# The New CAP Theorem on Blockchain Consensus Systems
## 5 Discussion
### Large-Scale Heterogenous Blockchain Systems Implications  
The findings of this work do not depend on the actual scale or the absolute energy consumption of the systems. This work focuses on revealing the intrinsic constraints between Autonomy (A), Consensus achievement (C), and entropic Performance (P). The constraints among the three properties hold strong while considering large-scale heterogenous systems as well. To highlight their implications to the non-uniform, large-scale Blockchain systems, in Sections 5.2 and 5.4 we present benchmarks and real-world empirical validation data using Ethereum, Bitcoin, and Hyperledger datasets. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Blockchain System**} & **Consensus Mechanism** & **Main Vulnerability (Attad)** & **Autonomy (A)** & **Consensus Achievement (C)** & **Entropic Performance (P)** \\ \hline \multirow{4}{*}{Bitcoin} & **Proof-of-Work** & **Low** & **High** & **Low** \\  & Fully open & **Low** & Miners & Global & Energy efficiency due to \\  & Competitive & (51\%, 5 ybil) & depend on entire & Consensus & maximum W and \\  & Mining & & network & W \(\rightarrow\) N & competitive hash mining \\ \hline \multirow{4}{*}{**Ethereum 2.0**} & **Proof-of-Stake** & **Medium** & **Medium** & **High** \\  & Open & **Medium** & Validators rely on & non-competing verifiers, & Energy efficiency due to \\  & Staking-based & (Sybil, Long Range) & stalking, not on & to & lower W, allowing \\  & & competitive mining & & \(\text{W}=\frac{2\text{W}}{2\text{W}}\) & non-competitive hashing \\  & & & validators & and trusted nodes \\ \hline \multirow{4}{*}{**Hyperledger Fabric 3.0**} & **Raft, PBFT** & **Low** & **High** & **Low** & **High** \\  & **Raft, PBFT** & (PBFT:Sybil) & Preselected validators & Only selected trusted & Energy efficiency due to \\  & Ad-hoc private & **Low** & reduce & nodes reach & lower W, allowing \\  & & (Raft: DoS) & reliance on the other & Consensus & non-competitive hashing \\  & & nodes & \(\text{W}\leq\frac{2\text{W}}{2\text{W}}\) & and trusted nodes \\ \hline \multirow{2}{*}{**IoT micro-Blockchain**} & **Event witnessing DAG** & **High** & **Variable** & **Variable** & **Variable** \\  & & (Sybil) & & & \\ \hline \hline \end{tabular}  
* The data summarized in Table 2 fall beyond the core scope of this work and are given as a reference to the reader.
* Discussed in Section 5.4.  
\end{table} 
Table 2: (A), (C), and (P) implications as observed on heterogenous real-world Blockchain systems *. The intrinsic constraints among Autonomy (A), Consensus achievement (C), and entropic Performance (P) in the practical performance of the Blockchain systems in terms of latency, throughput, and energy consumption, have been shaping the architectures of the Blockchain systems since their very beginning. They affect every aspect of the consensus mechanisms' performance, including the transaction finality time, and the scalability capability of the systems. The implications of the _new CAP theorem_ are immense. They drive fundamental design decisions of the Blockchain consensus architectures, like, for example, the heterogeneity of the nodes and the adoption of node hierarchies:  
* Light nodes and digital wallets are introduced to deliver increased autonomy and energy efficiency. * Larger capacity full nodes usually undertake the heavier duties of running the more demanding core of the consensus process. This understanding constitutes an additional practical demonstration of the intrinsic constraints existing among (A), (C), and (P) and further fortifies the validity of the theorem. The _new CAP theorem_ constrains the'somehow illusionary' vision of the early Blockchain technologists for absolute peerness, autonomy, and infinite decentralization for zero cost. Acknowledging the adverse impact of high values of \(W\) to the efficiency of the system, many contemporary large-scale Blockchain architectures intentionally limit the number of required per-event witnesses.