Embracing the P/NP paradigm: from the success of Bitcoin to the implementation of GEB projects The development of modern blockchain technology is at a critical crossroads, and we are beginning to recognize the limitations of traditional computing models, especially in building distributed systems that can interact with the complex real world and achieve strong consensus. As discussed in the previous section on the P/NP paradigm shift and illustrated in the image, relying solely on a single formal system (such as Turing machines) is no longer sufficient to meet the needs of building the next generation of intelligent systems. It is worth noting that the BEVM (λ) mentioned in this article is exactly the name before the GEB project. The four core principles of BEVM (λ) are the core guidelines for GEB project design. The GEB project will soon release a new version of its white paper, which will delve into how to implement these advanced concepts in practical applications while inheriting the four design principles of BEVM (λ). The image clearly depicts the differences in system architecture between Bitcoin and Ethereum, and indicates the future direction of the GEB project. We can connect these visual elements with formal concepts: Formal A (representative of Ethereum): The circle in the image, individually and filled with stripes, labeled as "Ethereum", symbolizes the traditional blockchain technology represented by Ethereum, whose core is to build a consensus ledger system. This corresponds to the (lambda calculus+consensus algorithm) module in BEVM (lambda) (as well as the current GEB project). Ethereum is committed to implementing decentralized applications in a trusted code environment through Turing complete virtual machines (EVMs), with a primary focus on formal state transitions and transaction verification. However, as discussed in the P/NP paradigm, this single formalized system may have limitations when facing the complexity and uncertainty of the real world. Formal B (Partial Composition of Bitcoin): The circle of Bitcoin in the image is divided into multiple parts, with one part labeled as "B", representing the Individual model implemented by human-computer interaction technology. In the context of Bitcoin, this is specifically reflected in the distributed UTXO (Unspoken Transaction Output) account technology. The UTXO model achieves a 1:1 mapping between users and on chain assets, with each UTXO directly corresponding to individual control rights. This is a more intuitive and operational way of interaction for users. This individual model is also one of the core design principles of the GEB project. Formal C (Partial Composition of Bitcoin): The other part marked as "C" in the Bitcoin circle symbolizes the consensus aware algorithm brought by the P/NP computing paradigm, corresponding to the corresponding module in BEVM (λ) (and GEB project). The reason why Bitcoin can demonstrate strong consensus is not only due to its consensus ledger model (formal A), but also because it uniquely integrates the Individual model represented by formal B and the consensus perception technology represented by formal C. The Proof of Work (PoW) mechanism is a manifestation of the P/NP principle: miners need to invest a large amount of computing resources (NP problem) to find effective block hashes, while other nodes in the network can efficiently verify the validity of these hashes (P problem). This mechanism enables Bitcoin to convert real-world energy consumption into monetary value, forming a positive feedback loop. Consensus aware algorithms are also an important focus of the GEB project. The Path to Bitcoin's Success: Beyond a Single Formalization, Inspiring GEB Unlike blockchain technologies such as Ethereum that are primarily limited to formal A, Bitcoin's strong consensus stems from its integration of three key elements: formal A, B, and C. The UTXO model (formal B) achieves more direct human-computer interaction, while the proof of work mechanism (formal C) enhances its consensus stability and value foundation by anchoring to real-world energy. The connection between formal system C (consensus awareness) and formal system A (consensus ledger) in Bitcoin is achieved through the implicit "oracle" of the longest chain. Miners contribute computing power by competing to extend the longest chain, and the accumulated workload of the longest chain becomes the consensus of the network on history. The successful experience of Bitcoin provides important insights for the design of GEB projects. GEB Project: Inheriting the Four Principles and Exploring the Path to Implementation As the successor of the BEVM (λ) concept, the core program of the GEB project is derived from the four design principles of BEVM (λ). The upcoming new white paper will delve deeper into how to implement these advanced concepts in practical applications based on these principles. This indicates that the GEB project will not only focus on building an efficient and secure consensus ledger, but also on how to design individual models that are more in line with user intuition, and how to use consensus aware algorithms to better interact with the real world and build more adaptive and practical distributed systems. As emphasized by the P/NP paradigm, by constructing architectures that interact with different types of formal systems and utilizing nonlinear dynamics and reliable oracle mechanisms, we can design systems that can learn, adapt, and emerge intelligent behaviors from the environment. The GEB project is committed to exploring the implementation path of next-generation blockchain technology in this context. Its new white paper will undoubtedly reveal how it can achieve these visions in practical applications based on inheriting the core ideas of BEVM (λ).