The paper doesn't say so I am making some assumptions here but if you had a bloom filter per array then as these doubling arrays get really big all the bloom fi

The paper doesn't say so I am making some assumptions here but if you had a bloom filter per array then as these doubling arrays get really big all the bloom filter would tell you is that the target entry is probably contained in this giant array. A false positive in the bloom filter would cause a pretty significant amount of work. The stratified b-trees use forward pointers to help target the search in the next array down the tree. Like regular b-trees the smaller root arrays will likely be cached in memory so the the number of random I/O's will be small.