],"cuts":[1],"new_mark":2,"potential_delta":3,"promoted_count":1,"visits":2},"check":"regression certificate 4","expected":{"cleared":[1],"cuts":[1],"new_mark":2,"potential_delta":1,"promoted_count":1,"visits":2},"passed":false},{"actual":{"cleared":[1,2],"cuts":[1,2],"new_mark":null,"potential_delta":2,"promoted_count":2,"visits":3},"check":"regression certificate 5","expected":{"cleared":[1,2],"cuts":[1,2],"new_mark":null,"potential_delta":-2,"promoted_count":2,"visits":3},"passed":false},{"actual":{"cleared":[],"cuts":[],"new_mark":1,"potential_delta":2,"promoted_count":0,"visits":1},"check":"regression certificate 6","expected":{"cleared":[],"cuts":[],"new_mark":1,"potential_delta":2,"promoted_count":0,"visits":1},"passed":true},{"actual":{"cleared":[100],"cuts":[100],"new_mark":1,"potential_delta":3,"promoted_count":1,"visits":2},"check":"variant-dependent certificate","expected":{"cleared":[100],"cuts":[100],"new_mark":1,"potential_delta":1,"promoted_count":1,"visits":2},"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression certificate 1\", \"actual\": {\"cuts\": [], \"new_mark\": null, \"cleared\": [], \"visits\": 0, \"promoted_count\": 0, \"potential_delta\": 0}, \"expected\": {\"cuts\": [], \"new_mark\": null, \"cleared\": [], \"visits\": 0, \"promoted_count\": 0, \"potential_delta\": 0}, \"passed\": true}, {\"check\": \"regression certificate 2\", \"actual\": {\"cuts\": [], \"new_mark\": null, \"cleared\": [], \"visits\": 1, \"promoted_count\": 0, \"potential_delta\": 0}, \"expected\": {\"cuts\": [], \"new_mark\": null, \"cleared\": [], \"visits\": 1, \"promoted_count\": 0, \"potential_delta\": 0}, \"passed\": true}, {\"check\": \"regression certificate 3\", \"actual\": {\"cuts\": [], \"new_mark\": 1, \"cleared\": [], \"visits\": 1, \"promoted_count\": 0, \"potential_delta\": 2}, \"expected\": {\"cuts\": [], \"new_mark\": 1, \"cleared\": [], \"visits\": 1, \"promoted_count\": 0, \"potential_delta\": 2}, \"passed\": true}, {\"check\": \"regression certificate 4\", \"actual\": {\"cuts\": [1], \"new_mark\": 2, \"cleared\": [1], \"visits\": 2, \"promoted_count\": 1, \"potential_delta\": 3}, \"expected\": {\"cuts\": [1], \"new_mark\": 2, \"cleared\": [1], \"visits\": 2, \"promoted_count\": 1, \"potential_delta\": 1}, \"passed\": false}, {\"check\": \"regression certificate 5\", \"actual\": {\"cuts\": [1, 2], \"new_mark\": null, \"cleared\": [1, 2], \"visits\": 3, \"promoted_count\": 2, \"potential_delta\": 2}, \"expected\": {\"cuts\": [1, 2], \"new_mark\": null, \"cleared\": [1, 2], \"visits\": 3, \"promoted_count\": 2, \"potential_delta\": -2}, \"passed\": false}, {\"check\": \"regression certificate 6\", \"actual\": {\"cuts\": [], \"new_mark\": 1, \"cleared\": [], \"visits\": 1, \"promoted_count\": 0, \"potential_delta\": 2}, \"expected\": {\"cuts\": [], \"new_mark\": 1, \"cleared\": [], \"visits\": 1, \"promoted_count\": 0, \"potential_delta\": 2}, \"passed\": true}, {\"check\": \"variant-dependent certificate\", \"actual\": {\"cuts\": [100], \"new_mark\": 1, \"cleared\": [100], \"visits\": 2, \"promoted_count\": 1, \"potential_delta\": 3}, \"expected\": {\"cuts\": [100], \"new_mark\": 1, \"cleared\": [100], \"visits\": 2, \"promoted_count\": 1, \"potential_delta\": 1}, \"passed\": false}], \"passed\": false}\n"},"fixed":{"elapsed_ms":43.407,"exit_code":0,"observations":[{"actual":{"cleared":[],"cuts":[],"new_mark":null,"potential_delta":0,"promoted_count":0,"visits":0},"check":"regression certificate 1","expected":{"cleared":[],"cuts":[],"new_mark":null,"potential_delta":0,"promoted_count":0,"visits":0},"passed":true},{"actual":{"cleared":[],"cuts":[],"new_mark":null,"potential_delta":0,"promoted_count":0,"visits":1},"check":"regression certificate 2","expected":{"cleared":[],"cuts":[],"new_mark":null,"potential_delta":0,"promoted_count":0,"visits":1},"passed":true},{"actual":{"cleared":[],"cuts":[],"new_mark":1,"potential_delta":2,"promoted_count":0,"visits":1},"check":"regression certificate 3","expected":{"cleared":[],"cuts":[],"new_mark":1,"potential_delta":2,"promoted_count":0,"visits":1},"passed":true},{"actual":{"cleared":[1],"cuts":[1],"new_mark":2,"potential_delta":1,"promoted_count":1,"visits":2},"check":"regression certificate 4","expected":{"cleared":[1],"cuts":[1],"new_mark":2,"potential_delta":1,"promoted_count":1,"visits":2},"passed":true},{"actual":{"cleared":[1,2],"cuts":[1,2],"new_mark":null,"potential_delta":-2,"promoted_count":2,"visits":3},"check":"regression certificate 5","expected":{"cleared":[1,2],"cuts":[1,2],"new_mark":null,"potential_delta":-2,"promoted_count":2,"visits":3},"passed":true},{"actual":{"cleared":[],"cuts":[],"new_mark":1,"potential_delta":2,"promoted_count":0,"visits":1},"check":"regression certificate 6","expected":{"cleared":[],"cuts":[],"new_mark":1,"potential_delta":2,"promoted_count":0,"visits":1},"passed":true},{"actual":{"cleared":[100],"cuts":[100],"new_mark":1,"potential_delta":1,"promoted_count":1,"visits":2},"check":"variant-dependent certificate","expected":{"cleared":[100],"cuts":[100],"new_mark":1,"potential_delta":1,"promoted_count":1,"visits":2},"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression certificate 1\", \"actual\": {\"cuts\": [], \"new_mark\": null, \"cleared\": [], \"visits\": 0, \"promoted_count\": 0, \"potential_delta\": 0}, \"expected\": {\"cuts\": [], \"new_mark\": null, \"cleared\": [], \"visits\": 0, \"promoted_count\": 0, \"potential_delta\": 0}, \"passed\": true}, {\"check\": \"regression certificate 2\", \"actual\": {\"cuts\": [], \"new_mark\": null, \"cleared\": [], \"visits\": 1, \"promoted_count\": 0, \"potential_delta\": 0}, \"expected\": {\"cuts\": [], \"new_mark\": null, \"cleared\": [], \"visits\": 1, \"promoted_count\": 0, \"potential_delta\": 0}, \"passed\": true}, {\"check\": \"regression certificate 3\", \"actual\": {\"cuts\": [], \"new_mark\": 1, \"cleared\": [], \"visits\": 1, \"promoted_count\": 0, \"potential_delta\": 2}, \"expected\": {\"cuts\": [], \"new_mark\": 1, \"cleared\": [], \"visits\": 1, \"promoted_count\": 0, \"potential_delta\": 2}, \"passed\": true}, {\"check\": \"regression certificate 4\", \"actual\": {\"cuts\": [1], \"new_mark\": 2, \"cleared\": [1], \"visits\": 2, \"promoted_count\": 1, \"potential_delta\": 1}, \"expected\": {\"cuts\": [1], \"new_mark\": 2, \"cleared\": [1], \"visits\": 2, \"promoted_count\": 1, \"potential_delta\": 1}, \"passed\": true}, {\"check\": \"regression certificate 5\", \"actual\": {\"cuts\": [1, 2], \"new_mark\": null, \"cleared\": [1, 2], \"visits\": 3, \"promoted_count\": 2, \"potential_delta\": -2}, \"expected\": {\"cuts\": [1, 2], \"new_mark\": null, \"cleared\": [1, 2], \"visits\": 3, \"promoted_count\": 2, \"potential_delta\": -2}, \"passed\": true}, {\"check\": \"regression certificate 6\", \"actual\": {\"cuts\": [], \"new_mark\": 1, \"cleared\": [], \"visits\": 1, \"promoted_count\": 0, \"potential_delta\": 2}, \"expected\": {\"cuts\": [], \"new_mark\": 1, \"cleared\": [], \"visits\": 1, \"promoted_count\": 0, \"potential_delta\": 2}, \"passed\": true}, {\"check\": \"variant-dependent certificate\", \"actual\": {\"cuts\": [100], \"new_mark\": 1, \"cleared\": [100], \"visits\": 2, \"promoted_count\": 1, \"potential_delta\": 1}, \"expected\": {\"cuts\": [100], \"new_mark\": 1, \"cleared\": [100], \"visits\": 2, \"promoted_count\": 1, \"potential_delta\": 1}, \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}