Recent advances in blockchain research have been made in two important directions. One is refined resilience analysis utilizing game theory to study the consequences of selfish behavior of users (miners), and the other is the extension from a linear (chain) structure to a non-linear (graphical) structure for performance improvements, such as IOTA and Graphcoin. The first question that comes to mind is what improvements a blockchain system would see by leveraging these new advances. In this article, we consider three major properties for a blockchain system: α-partial verification, scalability, and finality-duration. We establish a formal framework and prove that no blockchain system can achieve α-partial verification for any fixed constant α, high scalability, and low finality-duration simultaneously. We observe that classical blockchain systems like Bitcoin achieve full verification (α =1) and low finality-duration, Ethereum 2.0 Sharding achieves low finality-duration and high scalability. We are interested in whether it is possible to partially satisfy the three properties.