1. A system, comprising: at least one computing device configured to implement one or more services, wherein the one or more services are configured to: access a data structure comprising a plurality of nodes that are hierarchically related, the data structure being an append tree data structure that includes: a plurality of leaf nodes at a first hierarchical level of the data structure, the plurality of leaf nodes being unrelated as a parent of other nodes; and one or more parent nodes at one or more second hierarchical levels of the data structure, at least one of the one or more parent nodes being related as a parent of at least two of the plurality of leaf nodes; examine a binary counter incremented for each leaf node added to the plurality of leaf nodes of the data structure, the binary counter indicating a value associated with an order in which the plurality of leaf nodes were added to the data structure; and determine a value of a binary count of 1-valued bits in a portion of the binary counter inclusively ranging from a least significant bit of the binary counter to a least significant 0-valued bit of the binary counter, the value of the binary count indicating a number of additional parent nodes to be added to the data structure prior to adding an additional leaf node to the data structure.