## 6 Discussion
Although our findings are significant, there are several limitations that warrant further exploration. Our formal proof is constructed under specific assumptions regarding network synchrony and adversary models. Future work should investigate how these assumptions impact the applicability of the trilemma in asynchronous environments or in networks where nodes have varying computational power and network latency. In asynchronous networks, the primary challenge arises from unpredictable message delays, which introduce additional complexity to the consensus process. This complexity can be further examined by analyzing asynchronous fault-tolerant consensus protocols, focusing on how throughput, latency, and security guarantees evolve in the absence of reliable synchronization. Such analyses would consider factors like timeouts, view changes, and leader rotations. For networks where nodes have varying computational capacities, a useful approach involves weighting nodes by their effective resource contributions, similar to how PoS or PoW protocols allocate influence based on resource metrics. By explicitly modeling computational and bandwidth constraints, it becomes possible to assess how these disparities affect the balance among scalability, security, and decentralization. This may include evaluating how adaptive parameter adjustments (e.g., dynamic block sizes or flexible difficulty targets) influence the attainable equilibrium among the three dimensions of the trilemma. Furthermore, there is an opportunity to explore alternative blockchain architectures, such as Layer-2 solutions [35], that could potentially bypass some aspects of the trilemma by offloading certain operations from the main blockchain. Specifically, exploring the interplay between on-chain and off-chain scaling solutions may provide new insights into whether and how parts of the trilemma can be \"outsourced\" while maintaining desirable properties on the base layer. That said, our framework can also be employed to analyze L2 layers, helping determine how best to migrate high-throughput activities off-chain without overextending the L1 network's capacity or undermining its security properties. Since L2 solutions periodically anchor their state to the L1 chain, understanding the L1 security model is critical. Our framework clarifies how L1 parameters--such as participation distribution and consensus resilience--interact with the assumptions underlying L2 solutions. This alignment enables L2 protocols to maintain robust security guarantees that remain consistent with the decentralization principles upheld by the L1. Another promising direction lies in the potential of hybrid consensus mechanisms. Studies suggest that combining aspects of different consensus protocols might offer a better compromise between scalability and security. For instance, integrating PoW's robust security guarantees with PoS's resource efficiency and BFT's rapid finality could yield consensus models that better balance throughput, latency, and decentralization. An in-depth investigation into the design and implementation of these hybrid approaches could reveal whether they effectively mitigate the trade-offs highlighted by our formal proof. Finally, future research could benefit from empirical studies that validate our theoretical findings through real-world deployments. By analyzing the evolution of networks like Ethereum 2.0 and its subsequent sharding phases, researchers can gain a better understand ing of how scalability techniques impact network security and decentralization under real network conditions and user behaviors.