{"abstract":"The bounded indexed erase routing certificate reports an incorrect slots.","category":"Heap invariants","checks":7,"contract":"An indexed heap erasure certificate gives slots [id,key], selected slot i, and a valid min-heap prefix before deletion. Fill the hole with the last record unless erasing the tail. Decide upward repair if replacement is smaller than its parent, otherwise downward; return shortened slots, removed id, direction, replacement handle location, retained identities, and logical size.","evaluation_group":"s3-heap-model-indexed-erase-routing","failed_approach":"The local patch uses a[:-1] and still violates the stated relation.","family":"s3-heap-indexed-erase-routing-slots","id":"FA-40801","implementations":{"attempt":{"sha256":"ac741327e081b1624e119edfb546157f383d29afb783854fc5aa1ba210061bdb","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(d):\n    a=d['slots']; i=d['index']; last=len(a)-1; out=[list(x) for x in a[:-1]]\n    if i<last: out[i]=list(a[-1])\n    direction='none' if i==last else ('up' if i>0 and out[i][1]<out[(i-1)//2][1] else 'down')\n    return {'slots': a[:-1],\n    'removed': a[i][0],\n    'direction': direction,\n    'replacement_location': None if i==last else [a[-1][0],i],\n    'retained': sorted(x[0] for x in out),\n    'size': len(a)-1}\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncases = [[({'slots': [['a', 1]], 'index': 0}, {'slots': [], 'removed': 'a', 'direction': 'none', 'replacement_location': None, 'retained': [], 'size': 0}), ({'slots': [['a', 1], ['b', 5], ['c', 2], ['d', 7], ['e', 8], ['f', 3], ['g', 4]], 'index': 4}, {'slots': [['a', 1], ['b', 5], ['c', 2], ['d', 7], ['g', 4], ['f', 3]], 'removed': 'e', 'direction': 'up', 'replacement_location': ['g', 4], 'retained': ['a', 'b', 'c', 'd', 'f', 'g'], 'size': 6}), ({'slots': [['a', 1], ['b', 2], ['c', 3]], 'index': 0}, {'slots': [['c', 3], ['b', 2]], 'removed': 'a', 'direction': 'down', 'replacement_location': ['c', 0], 'retained': ['b', 'c'], 'size': 2}), ({'slots': [['a', 1], ['b', 2], ['c', 3], ['d', 4]], 'index': 3}, {'slots': [['a', 1], ['b', 2], ['c', 3]], 'removed': 'd', 'direction': 'none', 'replacement_location': None, 'retained': ['a', 'b', 'c'], 'size': 3}), ({'slots': [['a', 1], ['b', 5], ['c', 2], ['d', 7], ['e', 8], ['f', 3], ['g', 4]], 'index': 3}, {'slots': [['a', 1], ['b', 5], ['c', 2], ['g', 4], ['e', 8], ['f', 3]], 'removed': 'd', 'direction': 'up', 'replacement_location': ['g', 3], 'retained': ['a', 'b', 'c', 'e', 'f', 'g'], 'size': 6}), ({'slots': [['a', 1], ['b', 2], ['c', 2], ['d', 4], ['e', 5], ['f', 2], ['g', 3]], 'index': 1}, {'slots': [['a', 1], ['g', 3], ['c', 2], ['d', 4], ['e', 5], ['f', 2]], 'removed': 'b', 'direction': 'down', 'replacement_location': ['g', 1], 'retained': ['a', 'c', 'd', 'e', 'f', 'g'], 'size': 6}), ({'slots': [['a', 1], ['b', 2], ['c', 2], ['d', 4], ['e', 5], ['f', 2], ['g', 3]], 'index': 1}, {'slots': [['a', 1], ['g', 3], ['c', 2], ['d', 4], ['e', 5], ['f', 2]], 'removed': 'b', 'direction': 'down', 'replacement_location': ['g', 1], 'retained': ['a', 'c', 'd', 'e', 'f', 'g'], 'size': 6})], [({'slots': [['a', 1]], 'index': 0}, {'slots': [], 'removed': 'a', 'direction': 'none', 'replacement_location': None, 'retained': [], 'size': 0}), ({'slots': [['a', 1], ['b', 5], ['c', 2], ['d', 7], ['e', 8], ['f', 3], ['g', 4]], 'index': 4}, {'slots': [['a', 1], ['b', 5], ['c', 2], ['d', 7], ['g', 4], ['f', 3]], 'removed': 'e', 'direction': 'up', 'replacement_location': ['g', 4], 'retained': ['a', 'b', 'c', 'd', 'f', 'g'], 'size': 6}), ({'slots': [['a', 1], ['b', 2], ['c', 3]], 'index': 0}, {'slots': [['c', 3], ['b', 2]], 'removed': 'a', 'direction': 'down', 'replacement_location': ['c', 0], 'retained': ['b', 'c'], 'size': 2}), ({'slots': [['a', 1], ['b', 2], ['c', 3], ['d', 4]], 'index': 3}, {'slots': [['a', 1], ['b', 2], ['c', 3]], 'removed': 'd', 'direction': 'none', 'replacement_location': None, 'retained': ['a', 'b', 'c'], 'size': 3}), ({'slots': [['a', 1], ['b', 5], ['c', 2], ['d', 7], ['e', 8], ['f', 3], ['g', 4]], 'index': 3}, {'slots': [['a', 1], ['b', 5], ['c', 2], ['g', 4], ['e', 8], ['f', 3]], 'removed': 'd', 'direction': 'up', 'replacement_location': ['g', 3], 'retained': ['a', 'b', 'c', 'e', 'f', 'g'], 'size': 6}), ({'slots': [['a', 1], ['b', 2], ['c', 2], ['d', 4], ['e', 5], ['f', 2], ['g', 3]], 'index': 1}, {'slots': [['a', 1], ['g', 3], ['c', 2], ['d', 4], ['e', 5], ['f', 2]], 'removed': 'b', 'direction': 'down', 'replacement_location': ['g', 1], 'retained': ['a', 'c', 'd', 'e', 'f', 'g'], 'size': 6}), ({'slots': [['a', 1], ['b', 2], ['c', 2], ['d', 4], ['e', 5], ['f', 2], ['g', 3]], 'index': 2}, {'slots': [['a', 1], ['b', 2], ['g', 3], ['d', 4], ['e', 5], ['f', 2]], 'removed': 'c', 'direction': 'down', 'replacement_location': ['g', 2], 'retained': ['a', 'b', 'd', 'e', 'f', 'g'], 'size': 6})], [({'slots': [['a', 1]], 'index': 0}, {'slots': [], 'removed': 'a', 'direction': 'none', 'replacement_location': None, 'retained': [], 'size': 0}), ({'slots': [['a', 1], ['b', 5], ['c', 2], ['d', 7], ['e', 8], ['f', 3], ['g', 4]], 'index': 4}, {'slots': [['a', 1], ['b', 5], ['c', 2], ['d', 7], ['g', 4], ['f', 3]], 'removed': 'e', 'direction': 'up', 'replacement_location': ['g', 4], 'retained': ['a', 'b', 'c', 'd', 'f', 'g'], 'size': 6}), ({'slots': [['a', 1], ['b', 2], ['c', 3]], 'index': 0}, {'slots': [['c', 3], ['b', 2]], 'removed': 'a', 'direction': 'down', 'replacement_location': ['c', 0], 'retained': ['b', 'c'], 'size': 2}), ({'slots': [['a', 1], ['b', 2], ['c', 3], ['d', 4]], 'index': 3}, {'slots': [['a', 1], ['b', 2], ['c', 3]], 'removed': 'd', 'direction': 'none', 'replacement_location': None, 'retained': ['a', 'b', 'c'], 'size': 3}), ({'slots': [['a', 1], ['b', 5], ['c', 2], ['d', 7], ['e', 8], ['f', 3], ['g', 4]], 'index': 3}, {'slots': [['a', 1], ['b', 5], ['c', 2], ['g', 4], ['e', 8], ['f', 3]], 'removed': 'd', 'direction': 'up', 'replacement_location': ['g', 3], 'retained': ['a', 'b', 'c', 'e', 'f', 'g'], 'size': 6}), ({'slots': [['a', 1], ['b', 2], ['c', 2], ['d', 4], ['e', 5], ['f', 2], ['g', 3]], 'index': 1}, {'slots': [['a', 1], ['g', 3], ['c', 2], ['d', 4], ['e', 5], ['f', 2]], 'removed': 'b', 'direction': 'down', 'replacement_location': ['g', 1], 'retained': ['a', 'c', 'd', 'e', 'f', 'g'], 'size': 6}), ({'slots': [['a', 1], ['b', 2], ['c', 2], ['d', 4], ['e', 5], ['f', 2], ['g', 3]], 'index': 3}, {'slots': [['a', 1], ['b', 2], ['c', 2], ['g', 3], ['e', 5], ['f', 2]], 'removed': 'd', 'direction': 'down', 'replacement_location': ['g', 3], 'retained': ['a', 'b', 'c', 'e', 'f', 'g'], 'size': 6})], [({'slots': [['a', 1]], 'index': 0}, {'slots': [], 'removed': 'a', 'direction': 'none', 'replacement_location': None, 'retained': [], 'size': 0}), ({'slots': [['a', 1], ['b', 5], ['c', 2], ['d', 7], ['e', 8], ['f', 3], ['g', 4]], 'index': 4}, {'slots': [['a', 1], ['b', 5], ['c', 2], ['d', 7], ['g', 4], ['f', 3]], 'removed': 'e', 'direction': 'up', 'replacement_location': ['g', 4], 'retained': ['a', 'b', 'c', 'd', 'f', 'g'], 'size': 6}), ({'slots': [['a', 1], ['b', 2], ['c', 3]], 'index': 0}, {'slots': [['c', 3], ['b', 2]], 'removed': 'a', 'direction': 'down', 'replacement_location': ['c', 0], 'retained': ['b', 'c'], 'size': 2}), ({'slots': [['a', 1], ['b', 2], ['c', 3], ['d', 4]], 'index': 3}, {'slots': [['a', 1], ['b', 2], ['c', 3]], 'removed': 'd', 'direction': 'none', 'replacement_location': None, 'retained': ['a', 'b', 'c'], 'size': 3}), ({'slots': [['a', 1], ['b', 5], ['c', 2], ['d', 7], ['e', 8], ['f', 3], ['g', 4]], 'index': 3}, {'slots': [['a', 1], ['b', 5], ['c', 2], ['g', 4], ['e', 8], ['f', 3]], 'removed': 'd', 'direction': 'up', 'replacement_location': ['g', 3], 'retained': ['a', 'b', 'c', 'e', 'f', 'g'], 'size': 6}), ({'slots': [['a', 1], ['b', 2], ['c', 2], ['d', 4], ['e', 5], ['f', 2], ['g', 3]], 'index': 1}, {'slots': [['a', 1], ['g', 3], ['c', 2], ['d', 4], ['e', 5], ['f', 2]], 'removed': 'b', 'direction': 'down', 'replacement_location': ['g', 1], 'retained': ['a', 'c', 'd', 'e', 'f', 'g'], 'size': 6}), ({'slots': [['a', 1], ['b', 2], ['c', 2], ['d', 4], ['e', 5], ['f', 2], ['g', 3]], 'index': 4}, {'slots': [['a', 1], ['b', 2], ['c', 2], ['d', 4], ['g', 3], ['f', 2]], 'removed': 'e', 'direction': 'down', 'replacement_location': ['g', 4], 'retained': ['a', 'b', 'c', 'd', 'f', 'g'], 'size': 6})], [({'slots': [['a', 1]], 'index': 0}, {'slots': [], 'removed': 'a', 'direction': 'none', 'replacement_location': None, 'retained': [], 'size': 0}), ({'slots': [['a', 1], ['b', 5], ['c', 2], ['d', 7], ['e', 8], ['f', 3], ['g', 4]], 'index': 4}, {'slots': [['a', 1], ['b', 5], ['c', 2], ['d', 7], ['g', 4], ['f', 3]], 'removed': 'e', 'direction': 'up', 'replacement_location': ['g', 4], 'retained': ['a', 'b', 'c', 'd', 'f', 'g'], 'size': 6}), ({'slots': [['a', 1], ['b', 2], ['c', 3]], 'index': 0}, {'slots': [['c', 3], ['b', 2]], 'removed': 'a', 'direction': 'down', 'replacement_location': ['c', 0], 'retained': ['b', 'c'], 'size': 2}), ({'slots': [['a', 1], ['b', 2], ['c', 3], ['d', 4]], 'index': 3}, {'slots': [['a', 1], ['b', 2], ['c', 3]], 'removed': 'd', 'direction': 'none', 'replacement_location': None, 'retained': ['a', 'b', 'c'], 'size': 3}), ({'slots': [['a', 1], ['b', 5], ['c', 2], ['d', 7], ['e', 8], ['f', 3], ['g', 4]], 'index': 3}, {'slots': [['a', 1], ['b', 5], ['c', 2], ['g', 4], ['e', 8], ['f', 3]], 'removed': 'd', 'direction': 'up', 'replacement_location': ['g', 3], 'retained': ['a', 'b', 'c', 'e', 'f', 'g'], 'size': 6}), ({'slots': [['a', 1], ['b', 2], ['c', 2], ['d', 4], ['e', 5], ['f', 2], ['g', 3]], 'index': 1}, {'slots': [['a', 1], ['g', 3], ['c', 2], ['d', 4], ['e', 5], ['f', 2]], 'removed': 'b', 'direction': 'down', 'replacement_location': ['g', 1], 'retained': ['a', 'c', 'd', 'e', 'f', 'g'], 'size': 6}), ({'slots': [['a', 1], ['b', 2], ['c', 2], ['d', 4], ['e', 5], ['f', 2], ['g', 3]], 'index': 5}, {'slots': [['a', 1], ['b', 2], ['c', 2], ['d', 4], ['e', 5], ['g', 3]], 'removed': 'f', 'direction': 'down', 'replacement_location': ['g', 5], 'retained': ['a', 'b', 'c', 'd', 'e', 'g'], 'size': 6})]][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":"c051f3da7e72399349fb00785d0167c57135c671237f89291a852d60a446bcd2","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(d):\n    a=d['slots']; i=d['index']; last=len(a)-1; out=[list(x) for x in a[:-1]]\n    if i<last: out[i]=list(a[-1])\n    direction='none' if i==last else ('up' if i>0 and out[i][1]<out[(i-1)//2][1] else 'down')\n    return {'slots': [x for k,x in enumerate(a) if k!=i],\n    'removed': a[i][0],\n    'direction': direction,\n    'replacement_location': None if i==last else [a[-1][0],i],\n    'retained': sorted(x[0] for x in out),\n    'size': len(a)-1}\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncases = [[({'slots': [['a', 1]], 'index': 0}, {'slots': [], 'removed': 'a', 'direction': 'none', 'replacement_location': None, 'retained': [], 'size': 0}), ({'slots': [['a', 1], ['b', 5], ['c', 2], ['d', 7], ['e', 8], ['f', 3], ['g', 4]], 'index': 4}, {'slots': [['a', 1], ['b', 5], ['c', 2], ['d', 7], ['g', 4], ['f', 3]], 'removed': 'e', 'direction': 'up', 'replacement_location': ['g', 4], 'retained': ['a', 'b', 'c', 'd', 'f', 'g'], 'size': 6}), ({'slots': [['a', 1], ['b', 2], ['c', 3]], 'index': 0}, {'slots': [['c', 3], ['b', 2]], 'removed': 'a', 'direction': 'down', 'replacement_location': ['c', 0], 'retained': ['b', 'c'], 'size': 2}), ({'slots': [['a', 1], ['b', 2], ['c', 3], ['d', 4]], 'index': 3}, {'slots': [['a', 1], ['b', 2], ['c', 3]], 'removed': 'd', 'direction': 'none', 'replacement_location': None, 'retained': ['a', 'b', 'c'], 'size': 3}), ({'slots': [['a', 1], ['b', 5], ['c', 2], ['d', 7], ['e', 8], ['f', 3], ['g', 4]], 'index': 3}, {'slots': [['a', 1], ['b', 5], ['c', 2], ['g', 4], ['e', 8], ['f', 3]], 'removed': 'd', 'direction': 'up', 'replacement_location': ['g', 3], 'retained': ['a', 'b', 'c', 'e', 'f', 'g'], 'size': 6}), ({'slots': [['a', 1], ['b', 2], ['c', 2], ['d', 4], ['e', 5], ['f', 2], ['g', 3]], 'index': 1}, {'slots': [['a', 1], ['g', 3], ['c', 2], ['d', 4], ['e', 5], ['f', 2]], 'removed': 'b', 'direction': 'down', 'replacement_location': ['g', 1], 'retained': ['a', 'c', 'd', 'e', 'f', 'g'], 'size': 6}), ({'slots': [['a', 1], ['b', 2], ['c', 2], ['d', 4], ['e', 5], ['f', 2], ['g', 3]], 'index': 1}, {'slots': [['a', 1], ['g', 3], ['c', 2], ['d', 4], ['e', 5], ['f', 2]], 'removed': 'b', 'direction': 'down', 'replacement_location': ['g', 1], 'retained': ['a', 'c', 'd', 'e', 'f', 'g'], 'size': 6})], [({'slots': [['a', 1]], 'index': 0}, {'slots': [], 'removed': 'a', 'direction': 'none', 'replacement_location': None, 'retained': [], 'size': 0}), ({'slots': [['a', 1], ['b', 5], ['c', 2], ['d', 7], ['e', 8], ['f', 3], ['g', 4]], 'index': 4}, {'slots': [['a', 1], ['b', 5], ['c', 2], ['d', 7], ['g', 4], ['f', 3]], 'removed': 'e', 'direction': 'up', 'replacement_location': ['g', 4], 'retained': ['a', 'b', 'c', 'd', 'f', 'g'], 'size': 6}), ({'slots': [['a', 1], ['b', 2], ['c', 3]], 'index': 0}, {'slots': [['c', 3], ['b', 2]], 'removed': 'a', 'direction': 'down', 'replacement_location': ['c', 0], 'retained': ['b', 'c'], 'size': 2}), ({'slots': [['a', 1], ['b', 2], ['c', 3], ['d', 4]], 'index': 3}, {'slots': [['a', 1], ['b', 2], ['c', 3]], 'removed': 'd', 'direction': 'none', 'replacement_location': None, 'retained': ['a', 'b', 'c'], 'size': 3}), ({'slots': [['a', 1], ['b', 5], ['c', 2], ['d', 7], ['e', 8], ['f', 3], ['g', 4]], 'index': 3}, {'slots': [['a', 1], ['b', 5], ['c', 2], ['g', 4], ['e', 8], ['f', 3]], 'removed': 'd', 'direction': 'up', 'replacement_location': ['g', 3], 'retained': ['a', 'b', 'c', 'e', 'f', 'g'], 'size': 6}), ({'slots': [['a', 1], ['b', 2], ['c', 2], ['d', 4], ['e', 5], ['f', 2], ['g', 3]], 'index': 1}, {'slots': [['a', 1], ['g', 3], ['c', 2], ['d', 4], ['e', 5], ['f', 2]], 'removed': 'b', 'direction': 'down', 'replacement_location': ['g', 1], 'retained': ['a', 'c', 'd', 'e', 'f', 'g'], 'size': 6}), ({'slots': [['a', 1], ['b', 2], ['c', 2], ['d', 4], ['e', 5], ['f', 2], ['g', 3]], 'index': 2}, {'slots': [['a', 1], ['b', 2], ['g', 3], ['d', 4], ['e', 5], ['f', 2]], 'removed': 'c', 'direction': 'down', 'replacement_location': ['g', 2], 'retained': ['a', 'b', 'd', 'e', 'f', 'g'], 'size': 6})], [({'slots': [['a', 1]], 'index': 0}, {'slots': [], 'removed': 'a', 'direction': 'none', 'replacement_location': None, 'retained': [], 'size': 0}), ({'slots': [['a', 1], ['b', 5], ['c', 2], ['d', 7], ['e', 8], ['f', 3], ['g', 4]], 'index': 4}, {'slots': [['a', 1], ['b', 5], ['c', 2], ['d', 7], ['g', 4], ['f', 3]], 'removed': 'e', 'direction': 'up', 'replacement_location': ['g', 4], 'retained': ['a', 'b', 'c', 'd', 'f', 'g'], 'size': 6}), ({'slots': [['a', 1], ['b', 2], ['c', 3]], 'index': 0}, {'slots': [['c', 3], ['b', 2]], 'removed': 'a', 'direction': 'down', 'replacement_location': ['c', 0], 'retained': ['b', 'c'], 'size': 2}), ({'slots': [['a', 1], ['b', 2], ['c', 3], ['d', 4]], 'index': 3}, {'slots': [['a', 1], ['b', 2], ['c', 3]], 'removed': 'd', 'direction': 'none', 'replacement_location': None, 'retained': ['a', 'b', 'c'], 'size': 3}), ({'slots': [['a', 1], ['b', 5], ['c', 2], ['d', 7], ['e', 8], ['f', 3], ['g', 4]], 'index': 3}, {'slots': [['a', 1], ['b', 5], ['c', 2], ['g', 4], ['e', 8], ['f', 3]], 'removed': 'd', 'direction': 'up', 'replacement_location': ['g', 3], 'retained': ['a', 'b', 'c', 'e', 'f', 'g'], 'size': 6}), ({'slots': [['a', 1], ['b', 2], ['c', 2], ['d', 4], ['e', 5], ['f', 2], ['g', 3]], 'index': 1}, {'slots': [['a', 1], ['g', 3], ['c', 2], ['d', 4], ['e', 5], ['f', 2]], 'removed': 'b', 'direction': 'down', 'replacement_location': ['g', 1], 'retained': ['a', 'c', 'd', 'e', 'f', 'g'], 'size': 6}), ({'slots': [['a', 1], ['b', 2], ['c', 2], ['d', 4], ['e', 5], ['f', 2], ['g', 3]], 'index': 3}, {'slots': [['a', 1], ['b', 2], ['c', 2], ['g', 3], ['e', 5], ['f', 2]], 'removed': 'd', 'direction': 'down', 'replacement_location': ['g', 3], 'retained': ['a', 'b', 'c', 'e', 'f', 'g'], 'size': 6})], [({'slots': [['a', 1]], 'index': 0}, {'slots': [], 'removed': 'a', 'direction': 'none', 'replacement_location': None, 'retained': [], 'size': 0}), ({'slots': [['a', 1], ['b', 5], ['c', 2], ['d', 7], ['e', 8], ['f', 3], ['g', 4]], 'index': 4}, {'slots': [['a', 1], ['b', 5], ['c', 2], ['d', 7], ['g', 4], ['f', 3]], 'removed': 'e', 'direction': 'up', 'replacement_location': ['g', 4], 'retained': ['a', 'b', 'c', 'd', 'f', 'g'], 'size': 6}), ({'slots': [['a', 1], ['b', 2], ['c', 3]], 'index': 0}, {'slots': [['c', 3], ['b', 2]], 'removed': 'a', 'direction': 'down', 'replacement_location': ['c', 0], 'retained': ['b', 'c'], 'size': 2}), ({'slots': [['a', 1], ['b', 2], ['c', 3], ['d', 4]], 'index': 3}, {'slots': [['a', 1], ['b', 2], ['c', 3]], 'removed': 'd', 'direction': 'none', 'replacement_location': None, 'retained': ['a', 'b', 'c'], 'size': 3}), ({'slots': [['a', 1], ['b', 5], ['c', 2], ['d', 7], ['e', 8], ['f', 3], ['g', 4]], 'index': 3}, {'slots': [['a', 1], ['b', 5], ['c', 2], ['g', 4], ['e', 8], ['f', 3]], 'removed': 'd', 'direction': 'up', 'replacement_location': ['g', 3], 'retained': ['a', 'b', 'c', 'e', 'f', 'g'], 'size': 6}), ({'slots': [['a', 1], ['b', 2], ['c', 2], ['d', 4], ['e', 5], ['f', 2], ['g', 3]], 'index': 1}, {'slots': [['a', 1], ['g', 3], ['c', 2], ['d', 4], ['e', 5], ['f', 2]], 'removed': 'b', 'direction': 'down', 'replacement_location': ['g', 1], 'retained': ['a', 'c', 'd', 'e', 'f', 'g'], 'size': 6}), ({'slots': [['a', 1], ['b', 2], ['c', 2], ['d', 4], ['e', 5], ['f', 2], ['g', 3]], 'index': 4}, {'slots': [['a', 1], ['b', 2], ['c', 2], ['d', 4], ['g', 3], ['f', 2]], 'removed': 'e', 'direction': 'down', 'replacement_location': ['g', 4], 'retained': ['a', 'b', 'c', 'd', 'f', 'g'], 'size': 6})], [({'slots': [['a', 1]], 'index': 0}, {'slots': [], 'removed': 'a', 'direction': 'none', 'replacement_location': None, 'retained': [], 'size': 0}), ({'slots': [['a', 1], ['b', 5], ['c', 2], ['d', 7], ['e', 8], ['f', 3], ['g', 4]], 'index': 4}, {'slots': [['a', 1], ['b', 5], ['c', 2], ['d', 7], ['g', 4], ['f', 3]], 'removed': 'e', 'direction': 'up', 'replacement_location': ['g', 4], 'retained': ['a', 'b', 'c', 'd', 'f', 'g'], 'size': 6}), ({'slots': [['a', 1], ['b', 2], ['c', 3]], 'index': 0}, {'slots': [['c', 3], ['b', 2]], 'removed': 'a', 'direction': 'down', 'replacement_location': ['c', 0], 'retained': ['b', 'c'], 'size': 2}), ({'slots': [['a', 1], ['b', 2], ['c', 3], ['d', 4]], 'index': 3}, {'slots': [['a', 1], ['b', 2], ['c', 3]], 'removed': 'd', 'direction': 'none', 'replacement_location': None, 'retained': ['a', 'b', 'c'], 'size': 3}), ({'slots': [['a', 1], ['b', 5], ['c', 2], ['d', 7], ['e', 8], ['f', 3], ['g', 4]], 'index': 3}, {'slots': [['a', 1], ['b', 5], ['c', 2], ['g', 4], ['e', 8], ['f', 3]], 'removed': 'd', 'direction': 'up', 'replacement_location': ['g', 3], 'retained': ['a', 'b', 'c', 'e', 'f', 'g'], 'size': 6}), ({'slots': [['a', 1], ['b', 2], ['c', 2], ['d', 4], ['e', 5], ['f', 2], ['g', 3]], 'index': 1}, {'slots': [['a', 1], ['g', 3], ['c', 2], ['d', 4], ['e', 5], ['f', 2]], 'removed': 'b', 'direction': 'down', 'replacement_location': ['g', 1], 'retained': ['a', 'c', 'd', 'e', 'f', 'g'], 'size': 6}), ({'slots': [['a', 1], ['b', 2], ['c', 2], ['d', 4], ['e', 5], ['f', 2], ['g', 3]], 'index': 5}, {'slots': [['a', 1], ['b', 2], ['c', 2], ['d', 4], ['e', 5], ['g', 3]], 'removed': 'f', 'direction': 'down', 'replacement_location': ['g', 5], 'retained': ['a', 'b', 'c', 'd', 'e', 'g'], 'size': 6})]][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":"6b1a6cecfd05fa25ff52a8e10d893a98f661cfec641351dcc27ecf7eff59ad01","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(d):\n    a=d['slots']; i=d['index']; last=len(a)-1; out=[list(x) for x in a[:-1]]\n    if i<last: out[i]=list(a[-1])\n    direction='none' if i==last else ('up' if i>0 and out[i][1]<out[(i-1)//2][1] else 'down')\n    return {'slots': out,\n    'removed': a[i][0],\n    'direction': direction,\n    'replacement_location': None if i==last else [a[-1][0],i],\n    'retained': sorted(x[0] for x in out),\n    'size': len(a)-1}\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncases = [[({'slots': [['a', 1]], 'index': 0}, {'slots': [], 'removed': 'a', 'direction': 'none', 'replacement_location': None, 'retained': [], 'size': 0}), ({'slots': [['a', 1], ['b', 5], ['c', 2], ['d', 7], ['e', 8], ['f', 3], ['g', 4]], 'index': 4}, {'slots': [['a', 1], ['b', 5], ['c', 2], ['d', 7], ['g', 4], ['f', 3]], 'removed': 'e', 'direction': 'up', 'replacement_location': ['g', 4], 'retained': ['a', 'b', 'c', 'd', 'f', 'g'], 'size': 6}), ({'slots': [['a', 1], ['b', 2], ['c', 3]], 'index': 0}, {'slots': [['c', 3], ['b', 2]], 'removed': 'a', 'direction': 'down', 'replacement_location': ['c', 0], 'retained': ['b', 'c'], 'size': 2}), ({'slots': [['a', 1], ['b', 2], ['c', 3], ['d', 4]], 'index': 3}, {'slots': [['a', 1], ['b', 2], ['c', 3]], 'removed': 'd', 'direction': 'none', 'replacement_location': None, 'retained': ['a', 'b', 'c'], 'size': 3}), ({'slots': [['a', 1], ['b', 5], ['c', 2], ['d', 7], ['e', 8], ['f', 3], ['g', 4]], 'index': 3}, {'slots': [['a', 1], ['b', 5], ['c', 2], ['g', 4], ['e', 8], ['f', 3]], 'removed': 'd', 'direction': 'up', 'replacement_location': ['g', 3], 'retained': ['a', 'b', 'c', 'e', 'f', 'g'], 'size': 6}), ({'slots': [['a', 1], ['b', 2], ['c', 2], ['d', 4], ['e', 5], ['f', 2], ['g', 3]], 'index': 1}, {'slots': [['a', 1], ['g', 3], ['c', 2], ['d', 4], ['e', 5], ['f', 2]], 'removed': 'b', 'direction': 'down', 'replacement_location': ['g', 1], 'retained': ['a', 'c', 'd', 'e', 'f', 'g'], 'size': 6}), ({'slots': [['a', 1], ['b', 2], ['c', 2], ['d', 4], ['e', 5], ['f', 2], ['g', 3]], 'index': 1}, {'slots': [['a', 1], ['g', 3], ['c', 2], ['d', 4], ['e', 5], ['f', 2]], 'removed': 'b', 'direction': 'down', 'replacement_location': ['g', 1], 'retained': ['a', 'c', 'd', 'e', 'f', 'g'], 'size': 6})], [({'slots': [['a', 1]], 'index': 0}, {'slots': [], 'removed': 'a', 'direction': 'none', 'replacement_location': None, 'retained': [], 'size': 0}), ({'slots': [['a', 1], ['b', 5], ['c', 2], ['d', 7], ['e', 8], ['f', 3], ['g', 4]], 'index': 4}, {'slots': [['a', 1], ['b', 5], ['c', 2], ['d', 7], ['g', 4], ['f', 3]], 'removed': 'e', 'direction': 'up', 'replacement_location': ['g', 4], 'retained': ['a', 'b', 'c', 'd', 'f', 'g'], 'size': 6}), ({'slots': [['a', 1], ['b', 2], ['c', 3]], 'index': 0}, {'slots': [['c', 3], ['b', 2]], 'removed': 'a', 'direction': 'down', 'replacement_location': ['c', 0], 'retained': ['b', 'c'], 'size': 2}), ({'slots': [['a', 1], ['b', 2], ['c', 3], ['d', 4]], 'index': 3}, {'slots': [['a', 1], ['b', 2], ['c', 3]], 'removed': 'd', 'direction': 'none', 'replacement_location': None, 'retained': ['a', 'b', 'c'], 'size': 3}), ({'slots': [['a', 1], ['b', 5], ['c', 2], ['d', 7], ['e', 8], ['f', 3], ['g', 4]], 'index': 3}, {'slots': [['a', 1], ['b', 5], ['c', 2], ['g', 4], ['e', 8], ['f', 3]], 'removed': 'd', 'direction': 'up', 'replacement_location': ['g', 3], 'retained': ['a', 'b', 'c', 'e', 'f', 'g'], 'size': 6}), ({'slots': [['a', 1], ['b', 2], ['c', 2], ['d', 4], ['e', 5], ['f', 2], ['g', 3]], 'index': 1}, {'slots': [['a', 1], ['g', 3], ['c', 2], ['d', 4], ['e', 5], ['f', 2]], 'removed': 'b', 'direction': 'down', 'replacement_location': ['g', 1], 'retained': ['a', 'c', 'd', 'e', 'f', 'g'], 'size': 6}), ({'slots': [['a', 1], ['b', 2], ['c', 2], ['d', 4], ['e', 5], ['f', 2], ['g', 3]], 'index': 2}, {'slots': [['a', 1], ['b', 2], ['g', 3], ['d', 4], ['e', 5], ['f', 2]], 'removed': 'c', 'direction': 'down', 'replacement_location': ['g', 2], 'retained': ['a', 'b', 'd', 'e', 'f', 'g'], 'size': 6})], [({'slots': [['a', 1]], 'index': 0}, {'slots': [], 'removed': 'a', 'direction': 'none', 'replacement_location': None, 'retained': [], 'size': 0}), ({'slots': [['a', 1], ['b', 5], ['c', 2], ['d', 7], ['e', 8], ['f', 3], ['g', 4]], 'index': 4}, {'slots': [['a', 1], ['b', 5], ['c', 2], ['d', 7], ['g', 4], ['f', 3]], 'removed': 'e', 'direction': 'up', 'replacement_location': ['g', 4], 'retained': ['a', 'b', 'c', 'd', 'f', 'g'], 'size': 6}), ({'slots': [['a', 1], ['b', 2], ['c', 3]], 'index': 0}, {'slots': [['c', 3], ['b', 2]], 'removed': 'a', 'direction': 'down', 'replacement_location': ['c', 0], 'retained': ['b', 'c'], 'size': 2}), ({'slots': [['a', 1], ['b', 2], ['c', 3], ['d', 4]], 'index': 3}, {'slots': [['a', 1], ['b', 2], ['c', 3]], 'removed': 'd', 'direction': 'none', 'replacement_location': None, 'retained': ['a', 'b', 'c'], 'size': 3}), ({'slots': [['a', 1], ['b', 5], ['c', 2], ['d', 7], ['e', 8], ['f', 3], ['g', 4]], 'index': 3}, {'slots': [['a', 1], ['b', 5], ['c', 2], ['g', 4], ['e', 8], ['f', 3]], 'removed': 'd', 'direction': 'up', 'replacement_location': ['g', 3], 'retained': ['a', 'b', 'c', 'e', 'f', 'g'], 'size': 6}), ({'slots': [['a', 1], ['b', 2], ['c', 2], ['d', 4], ['e', 5], ['f', 2], ['g', 3]], 'index': 1}, {'slots': [['a', 1], ['g', 3], ['c', 2], ['d', 4], ['e', 5], ['f', 2]], 'removed': 'b', 'direction': 'down', 'replacement_location': ['g', 1], 'retained': ['a', 'c', 'd', 'e', 'f', 'g'], 'size': 6}), ({'slots': [['a', 1], ['b', 2], ['c', 2], ['d', 4], ['e', 5], ['f', 2], ['g', 3]], 'index': 3}, {'slots': [['a', 1], ['b', 2], ['c', 2], ['g', 3], ['e', 5], ['f', 2]], 'removed': 'd', 'direction': 'down', 'replacement_location': ['g', 3], 'retained': ['a', 'b', 'c', 'e', 'f', 'g'], 'size': 6})], [({'slots': [['a', 1]], 'index': 0}, {'slots': [], 'removed': 'a', 'direction': 'none', 'replacement_location': None, 'retained': [], 'size': 0}), ({'slots': [['a', 1], ['b', 5], ['c', 2], ['d', 7], ['e', 8], ['f', 3], ['g', 4]], 'index': 4}, {'slots': [['a', 1], ['b', 5], ['c', 2], ['d', 7], ['g', 4], ['f', 3]], 'removed': 'e', 'direction': 'up', 'replacement_location': ['g', 4], 'retained': ['a', 'b', 'c', 'd', 'f', 'g'], 'size': 6}), ({'slots': [['a', 1], ['b', 2], ['c', 3]], 'index': 0}, {'slots': [['c', 3], ['b', 2]], 'removed': 'a', 'direction': 'down', 'replacement_location': ['c', 0], 'retained': ['b', 'c'], 'size': 2}), ({'slots': [['a', 1], ['b', 2], ['c', 3], ['d', 4]], 'index': 3}, {'slots': [['a', 1], ['b', 2], ['c', 3]], 'removed': 'd', 'direction': 'none', 'replacement_location': None, 'retained': ['a', 'b', 'c'], 'size': 3}), ({'slots': [['a', 1], ['b', 5], ['c', 2], ['d', 7], ['e', 8], ['f', 3], ['g', 4]], 'index': 3}, {'slots': [['a', 1], ['b', 5], ['c', 2], ['g', 4], ['e', 8], ['f', 3]], 'removed': 'd', 'direction': 'up', 'replacement_location': ['g', 3], 'retained': ['a', 'b', 'c', 'e', 'f', 'g'], 'size': 6}), ({'slots': [['a', 1], ['b', 2], ['c', 2], ['d', 4], ['e', 5], ['f', 2], ['g', 3]], 'index': 1}, {'slots': [['a', 1], ['g', 3], ['c', 2], ['d', 4], ['e', 5], ['f', 2]], 'removed': 'b', 'direction': 'down', 'replacement_location': ['g', 1], 'retained': ['a', 'c', 'd', 'e', 'f', 'g'], 'size': 6}), ({'slots': [['a', 1], ['b', 2], ['c', 2], ['d', 4], ['e', 5], ['f', 2], ['g', 3]], 'index': 4}, {'slots': [['a', 1], ['b', 2], ['c', 2], ['d', 4], ['g', 3], ['f', 2]], 'removed': 'e', 'direction': 'down', 'replacement_location': ['g', 4], 'retained': ['a', 'b', 'c', 'd', 'f', 'g'], 'size': 6})], [({'slots': [['a', 1]], 'index': 0}, {'slots': [], 'removed': 'a', 'direction': 'none', 'replacement_location': None, 'retained': [], 'size': 0}), ({'slots': [['a', 1], ['b', 5], ['c', 2], ['d', 7], ['e', 8], ['f', 3], ['g', 4]], 'index': 4}, {'slots': [['a', 1], ['b', 5], ['c', 2], ['d', 7], ['g', 4], ['f', 3]], 'removed': 'e', 'direction': 'up', 'replacement_location': ['g', 4], 'retained': ['a', 'b', 'c', 'd', 'f', 'g'], 'size': 6}), ({'slots': [['a', 1], ['b', 2], ['c', 3]], 'index': 0}, {'slots': [['c', 3], ['b', 2]], 'removed': 'a', 'direction': 'down', 'replacement_location': ['c', 0], 'retained': ['b', 'c'], 'size': 2}), ({'slots': [['a', 1], ['b', 2], ['c', 3], ['d', 4]], 'index': 3}, {'slots': [['a', 1], ['b', 2], ['c', 3]], 'removed': 'd', 'direction': 'none', 'replacement_location': None, 'retained': ['a', 'b', 'c'], 'size': 3}), ({'slots': [['a', 1], ['b', 5], ['c', 2], ['d', 7], ['e', 8], ['f', 3], ['g', 4]], 'index': 3}, {'slots': [['a', 1], ['b', 5], ['c', 2], ['g', 4], ['e', 8], ['f', 3]], 'removed': 'd', 'direction': 'up', 'replacement_location': ['g', 3], 'retained': ['a', 'b', 'c', 'e', 'f', 'g'], 'size': 6}), ({'slots': [['a', 1], ['b', 2], ['c', 2], ['d', 4], ['e', 5], ['f', 2], ['g', 3]], 'index': 1}, {'slots': [['a', 1], ['g', 3], ['c', 2], ['d', 4], ['e', 5], ['f', 2]], 'removed': 'b', 'direction': 'down', 'replacement_location': ['g', 1], 'retained': ['a', 'c', 'd', 'e', 'f', 'g'], 'size': 6}), ({'slots': [['a', 1], ['b', 2], ['c', 2], ['d', 4], ['e', 5], ['f', 2], ['g', 3]], 'index': 5}, {'slots': [['a', 1], ['b', 2], ['c', 2], ['d', 4], ['e', 5], ['g', 3]], 'removed': 'f', 'direction': 'down', 'replacement_location': ['g', 5], 'retained': ['a', 'b', 'c', 'd', 'e', 'g'], 'size': 6})]][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-indexed-erase-routing-slots","generated_at":"2026-09-29T14:43:34.594490+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 slots using out under the stated bounded certificate contract.","root_cause":"Indexed erase fills the selected hole instead of shifting unrelated heap slots.","sha256":"0086e463187c3a9775d5df891dbbd78f5a68a4bf91352456a54bc66e076fcbcf","title":"Indexed erase fills the selected hole instead of shifting unrelated heap slots · 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":44.036,"exit_code":1,"observations":[{"actual":{"direction":"none","removed":"a","replacement_location":null,"retained":[],"size":0,"slots":[]},"check":"regression certificate 1","expected":{"direction":"none","removed":"a","replacement_location":null,"retained":[],"size":0,"slots":[]},"passed":true},{"actual":{"direction":"up","removed":"e","replacement_location":["g",4],"retained":["a","b","c","d","f","g"],"size":6,"slots":[["a",1],["b",5],["c",2],["d",7],["e",8],["f",3]]},"check":"regression certificate 2","expected":{"direction":"up","removed":"e","replacement_location":["g",4],"retained":["a","b","c","d","f","g"],"size":6,"slots":[["a",1],["b",5],["c",2],["d",7],["g",4],["f",3]]},"passed":false},{"actual":{"direction":"down","removed":"a","replacement_location":["c",0],"retained":["b","c"],"size":2,"slots":[["a",1],["b",2]]},"check":"regression certificate 3","expected":{"direction":"down","removed":"a","replacement_location":["c",0],"retained":["b","c"],"size":2,"slots":[["c",3],["b",2]]},"passed":false},{"actual":{"direction":"none","removed":"d","replacement_location":null,"retained":["a","b","c"],"size":3,"slots":[["a",1],["b",2],["c",3]]},"check":"regression certificate 4","expected":{"direction":"none","removed":"d","replacement_location":null,"retained":["a","b","c"],"size":3,"slots":[["a",1],["b",2],["c",3]]},"passed":true},{"actual":{"direction":"up","removed":"d","replacement_location":["g",3],"retained":["a","b","c","e","f","g"],"size":6,"slots":[["a",1],["b",5],["c",2],["d",7],["e",8],["f",3]]},"check":"regression certificate 5","expected":{"direction":"up","removed":"d","replacement_location":["g",3],"retained":["a","b","c","e","f","g"],"size":6,"slots":[["a",1],["b",5],["c",2],["g",4],["e",8],["f",3]]},"passed":false},{"actual":{"direction":"down","removed":"b","replacement_location":["g",1],"retained":["a","c","d","e","f","g"],"size":6,"slots":[["a",1],["b",2],["c",2],["d",4],["e",5],["f",2]]},"check":"regression certificate 6","expected":{"direction":"down","removed":"b","replacement_location":["g",1],"retained":["a","c","d","e","f","g"],"size":6,"slots":[["a",1],["g",3],["c",2],["d",4],["e",5],["f",2]]},"passed":false},{"actual":{"direction":"down","removed":"b","replacement_location":["g",1],"retained":["a","c","d","e","f","g"],"size":6,"slots":[["a",1],["b",2],["c",2],["d",4],["e",5],["f",2]]},"check":"variant-dependent certificate","expected":{"direction":"down","removed":"b","replacement_location":["g",1],"retained":["a","c","d","e","f","g"],"size":6,"slots":[["a",1],["g",3],["c",2],["d",4],["e",5],["f",2]]},"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression certificate 1\", \"actual\": {\"slots\": [], \"removed\": \"a\", \"direction\": \"none\", \"replacement_location\": null, \"retained\": [], \"size\": 0}, \"expected\": {\"slots\": [], \"removed\": \"a\", \"direction\": \"none\", \"replacement_location\": null, \"retained\": [], \"size\": 0}, 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