{"abstract":"The bounded interval insert certificate reports an incorrect new size.","category":"Heap invariants","checks":7,"contract":"Insert key x into an interval-heap last-node decision. For a singleton last interval s, complete it as sorted(s,x). For a new singleton with parent [lo,hi], x below lo routes to the lower heap, above hi to the upper heap, otherwise stays. Return pair completion, lower route, upper route, contained route, parent endpoint displaced on crossing, and logical-size increment.","evaluation_group":"s3-heap-model-interval-insert","failed_approach":"The local patch uses d[\"size\"]+int(x!=s) and still violates the stated relation.","family":"s3-heap-interval-insert-new_size","id":"FA-40466","implementations":{"attempt":{"sha256":"3ba28a0d69f2bcbfef493e9e4b461b0efe1139b155cf7c02bb69ffc08d2206a5","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(d):\n    x=d['x']; s=d['singleton']; lo,hi=d['parent']\n    return {'completed': sorted([s,x]),\n    'lower': x<lo,\n    'upper': x>hi,\n    'contained': lo<=x<=hi,\n    'displaced': lo if x<lo else hi if x>hi else None,\n    'new_size': d[\"size\"]+int(x!=s)}\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncases = [[({'x': 1, 'singleton': 6, 'parent': [2, 8], 'size': 3}, {'completed': [1, 6], 'lower': True, 'upper': False, 'contained': False, 'displaced': 2, 'new_size': 4}), ({'x': 9, 'singleton': 4, 'parent': [2, 8], 'size': 5}, {'completed': [4, 9], 'lower': False, 'upper': True, 'contained': False, 'displaced': 8, 'new_size': 6}), ({'x': 5, 'singleton': 7, 'parent': [2, 8], 'size': 7}, {'completed': [5, 7], 'lower': False, 'upper': False, 'contained': True, 'displaced': None, 'new_size': 8}), ({'x': 2, 'singleton': 3, 'parent': [2, 8], 'size': 9}, {'completed': [2, 3], 'lower': False, 'upper': False, 'contained': True, 'displaced': None, 'new_size': 10}), ({'x': 8, 'singleton': 1, 'parent': [2, 8], 'size': 11}, {'completed': [1, 8], 'lower': False, 'upper': False, 'contained': True, 'displaced': None, 'new_size': 12}), ({'x': 6, 'singleton': 6, 'parent': [2, 8], 'size': 1}, {'completed': [6, 6], 'lower': False, 'upper': False, 'contained': True, 'displaced': None, 'new_size': 2}), ({'x': 7, 'singleton': 6, 'parent': [2, 8], 'size': 1}, {'completed': [6, 7], 'lower': False, 'upper': False, 'contained': True, 'displaced': None, 'new_size': 2})], [({'x': 1, 'singleton': 6, 'parent': [2, 8], 'size': 3}, {'completed': [1, 6], 'lower': True, 'upper': False, 'contained': False, 'displaced': 2, 'new_size': 4}), ({'x': 9, 'singleton': 4, 'parent': [2, 8], 'size': 5}, {'completed': [4, 9], 'lower': False, 'upper': True, 'contained': False, 'displaced': 8, 'new_size': 6}), ({'x': 5, 'singleton': 7, 'parent': [2, 8], 'size': 7}, {'completed': [5, 7], 'lower': False, 'upper': False, 'contained': True, 'displaced': None, 'new_size': 8}), ({'x': 2, 'singleton': 3, 'parent': [2, 8], 'size': 9}, {'completed': [2, 3], 'lower': False, 'upper': False, 'contained': True, 'displaced': None, 'new_size': 10}), ({'x': 8, 'singleton': 1, 'parent': [2, 8], 'size': 11}, {'completed': [1, 8], 'lower': False, 'upper': False, 'contained': True, 'displaced': None, 'new_size': 12}), ({'x': 6, 'singleton': 6, 'parent': [2, 8], 'size': 1}, {'completed': [6, 6], 'lower': False, 'upper': False, 'contained': True, 'displaced': None, 'new_size': 2}), ({'x': 8, 'singleton': 6, 'parent': [2, 8], 'size': 1}, {'completed': [6, 8], 'lower': False, 'upper': False, 'contained': True, 'displaced': None, 'new_size': 2})], [({'x': 1, 'singleton': 6, 'parent': [2, 8], 'size': 3}, {'completed': [1, 6], 'lower': True, 'upper': False, 'contained': False, 'displaced': 2, 'new_size': 4}), ({'x': 9, 'singleton': 4, 'parent': [2, 8], 'size': 5}, {'completed': [4, 9], 'lower': False, 'upper': True, 'contained': False, 'displaced': 8, 'new_size': 6}), ({'x': 5, 'singleton': 7, 'parent': [2, 8], 'size': 7}, {'completed': [5, 7], 'lower': False, 'upper': False, 'contained': True, 'displaced': None, 'new_size': 8}), ({'x': 2, 'singleton': 3, 'parent': [2, 8], 'size': 9}, {'completed': [2, 3], 'lower': False, 'upper': False, 'contained': True, 'displaced': None, 'new_size': 10}), ({'x': 8, 'singleton': 1, 'parent': [2, 8], 'size': 11}, {'completed': [1, 8], 'lower': False, 'upper': False, 'contained': True, 'displaced': None, 'new_size': 12}), ({'x': 6, 'singleton': 6, 'parent': [2, 8], 'size': 1}, {'completed': [6, 6], 'lower': False, 'upper': False, 'contained': True, 'displaced': None, 'new_size': 2}), ({'x': 9, 'singleton': 6, 'parent': [2, 8], 'size': 1}, {'completed': [6, 9], 'lower': False, 'upper': True, 'contained': False, 'displaced': 8, 'new_size': 2})], [({'x': 1, 'singleton': 6, 'parent': [2, 8], 'size': 3}, {'completed': [1, 6], 'lower': True, 'upper': False, 'contained': False, 'displaced': 2, 'new_size': 4}), ({'x': 9, 'singleton': 4, 'parent': [2, 8], 'size': 5}, {'completed': [4, 9], 'lower': False, 'upper': True, 'contained': False, 'displaced': 8, 'new_size': 6}), ({'x': 5, 'singleton': 7, 'parent': [2, 8], 'size': 7}, {'completed': [5, 7], 'lower': False, 'upper': False, 'contained': True, 'displaced': None, 'new_size': 8}), ({'x': 2, 'singleton': 3, 'parent': [2, 8], 'size': 9}, {'completed': [2, 3], 'lower': False, 'upper': False, 'contained': True, 'displaced': None, 'new_size': 10}), ({'x': 8, 'singleton': 1, 'parent': [2, 8], 'size': 11}, {'completed': [1, 8], 'lower': False, 'upper': False, 'contained': True, 'displaced': None, 'new_size': 12}), ({'x': 6, 'singleton': 6, 'parent': [2, 8], 'size': 1}, {'completed': [6, 6], 'lower': False, 'upper': False, 'contained': True, 'displaced': None, 'new_size': 2}), ({'x': 10, 'singleton': 6, 'parent': [2, 8], 'size': 1}, {'completed': [6, 10], 'lower': False, 'upper': True, 'contained': False, 'displaced': 8, 'new_size': 2})], [({'x': 1, 'singleton': 6, 'parent': [2, 8], 'size': 3}, {'completed': [1, 6], 'lower': True, 'upper': False, 'contained': False, 'displaced': 2, 'new_size': 4}), ({'x': 9, 'singleton': 4, 'parent': [2, 8], 'size': 5}, {'completed': [4, 9], 'lower': False, 'upper': True, 'contained': False, 'displaced': 8, 'new_size': 6}), ({'x': 5, 'singleton': 7, 'parent': [2, 8], 'size': 7}, {'completed': [5, 7], 'lower': False, 'upper': False, 'contained': True, 'displaced': None, 'new_size': 8}), ({'x': 2, 'singleton': 3, 'parent': [2, 8], 'size': 9}, {'completed': [2, 3], 'lower': False, 'upper': False, 'contained': True, 'displaced': None, 'new_size': 10}), ({'x': 8, 'singleton': 1, 'parent': [2, 8], 'size': 11}, {'completed': [1, 8], 'lower': False, 'upper': False, 'contained': True, 'displaced': None, 'new_size': 12}), ({'x': 6, 'singleton': 6, 'parent': [2, 8], 'size': 1}, {'completed': [6, 6], 'lower': False, 'upper': False, 'contained': True, 'displaced': None, 'new_size': 2}), ({'x': 11, 'singleton': 6, 'parent': [2, 8], 'size': 1}, {'completed': [6, 11], 'lower': False, 'upper': True, 'contained': False, 'displaced': 8, 'new_size': 2})]][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":"9d690fa3a35dc547ce2213f61f07d00917550017ff1dba01c9831a0525ac0f7d","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(d):\n    x=d['x']; s=d['singleton']; lo,hi=d['parent']\n    return {'completed': sorted([s,x]),\n    'lower': x<lo,\n    'upper': x>hi,\n    'contained': lo<=x<=hi,\n    'displaced': lo if x<lo else hi if x>hi else None,\n    'new_size': d[\"size\"]+2}\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncases = [[({'x': 1, 'singleton': 6, 'parent': [2, 8], 'size': 3}, {'completed': [1, 6], 'lower': True, 'upper': False, 'contained': False, 'displaced': 2, 'new_size': 4}), ({'x': 9, 'singleton': 4, 'parent': [2, 8], 'size': 5}, {'completed': [4, 9], 'lower': False, 'upper': True, 'contained': False, 'displaced': 8, 'new_size': 6}), ({'x': 5, 'singleton': 7, 'parent': [2, 8], 'size': 7}, {'completed': [5, 7], 'lower': False, 'upper': False, 'contained': True, 'displaced': None, 'new_size': 8}), ({'x': 2, 'singleton': 3, 'parent': [2, 8], 'size': 9}, {'completed': [2, 3], 'lower': False, 'upper': False, 'contained': True, 'displaced': None, 'new_size': 10}), ({'x': 8, 'singleton': 1, 'parent': [2, 8], 'size': 11}, {'completed': [1, 8], 'lower': False, 'upper': False, 'contained': True, 'displaced': None, 'new_size': 12}), ({'x': 6, 'singleton': 6, 'parent': [2, 8], 'size': 1}, {'completed': [6, 6], 'lower': False, 'upper': False, 'contained': True, 'displaced': None, 'new_size': 2}), ({'x': 7, 'singleton': 6, 'parent': [2, 8], 'size': 1}, {'completed': [6, 7], 'lower': False, 'upper': False, 'contained': True, 'displaced': None, 'new_size': 2})], [({'x': 1, 'singleton': 6, 'parent': [2, 8], 'size': 3}, {'completed': [1, 6], 'lower': True, 'upper': False, 'contained': False, 'displaced': 2, 'new_size': 4}), ({'x': 9, 'singleton': 4, 'parent': [2, 8], 'size': 5}, {'completed': [4, 9], 'lower': False, 'upper': True, 'contained': False, 'displaced': 8, 'new_size': 6}), ({'x': 5, 'singleton': 7, 'parent': [2, 8], 'size': 7}, {'completed': [5, 7], 'lower': False, 'upper': False, 'contained': True, 'displaced': None, 'new_size': 8}), ({'x': 2, 'singleton': 3, 'parent': [2, 8], 'size': 9}, {'completed': [2, 3], 'lower': False, 'upper': False, 'contained': True, 'displaced': None, 'new_size': 10}), ({'x': 8, 'singleton': 1, 'parent': [2, 8], 'size': 11}, {'completed': [1, 8], 'lower': False, 'upper': False, 'contained': True, 'displaced': None, 'new_size': 12}), ({'x': 6, 'singleton': 6, 'parent': [2, 8], 'size': 1}, {'completed': [6, 6], 'lower': False, 'upper': False, 'contained': True, 'displaced': None, 'new_size': 2}), ({'x': 8, 'singleton': 6, 'parent': [2, 8], 'size': 1}, {'completed': [6, 8], 'lower': False, 'upper': False, 'contained': True, 'displaced': None, 'new_size': 2})], [({'x': 1, 'singleton': 6, 'parent': [2, 8], 'size': 3}, {'completed': [1, 6], 'lower': True, 'upper': False, 'contained': False, 'displaced': 2, 'new_size': 4}), ({'x': 9, 'singleton': 4, 'parent': [2, 8], 'size': 5}, {'completed': [4, 9], 'lower': False, 'upper': True, 'contained': False, 'displaced': 8, 'new_size': 6}), ({'x': 5, 'singleton': 7, 'parent': [2, 8], 'size': 7}, {'completed': [5, 7], 'lower': False, 'upper': False, 'contained': True, 'displaced': None, 'new_size': 8}), ({'x': 2, 'singleton': 3, 'parent': [2, 8], 'size': 9}, {'completed': [2, 3], 'lower': False, 'upper': False, 'contained': True, 'displaced': None, 'new_size': 10}), ({'x': 8, 'singleton': 1, 'parent': [2, 8], 'size': 11}, {'completed': [1, 8], 'lower': False, 'upper': False, 'contained': True, 'displaced': None, 'new_size': 12}), ({'x': 6, 'singleton': 6, 'parent': [2, 8], 'size': 1}, {'completed': [6, 6], 'lower': False, 'upper': False, 'contained': True, 'displaced': None, 'new_size': 2}), ({'x': 9, 'singleton': 6, 'parent': [2, 8], 'size': 1}, {'completed': [6, 9], 'lower': False, 'upper': True, 'contained': False, 'displaced': 8, 'new_size': 2})], [({'x': 1, 'singleton': 6, 'parent': [2, 8], 'size': 3}, {'completed': [1, 6], 'lower': True, 'upper': False, 'contained': False, 'displaced': 2, 'new_size': 4}), ({'x': 9, 'singleton': 4, 'parent': [2, 8], 'size': 5}, {'completed': [4, 9], 'lower': False, 'upper': True, 'contained': False, 'displaced': 8, 'new_size': 6}), ({'x': 5, 'singleton': 7, 'parent': [2, 8], 'size': 7}, {'completed': [5, 7], 'lower': False, 'upper': False, 'contained': True, 'displaced': None, 'new_size': 8}), ({'x': 2, 'singleton': 3, 'parent': [2, 8], 'size': 9}, {'completed': [2, 3], 'lower': False, 'upper': False, 'contained': True, 'displaced': None, 'new_size': 10}), ({'x': 8, 'singleton': 1, 'parent': [2, 8], 'size': 11}, {'completed': [1, 8], 'lower': False, 'upper': False, 'contained': True, 'displaced': None, 'new_size': 12}), ({'x': 6, 'singleton': 6, 'parent': [2, 8], 'size': 1}, {'completed': [6, 6], 'lower': False, 'upper': False, 'contained': True, 'displaced': None, 'new_size': 2}), ({'x': 10, 'singleton': 6, 'parent': [2, 8], 'size': 1}, {'completed': [6, 10], 'lower': False, 'upper': True, 'contained': False, 'displaced': 8, 'new_size': 2})], [({'x': 1, 'singleton': 6, 'parent': [2, 8], 'size': 3}, {'completed': [1, 6], 'lower': True, 'upper': False, 'contained': False, 'displaced': 2, 'new_size': 4}), ({'x': 9, 'singleton': 4, 'parent': [2, 8], 'size': 5}, {'completed': [4, 9], 'lower': False, 'upper': True, 'contained': False, 'displaced': 8, 'new_size': 6}), ({'x': 5, 'singleton': 7, 'parent': [2, 8], 'size': 7}, {'completed': [5, 7], 'lower': False, 'upper': False, 'contained': True, 'displaced': None, 'new_size': 8}), ({'x': 2, 'singleton': 3, 'parent': [2, 8], 'size': 9}, {'completed': [2, 3], 'lower': False, 'upper': False, 'contained': True, 'displaced': None, 'new_size': 10}), ({'x': 8, 'singleton': 1, 'parent': [2, 8], 'size': 11}, {'completed': [1, 8], 'lower': False, 'upper': False, 'contained': True, 'displaced': None, 'new_size': 12}), ({'x': 6, 'singleton': 6, 'parent': [2, 8], 'size': 1}, {'completed': [6, 6], 'lower': False, 'upper': False, 'contained': True, 'displaced': None, 'new_size': 2}), ({'x': 11, 'singleton': 6, 'parent': [2, 8], 'size': 1}, {'completed': [6, 11], 'lower': False, 'upper': True, 'contained': False, 'displaced': 8, 'new_size': 2})]][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":"e85404eca133ad047294489268f657c2f47ea2cafb8a191ccd019a1202626077","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(d):\n    x=d['x']; s=d['singleton']; lo,hi=d['parent']\n    return {'completed': sorted([s,x]),\n    'lower': x<lo,\n    'upper': x>hi,\n    'contained': lo<=x<=hi,\n    'displaced': lo if x<lo else hi if x>hi else None,\n    'new_size': d[\"size\"]+1}\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncases = [[({'x': 1, 'singleton': 6, 'parent': [2, 8], 'size': 3}, {'completed': [1, 6], 'lower': True, 'upper': False, 'contained': False, 'displaced': 2, 'new_size': 4}), ({'x': 9, 'singleton': 4, 'parent': [2, 8], 'size': 5}, {'completed': [4, 9], 'lower': False, 'upper': True, 'contained': False, 'displaced': 8, 'new_size': 6}), ({'x': 5, 'singleton': 7, 'parent': [2, 8], 'size': 7}, {'completed': [5, 7], 'lower': False, 'upper': False, 'contained': True, 'displaced': None, 'new_size': 8}), ({'x': 2, 'singleton': 3, 'parent': [2, 8], 'size': 9}, {'completed': [2, 3], 'lower': False, 'upper': False, 'contained': True, 'displaced': None, 'new_size': 10}), ({'x': 8, 'singleton': 1, 'parent': [2, 8], 'size': 11}, {'completed': [1, 8], 'lower': False, 'upper': False, 'contained': True, 'displaced': None, 'new_size': 12}), ({'x': 6, 'singleton': 6, 'parent': [2, 8], 'size': 1}, {'completed': [6, 6], 'lower': False, 'upper': False, 'contained': True, 'displaced': None, 'new_size': 2}), ({'x': 7, 'singleton': 6, 'parent': [2, 8], 'size': 1}, {'completed': [6, 7], 'lower': False, 'upper': False, 'contained': True, 'displaced': None, 'new_size': 2})], [({'x': 1, 'singleton': 6, 'parent': [2, 8], 'size': 3}, {'completed': [1, 6], 'lower': True, 'upper': False, 'contained': False, 'displaced': 2, 'new_size': 4}), ({'x': 9, 'singleton': 4, 'parent': [2, 8], 'size': 5}, {'completed': [4, 9], 'lower': False, 'upper': True, 'contained': False, 'displaced': 8, 'new_size': 6}), ({'x': 5, 'singleton': 7, 'parent': [2, 8], 'size': 7}, {'completed': [5, 7], 'lower': False, 'upper': False, 'contained': True, 'displaced': None, 'new_size': 8}), ({'x': 2, 'singleton': 3, 'parent': [2, 8], 'size': 9}, {'completed': [2, 3], 'lower': False, 'upper': False, 'contained': True, 'displaced': None, 'new_size': 10}), ({'x': 8, 'singleton': 1, 'parent': [2, 8], 'size': 11}, {'completed': [1, 8], 'lower': False, 'upper': False, 'contained': True, 'displaced': None, 'new_size': 12}), ({'x': 6, 'singleton': 6, 'parent': [2, 8], 'size': 1}, {'completed': [6, 6], 'lower': False, 'upper': False, 'contained': True, 'displaced': None, 'new_size': 2}), ({'x': 8, 'singleton': 6, 'parent': [2, 8], 'size': 1}, {'completed': [6, 8], 'lower': False, 'upper': False, 'contained': True, 'displaced': None, 'new_size': 2})], [({'x': 1, 'singleton': 6, 'parent': [2, 8], 'size': 3}, {'completed': [1, 6], 'lower': True, 'upper': False, 'contained': False, 'displaced': 2, 'new_size': 4}), ({'x': 9, 'singleton': 4, 'parent': [2, 8], 'size': 5}, {'completed': [4, 9], 'lower': False, 'upper': True, 'contained': False, 'displaced': 8, 'new_size': 6}), ({'x': 5, 'singleton': 7, 'parent': [2, 8], 'size': 7}, {'completed': [5, 7], 'lower': False, 'upper': False, 'contained': True, 'displaced': None, 'new_size': 8}), ({'x': 2, 'singleton': 3, 'parent': [2, 8], 'size': 9}, {'completed': [2, 3], 'lower': False, 'upper': False, 'contained': True, 'displaced': None, 'new_size': 10}), ({'x': 8, 'singleton': 1, 'parent': [2, 8], 'size': 11}, {'completed': [1, 8], 'lower': False, 'upper': False, 'contained': True, 'displaced': None, 'new_size': 12}), ({'x': 6, 'singleton': 6, 'parent': [2, 8], 'size': 1}, {'completed': [6, 6], 'lower': False, 'upper': False, 'contained': True, 'displaced': None, 'new_size': 2}), ({'x': 9, 'singleton': 6, 'parent': [2, 8], 'size': 1}, {'completed': [6, 9], 'lower': False, 'upper': True, 'contained': False, 'displaced': 8, 'new_size': 2})], [({'x': 1, 'singleton': 6, 'parent': [2, 8], 'size': 3}, {'completed': [1, 6], 'lower': True, 'upper': False, 'contained': False, 'displaced': 2, 'new_size': 4}), ({'x': 9, 'singleton': 4, 'parent': [2, 8], 'size': 5}, {'completed': [4, 9], 'lower': False, 'upper': True, 'contained': False, 'displaced': 8, 'new_size': 6}), ({'x': 5, 'singleton': 7, 'parent': [2, 8], 'size': 7}, {'completed': [5, 7], 'lower': False, 'upper': False, 'contained': True, 'displaced': None, 'new_size': 8}), ({'x': 2, 'singleton': 3, 'parent': [2, 8], 'size': 9}, {'completed': [2, 3], 'lower': False, 'upper': False, 'contained': True, 'displaced': None, 'new_size': 10}), ({'x': 8, 'singleton': 1, 'parent': [2, 8], 'size': 11}, {'completed': [1, 8], 'lower': False, 'upper': False, 'contained': True, 'displaced': None, 'new_size': 12}), ({'x': 6, 'singleton': 6, 'parent': [2, 8], 'size': 1}, {'completed': [6, 6], 'lower': False, 'upper': False, 'contained': True, 'displaced': None, 'new_size': 2}), ({'x': 10, 'singleton': 6, 'parent': [2, 8], 'size': 1}, {'completed': [6, 10], 'lower': False, 'upper': True, 'contained': False, 'displaced': 8, 'new_size': 2})], [({'x': 1, 'singleton': 6, 'parent': [2, 8], 'size': 3}, {'completed': [1, 6], 'lower': True, 'upper': False, 'contained': False, 'displaced': 2, 'new_size': 4}), ({'x': 9, 'singleton': 4, 'parent': [2, 8], 'size': 5}, {'completed': [4, 9], 'lower': False, 'upper': True, 'contained': False, 'displaced': 8, 'new_size': 6}), ({'x': 5, 'singleton': 7, 'parent': [2, 8], 'size': 7}, {'completed': [5, 7], 'lower': False, 'upper': False, 'contained': True, 'displaced': None, 'new_size': 8}), ({'x': 2, 'singleton': 3, 'parent': [2, 8], 'size': 9}, {'completed': [2, 3], 'lower': False, 'upper': False, 'contained': True, 'displaced': None, 'new_size': 10}), ({'x': 8, 'singleton': 1, 'parent': [2, 8], 'size': 11}, {'completed': [1, 8], 'lower': False, 'upper': False, 'contained': True, 'displaced': None, 'new_size': 12}), ({'x': 6, 'singleton': 6, 'parent': [2, 8], 'size': 1}, {'completed': [6, 6], 'lower': False, 'upper': False, 'contained': True, 'displaced': None, 'new_size': 2}), ({'x': 11, 'singleton': 6, 'parent': [2, 8], 'size': 1}, {'completed': [6, 11], 'lower': False, 'upper': True, 'contained': False, 'displaced': 8, 'new_size': 2})]][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-insert-new_size","generated_at":"2026-09-29T14:43:31.467781+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 new size using d[\"size\"]+1 under the stated bounded certificate contract.","root_cause":"Interval insertion increases element count by one regardless of pair completion.","sha256":"58487ac4783e38b2efa059fdfad37a0ebba1228a20e1cbc4a2e76834dc53075c","title":"Interval insertion increases element count by one regardless of pair completion · case 01","variant":1,"variant_policy":"Six 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