## 10 Discussion
### Limitations and Future Directions  
While our model significantly advances the understanding of MPT behavior, there are several important limitations that remain to be discussed and suggest some useful directions for future research. First, our analysis assumes that addresses are uniformly at random. The current model's assumption of uniform random address distribution represents a theoretical baseline that warrants further examination in the context of real-world blockchain dynamics. In practice, address distribution patterns in Ethereum emerge from complex interactions between smart contracts, user behaviors, and protocol designs. Smart contract deployments introduce systematic patterns in address generation. Factory contracts, which deploy multiple similar contracts, create sequences of related addresses. Popular DeFi protocols tend to generate clusters of addresses within specific ranges, leading to local concentrations in the address space. These patterns deviate from our uniform distribution assumption and may affect local trie structure. \begin{table}
\begin{tabular}{l l l l l l} \hline \hline
**Study** & **Main Focus** & **Key Contribution** & \begin{tabular}{l} **Optimization** \\ **Approach** \\ \end{tabular} & \begin{tabular}{l} **Performance** \\ **Results** \\ \end{tabular} & **Limitations** \\ \hline \begin{tabular}{l} [PERSON] \\ et al. [14] \\ \end{tabular} & Query processing & Multi-State MPT & \begin{tabular}{l} Node structure \\ modifications \\ \end{tabular} & \begin{tabular}{l} Query processing \\ speedup \\ \end{tabular} & \begin{tabular}{l} Additional storage \\ overhead \\ \end{tabular} \\ Tabatabaei & State management & \begin{tabular}{l} Modified MPT \\ structure \\ \end{tabular} & \begin{tabular}{l} Protocol-level \\ changes \\ \end{tabular} & \
\begin{tabular}{l} Improved state \\ handling \\ \end{tabular} &
\begin{tabular}{l} Scalability \\ trade-offs \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 4: _Cont._User interaction patterns further shape address distribution. Active trading addresses (hot wallets) generate frequent state changes and create high-density regions in the trie. Conversely, long-term storage addresses (cold wallets) contribute to sparse regions. Multi-signature wallet deployments add another layer of complexity by creating correlated address clusters. While these non-uniform patterns affect local trie structure, our preliminary analysis suggests that the global path length distribution maintains its logarithmic character. This robustness stems from the fundamental properties of cryptographic hash functions used in address generation. However, specific distribution patterns can create opportunities for enhanced path compression and may modify balance factors in affected subtries. Future research should extend our model to incorporate these real-world distribution patterns. This requires empirical analysis of Ethereum mainnet address distributions, refinement of probability calculations to account for clustering effects and development of adaptive optimization strategies. Understanding these patterns could lead to more efficient trie structures tailored to actual blockchain usage patterns. Second, our model considers only static tries at certain timestamps. However, Ethereum's state is constantly updated by transactions and smart contract interactions. How path length distributions change dynamically during periods of rapid state change, such as during high-volume trading periods or NFT mints, is not characterized. This is particularly relevant for applications seeking to optimize state updates in real-time. Third, while our theoretical model is hardware-agnostic, practical implementation efficiency heavily relies on specific hardware characteristics. The hierarchy of caches, memory bandwidth, and storage I/O patterns can significantly affect the actual performance of different trie organizations. Such an in-depth analysis of these hardware-specific effects could yield optimization strategies with even more nuance.