It was clarified that any tree structure accommodating N leaves actually encompasses a total data size of O(N), not O(N log N) as previously thought. This adjustment highlights a fundamental aspect of data structuring in computational systems, where the representation of data significantly impacts storage and retrieval efficiency.

The discussion further delves into the specifics of how different tree structures affect the total data size through constant multipliers. For instance, a binary tree, which bifurcates at each node, has a constant multiplier of 2.0 on the data size relative to an array with N entries. This means that for every entry, the storage requirement doubles, embodying a straightforward increase in data volume. In contrast, a tree where nodes branch into four children exhibits a more efficient use of space. The multiplier in this scenario is reduced to 4/3, closely mimicking the efficiency of an array. This comparison draws a parallel with mipmaps in 2D textures, where each successive mipmap level only adds 33.33% more VRAM usage. This analogy effectively illustrates how increasing the fanout of a tree—akin to reducing the resolution of a texture—can optimize the storage requirement.

Furthermore, the discussion shifts to a specific type of tree structure, the CTV tree, which is acknowledged for its higher data size due to the inherent constant multipliers and the additional overhead introduced by using P2SH/P2WSH/P2TR. Despite these added complexities, it is emphasized that the CTV tree still operates within the O(N) complexity concerning the number of leaves. By increasing the fanout, the CTV tree approaches an optimal case akin to directly publishing all outputs, suggesting a strategic approach to managing data size and efficiency in blockchain-related applications.