{"abstract":"The bounded interval endpoints certificate reports an incorrect reversed.","category":"Heap invariants","checks":7,"contract":"An interval heap stores ordered pairs [lo,hi] except the last node may be singleton [x]. Report reversed intervals, low-end heap violations, high-end heap violations treating singleton as both endpoints, global minimum, global maximum, and member count.","evaluation_group":"s3-heap-model-interval-endpoints","failed_approach":"The local patch uses [i for i,x in enumerate(a) if len(x)==1] and still violates the stated relation.","family":"s3-heap-interval-endpoints-reversed","id":"FA-40411","implementations":{"attempt":{"sha256":"0f9c9718d16ff620907abee5a168fd7ad5e75e364444eb27a6e9f1d2cf3ac01d","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(d):\n    a=d['intervals']; n=len(a); lows=[x[0] for x in a]; highs=[x[-1] for x in a]\n    return {'reversed': [i for i,x in enumerate(a) if len(x)==1],\n    'low_order': [i for i in range(1,n) if lows[i]<lows[(i-1)//2]],\n    'high_order': [i for i in range(1,n) if highs[i]>highs[(i-1)//2]],\n    'minimum': lows[0] if a else None,\n    'maximum': highs[0] if a else None,\n    'members': sum(len(x) for x in a)}\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncases = [[({'intervals': []}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': None, 'maximum': None, 'members': 0}), ({'intervals': [[4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 4, 'maximum': 4, 'members': 1}), ({'intervals': [[1, 9], [2, 7], [3]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 9, 'members': 5}), ({'intervals': [[1, 8], [2, 7], [9]]}, {'reversed': [], 'low_order': [], 'high_order': [2], 'minimum': 1, 'maximum': 8, 'members': 5}), ({'intervals': [[5, 3], [1, 6], [4, 8]]}, {'reversed': [0], 'low_order': [1, 2], 'high_order': [1, 2], 'minimum': 5, 'maximum': 3, 'members': 6}), ({'intervals': [[1, 9], [2, 8], [3, 7], [4, 4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 9, 'members': 8}), ({'intervals': [[1, 10], [2, 8], [3, 7], [4, 4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 10, 'members': 8})], [({'intervals': []}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': None, 'maximum': None, 'members': 0}), ({'intervals': [[4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 4, 'maximum': 4, 'members': 1}), ({'intervals': [[1, 9], [2, 7], [3]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 9, 'members': 5}), ({'intervals': [[1, 8], [2, 7], [9]]}, {'reversed': [], 'low_order': [], 'high_order': [2], 'minimum': 1, 'maximum': 8, 'members': 5}), ({'intervals': [[5, 3], [1, 6], [4, 8]]}, {'reversed': [0], 'low_order': [1, 2], 'high_order': [1, 2], 'minimum': 5, 'maximum': 3, 'members': 6}), ({'intervals': [[1, 9], [2, 8], [3, 7], [4, 4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 9, 'members': 8}), ({'intervals': [[1, 11], [2, 8], [3, 7], [4, 4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 11, 'members': 8})], [({'intervals': []}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': None, 'maximum': None, 'members': 0}), ({'intervals': [[4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 4, 'maximum': 4, 'members': 1}), ({'intervals': [[1, 9], [2, 7], [3]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 9, 'members': 5}), ({'intervals': [[1, 8], [2, 7], [9]]}, {'reversed': [], 'low_order': [], 'high_order': [2], 'minimum': 1, 'maximum': 8, 'members': 5}), ({'intervals': [[5, 3], [1, 6], [4, 8]]}, {'reversed': [0], 'low_order': [1, 2], 'high_order': [1, 2], 'minimum': 5, 'maximum': 3, 'members': 6}), ({'intervals': [[1, 9], [2, 8], [3, 7], [4, 4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 9, 'members': 8}), ({'intervals': [[1, 12], [2, 8], [3, 7], [4, 4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 12, 'members': 8})], [({'intervals': []}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': None, 'maximum': None, 'members': 0}), ({'intervals': [[4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 4, 'maximum': 4, 'members': 1}), ({'intervals': [[1, 9], [2, 7], [3]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 9, 'members': 5}), ({'intervals': [[1, 8], [2, 7], [9]]}, {'reversed': [], 'low_order': [], 'high_order': [2], 'minimum': 1, 'maximum': 8, 'members': 5}), ({'intervals': [[5, 3], [1, 6], [4, 8]]}, {'reversed': [0], 'low_order': [1, 2], 'high_order': [1, 2], 'minimum': 5, 'maximum': 3, 'members': 6}), ({'intervals': [[1, 9], [2, 8], [3, 7], [4, 4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 9, 'members': 8}), ({'intervals': [[1, 13], [2, 8], [3, 7], [4, 4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 13, 'members': 8})], [({'intervals': []}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': None, 'maximum': None, 'members': 0}), ({'intervals': [[4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 4, 'maximum': 4, 'members': 1}), ({'intervals': [[1, 9], [2, 7], [3]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 9, 'members': 5}), ({'intervals': [[1, 8], [2, 7], [9]]}, {'reversed': [], 'low_order': [], 'high_order': [2], 'minimum': 1, 'maximum': 8, 'members': 5}), ({'intervals': [[5, 3], [1, 6], [4, 8]]}, {'reversed': [0], 'low_order': [1, 2], 'high_order': [1, 2], 'minimum': 5, 'maximum': 3, 'members': 6}), ({'intervals': [[1, 9], [2, 8], [3, 7], [4, 4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 9, 'members': 8}), ({'intervals': [[1, 14], [2, 8], [3, 7], [4, 4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 14, 'members': 8})]][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":"85e5959429856542a95243e0ca09fee8754f1445d422efb91ff2e1699078c12a","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(d):\n    a=d['intervals']; n=len(a); lows=[x[0] for x in a]; highs=[x[-1] for x in a]\n    return {'reversed': [i for i,x in enumerate(a) if x[0]>=x[-1]],\n    'low_order': [i for i in range(1,n) if lows[i]<lows[(i-1)//2]],\n    'high_order': [i for i in range(1,n) if highs[i]>highs[(i-1)//2]],\n    'minimum': lows[0] if a else None,\n    'maximum': highs[0] if a else None,\n    'members': sum(len(x) for x in a)}\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncases = [[({'intervals': []}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': None, 'maximum': None, 'members': 0}), ({'intervals': [[4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 4, 'maximum': 4, 'members': 1}), ({'intervals': [[1, 9], [2, 7], [3]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 9, 'members': 5}), ({'intervals': [[1, 8], [2, 7], [9]]}, {'reversed': [], 'low_order': [], 'high_order': [2], 'minimum': 1, 'maximum': 8, 'members': 5}), ({'intervals': [[5, 3], [1, 6], [4, 8]]}, {'reversed': [0], 'low_order': [1, 2], 'high_order': [1, 2], 'minimum': 5, 'maximum': 3, 'members': 6}), ({'intervals': [[1, 9], [2, 8], [3, 7], [4, 4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 9, 'members': 8}), ({'intervals': [[1, 10], [2, 8], [3, 7], [4, 4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 10, 'members': 8})], [({'intervals': []}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': None, 'maximum': None, 'members': 0}), ({'intervals': [[4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 4, 'maximum': 4, 'members': 1}), ({'intervals': [[1, 9], [2, 7], [3]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 9, 'members': 5}), ({'intervals': [[1, 8], [2, 7], [9]]}, {'reversed': [], 'low_order': [], 'high_order': [2], 'minimum': 1, 'maximum': 8, 'members': 5}), ({'intervals': [[5, 3], [1, 6], [4, 8]]}, {'reversed': [0], 'low_order': [1, 2], 'high_order': [1, 2], 'minimum': 5, 'maximum': 3, 'members': 6}), ({'intervals': [[1, 9], [2, 8], [3, 7], [4, 4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 9, 'members': 8}), ({'intervals': [[1, 11], [2, 8], [3, 7], [4, 4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 11, 'members': 8})], [({'intervals': []}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': None, 'maximum': None, 'members': 0}), ({'intervals': [[4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 4, 'maximum': 4, 'members': 1}), ({'intervals': [[1, 9], [2, 7], [3]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 9, 'members': 5}), ({'intervals': [[1, 8], [2, 7], [9]]}, {'reversed': [], 'low_order': [], 'high_order': [2], 'minimum': 1, 'maximum': 8, 'members': 5}), ({'intervals': [[5, 3], [1, 6], [4, 8]]}, {'reversed': [0], 'low_order': [1, 2], 'high_order': [1, 2], 'minimum': 5, 'maximum': 3, 'members': 6}), ({'intervals': [[1, 9], [2, 8], [3, 7], [4, 4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 9, 'members': 8}), ({'intervals': [[1, 12], [2, 8], [3, 7], [4, 4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 12, 'members': 8})], [({'intervals': []}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': None, 'maximum': None, 'members': 0}), ({'intervals': [[4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 4, 'maximum': 4, 'members': 1}), ({'intervals': [[1, 9], [2, 7], [3]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 9, 'members': 5}), ({'intervals': [[1, 8], [2, 7], [9]]}, {'reversed': [], 'low_order': [], 'high_order': [2], 'minimum': 1, 'maximum': 8, 'members': 5}), ({'intervals': [[5, 3], [1, 6], [4, 8]]}, {'reversed': [0], 'low_order': [1, 2], 'high_order': [1, 2], 'minimum': 5, 'maximum': 3, 'members': 6}), ({'intervals': [[1, 9], [2, 8], [3, 7], [4, 4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 9, 'members': 8}), ({'intervals': [[1, 13], [2, 8], [3, 7], [4, 4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 13, 'members': 8})], [({'intervals': []}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': None, 'maximum': None, 'members': 0}), ({'intervals': [[4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 4, 'maximum': 4, 'members': 1}), ({'intervals': [[1, 9], [2, 7], [3]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 9, 'members': 5}), ({'intervals': [[1, 8], [2, 7], [9]]}, {'reversed': [], 'low_order': [], 'high_order': [2], 'minimum': 1, 'maximum': 8, 'members': 5}), ({'intervals': [[5, 3], [1, 6], [4, 8]]}, {'reversed': [0], 'low_order': [1, 2], 'high_order': [1, 2], 'minimum': 5, 'maximum': 3, 'members': 6}), ({'intervals': [[1, 9], [2, 8], [3, 7], [4, 4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 9, 'members': 8}), ({'intervals': [[1, 14], [2, 8], [3, 7], [4, 4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 14, 'members': 8})]][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":"f85459689ba9f8267cd021e24f670f8584dd5b9561096043ca809993d3cc2ffe","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(d):\n    a=d['intervals']; n=len(a); lows=[x[0] for x in a]; highs=[x[-1] for x in a]\n    return {'reversed': [i for i,x in enumerate(a) if x[0]>x[-1]],\n    'low_order': [i for i in range(1,n) if lows[i]<lows[(i-1)//2]],\n    'high_order': [i for i in range(1,n) if highs[i]>highs[(i-1)//2]],\n    'minimum': lows[0] if a else None,\n    'maximum': highs[0] if a else None,\n    'members': sum(len(x) for x in a)}\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncases = [[({'intervals': []}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': None, 'maximum': None, 'members': 0}), ({'intervals': [[4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 4, 'maximum': 4, 'members': 1}), ({'intervals': [[1, 9], [2, 7], [3]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 9, 'members': 5}), ({'intervals': [[1, 8], [2, 7], [9]]}, {'reversed': [], 'low_order': [], 'high_order': [2], 'minimum': 1, 'maximum': 8, 'members': 5}), ({'intervals': [[5, 3], [1, 6], [4, 8]]}, {'reversed': [0], 'low_order': [1, 2], 'high_order': [1, 2], 'minimum': 5, 'maximum': 3, 'members': 6}), ({'intervals': [[1, 9], [2, 8], [3, 7], [4, 4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 9, 'members': 8}), ({'intervals': [[1, 10], [2, 8], [3, 7], [4, 4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 10, 'members': 8})], [({'intervals': []}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': None, 'maximum': None, 'members': 0}), ({'intervals': [[4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 4, 'maximum': 4, 'members': 1}), ({'intervals': [[1, 9], [2, 7], [3]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 9, 'members': 5}), ({'intervals': [[1, 8], [2, 7], [9]]}, {'reversed': [], 'low_order': [], 'high_order': [2], 'minimum': 1, 'maximum': 8, 'members': 5}), ({'intervals': [[5, 3], [1, 6], [4, 8]]}, {'reversed': [0], 'low_order': [1, 2], 'high_order': [1, 2], 'minimum': 5, 'maximum': 3, 'members': 6}), ({'intervals': [[1, 9], [2, 8], [3, 7], [4, 4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 9, 'members': 8}), ({'intervals': [[1, 11], [2, 8], [3, 7], [4, 4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 11, 'members': 8})], [({'intervals': []}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': None, 'maximum': None, 'members': 0}), ({'intervals': [[4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 4, 'maximum': 4, 'members': 1}), ({'intervals': [[1, 9], [2, 7], [3]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 9, 'members': 5}), ({'intervals': [[1, 8], [2, 7], [9]]}, {'reversed': [], 'low_order': [], 'high_order': [2], 'minimum': 1, 'maximum': 8, 'members': 5}), ({'intervals': [[5, 3], [1, 6], [4, 8]]}, {'reversed': [0], 'low_order': [1, 2], 'high_order': [1, 2], 'minimum': 5, 'maximum': 3, 'members': 6}), ({'intervals': [[1, 9], [2, 8], [3, 7], [4, 4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 9, 'members': 8}), ({'intervals': [[1, 12], [2, 8], [3, 7], [4, 4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 12, 'members': 8})], [({'intervals': []}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': None, 'maximum': None, 'members': 0}), ({'intervals': [[4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 4, 'maximum': 4, 'members': 1}), ({'intervals': [[1, 9], [2, 7], [3]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 9, 'members': 5}), ({'intervals': [[1, 8], [2, 7], [9]]}, {'reversed': [], 'low_order': [], 'high_order': [2], 'minimum': 1, 'maximum': 8, 'members': 5}), ({'intervals': [[5, 3], [1, 6], [4, 8]]}, {'reversed': [0], 'low_order': [1, 2], 'high_order': [1, 2], 'minimum': 5, 'maximum': 3, 'members': 6}), ({'intervals': [[1, 9], [2, 8], [3, 7], [4, 4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 9, 'members': 8}), ({'intervals': [[1, 13], [2, 8], [3, 7], [4, 4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 13, 'members': 8})], [({'intervals': []}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': None, 'maximum': None, 'members': 0}), ({'intervals': [[4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 4, 'maximum': 4, 'members': 1}), ({'intervals': [[1, 9], [2, 7], [3]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 9, 'members': 5}), ({'intervals': [[1, 8], [2, 7], [9]]}, {'reversed': [], 'low_order': [], 'high_order': [2], 'minimum': 1, 'maximum': 8, 'members': 5}), ({'intervals': [[5, 3], [1, 6], [4, 8]]}, {'reversed': [0], 'low_order': [1, 2], 'high_order': [1, 2], 'minimum': 5, 'maximum': 3, 'members': 6}), ({'intervals': [[1, 9], [2, 8], [3, 7], [4, 4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 9, 'members': 8}), ({'intervals': [[1, 14], [2, 8], [3, 7], [4, 4]]}, {'reversed': [], 'low_order': [], 'high_order': [], 'minimum': 1, 'maximum': 14, 'members': 8})]][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-interval-endpoints-reversed","generated_at":"2026-09-29T14:43:30.845572+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 reversed using [i for i,x in enumerate(a) if x[0]>x[-1]] under the stated bounded certificate contract.","root_cause":"Interval heap admits equal endpoints and a final singleton.","sha256":"783ea3ef9410b541f767595a6c723530dd04859faf44923892b1a7310eac9024","title":"Interval heap admits equal endpoints and a final singleton · 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":40.912,"exit_code":1,"observations":[{"actual":{"high_order":[],"low_order":[],"maximum":null,"members":0,"minimum":null,"reversed":[]},"check":"regression certificate 1","expected":{"high_order":[],"low_order":[],"maximum":null,"members":0,"minimum":null,"reversed":[]},"passed":true},{"actual":{"high_order":[],"low_order":[],"maximum":4,"members":1,"minimum":4,"reversed":[0]},"check":"regression certificate 2","expected":{"high_order":[],"low_order":[],"maximum":4,"members":1,"minimum":4,"reversed":[]},"passed":false},{"actual":{"high_order":[],"low_order":[],"maximum":9,"members":5,"minimum":1,"reversed":[2]},"check":"regression certificate 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