The development of modern blockchain technology is at a critical crossroads. We are beginning to realize the limitations of traditional computing models, especially in building distributed systems that can interact with the complex real world and achieve robust consensus. As discussed in the previous article P/NP Paradigm Shift: Designing Adaptive Intelligent Systems and illustrated in the accompanying image, relying solely on a single formal system (such as the Turing machine) is no longer sufficient for constructing the next generation of intelligent systems.

It is worth noting that BEVM (λ) mentioned in this article was the previous name of the GEB Project. The four core principles of BEVM (λ) form the central tenets of the GEB Project’s design. The GEB Project will soon release a new version of its white paper, which, based on inheriting these four design principles from BEVM (λ), will further explore how to implement these advanced ideas in practical applications.

• Formal System A: Blockchain technology. (ETH only contains this single formal blockchain model; BTC’s transaction script verification and block validation belong to this formal model.)
• Formal System B: Human-computer interaction technology. (BTC’s UTXO model falls under this category.)
• Formal System C: Oracle-machine-driven distributed NP consensus sensing technology. (BTC’s miner-based distributed computation model falls under this category.)

The image clearly depicts the architectural differences between Bitcoin and Ethereum and indicates the future direction of the GEB Project. We can connect these visual elements with formal concepts:

• Formal System A (represented by Ethereum): The isolated, stripe-filled circle labeled “Ethereum” in the image symbolizes traditional blockchain technology represented by Ethereum, whose core is to build a consensus ledger system. This corresponds to the (λ calculus + consensus algorithm) module in BEVM (λ) and now in the GEB Project. Ethereum aims to realize decentralized applications through a Turing-complete virtual machine (EVM) in a trusted code environment, focusing mainly on formalized state transitions and transaction verification. However, as the P/NP paradigm discussion points out, this single formal system faces limitations when dealing with the complexity and uncertainty of the real world.
• Formal System B (part of Bitcoin): The Bitcoin circle in the image is divided into several sections, one labeled “B”, representing the Individual model achieved through human-computer interaction technology. In Bitcoin’s context, this is embodied by the distributed UTXO (Unspent Transaction Output) account model. The UTXO model realizes a 1:1 mapping between users and on-chain assets, with each UTXO directly corresponding to individual control, making it a more intuitive and operable interactive approach for users. This Individual model is also one of the core design principles of the GEB Project.
• Formal System C (part of Bitcoin): Another section of the Bitcoin circle labeled “C” symbolizes the consensus sensing algorithms brought by the P/NP computation paradigm, corresponding to the related modules in BEVM (λ) and the GEB Project. Bitcoin’s strong consensus is not only based on its consensus ledger model (Formal System A), but also its unique integration of the Individual model (Formal System B) and consensus sensing technology (Formal System C). The Proof-of-Work (PoW) mechanism is precisely a reflection of the P/NP principle: miners must invest substantial computing resources (an NP problem) to find valid block hashes, while other nodes in the network can efficiently verify these hashes (a P problem). This mechanism enables Bitcoin to convert real-world energy consumption into monetary value, forming a positive feedback loop. Consensus sensing algorithms are also a key focus of the GEB Project.

The Key to Bitcoin’s Success: Going Beyond a Single Formal System, and the Inspiration for GEB

Unlike Ethereum and other blockchain technologies mainly confined to Formal System A, Bitcoin’s strong consensus arises from its integration of the three key elements: Formal Systems A, B, and C. The UTXO model (Formal System B) provides a more direct human-computer interaction, while the PoW mechanism (Formal System C) anchors the system to real-world energy, enhancing the robustness and value foundation of its consensus. The connection between Formal System C (consensus sensing) and Formal System A (consensus ledger) in Bitcoin is implicitly implemented through the “oracle machine” of the longest chain. Miners compete to extend the longest chain, contributing computational power, while the accumulated work of the longest chain becomes the network’s consensus over history. Bitcoin’s successful experience provides critical insight into the GEB Project’s design.

The GEB Project: Inheriting Four Principles, Exploring Implementation Paths

As the successor of the BEVM (λ) philosophy, the GEB Project’s core tenets originate from the four design principles of BEVM (λ). The upcoming white paper will delve deeper into how these advanced ideas can be realized in practical applications. This signifies that the GEB Project will not only focus on building an efficient and secure consensus ledger but will also emphasize designing Individual models more aligned with user intuition and leveraging consensus sensing algorithms to better interact with the real world, constructing more adaptive and practical distributed systems.

As the P/NP paradigm emphasizes, by building an architecture where different types of formal systems interact and by utilizing nonlinear dynamics and reliable oracle mechanisms, we can design systems that can learn, adapt, and exhibit intelligent behavior emerging from their environment. The GEB Project, in this context, is committed to exploring the implementation path of next-generation blockchain technology. Its new white paper will undoubtedly reveal how it plans to realize these visions in practice, while staying true to the core ideas inherited from BEVM (λ).