Beyond the limitations of Turing machines: Design of adaptive intelligent systems based on P/NP paradigm for GEB project The cornerstone of modern computing, the Turing machine, has played an indispensable role in defining the boundaries of algorithmic computability. However, its inherent linear and deterministic characteristics show significant limitations in dealing with complex and nonlinear real-world situations, as well as in building intelligent systems with emergent behavior. As revealed by G ö del's incompleteness theorem, any sufficiently complex single formal system has inherent incompleteness. Therefore, building systems that can effectively interact with the unpredictable real world and achieve powerful distributed consensus requires us to go beyond the constraints of a single formality and embrace new computing paradigms. Inspiration from the P/NP paradigm: Multi system interaction and emergent intelligence The P/NP problem framework provides us with a potential breakthrough. The core idea is to design computing systems as interactive collections of different types of distributed formal systems: NP class "solvers" that handle complex searches and P-type "validators" that efficiently validate schemes. This non-linear computational difference provides the foundation for the emergence of emergent behavior, and the overall capability of the system surpasses the simple superposition of individual components. GEB project: Integrating three major formal submodules In this context, we focus on the GEB project, which aims to build an adaptive intelligent system with a core architecture consisting of three key formal submodules: Formal blockchain technology: As the cornerstone of the system, it is responsible for building and maintaining a decentralized consensus ledger, ensuring consistency and immutability of transactions and states. This corresponds to the (lambda calculus+consensus algorithm) module in the BEVM (lambda) concept, which aims to provide a trusted execution environment. Formal System of Human Computer Interaction Theory: GEB emphasizes user centered design and formalizes human-computer interaction theory to build an "individual" self mapping account system. The term 'Individual' here represents an account model that is directly associated with users or entities, reflecting their autonomy and interactive behavior. This corresponds to the Individual model in BEVM (λ), aiming to achieve a more intuitive and user friendly interactive experience. The UTXO model of Bitcoin is an early manifestation of this idea, achieving a 1:1 mapping between users and on chain assets. The formal system of nonlinear computational models emerging from P/NP self referential: This is a key innovation in GEB design. This module aims to construct mechanisms that can perceive and respond to real-world information by utilizing the computational complexity of P/NP problems. The core idea is to simulate complex systems in nature through self pointing and emergence, ultimately achieving symbiosis between humans and machines, and possessing the ability for adaptive and self-organizing evolution. This corresponds to the consensus aware algorithm in BEVM (λ). Bitcoin's Proof of Work (PoW) mechanism can be seen as an early practice of this idea, which ensures network security and value by consuming real-world energy, while longest chain consensus acts as a distributed, implicit "oracle" connecting computing systems with some form of "reality". Overcoming the limitations of traditional blockchain: using Bitcoin as a benchmark Traditional blockchain technologies, such as Ethereum, mainly focus on formalized consensus ledgers (corresponding to the first submodule of GEB). However, as the analysis points out, relying solely on this single formalized system may lead to its disconnection from the real world and neglect the needs of individual users, ultimately leading to centralization and closure. The success of Bitcoin lies in its integration of the "Individual" model (UTXO) and consensus aware mechanisms based on P/NP principles (PoW and longest chain) on top of the consensus ledger. The UTXO model achieves more direct human-computer interaction, while PoW enhances the stability and value foundation of consensus by anchoring to real-world energy. The longest chain consensus, as an implicit oracle, connects the computing system with the "reality" of computing power investment. GEB's Vision: Building an Adaptive Future The GEB project has drawn on the successful experience of Bitcoin and elevated it to a new theoretical level. GEB aims to build the next generation of distributed systems that can overcome the limitations of traditional blockchain by explicitly integrating formal blockchain technology, human-computer interaction theory, and P/NP self referential nonlinear computing models into three key sub modules. Its goal is to create an intelligent ecosystem that is closer to users, more able to perceive the real world, and has adaptive and self-organizing capabilities. The upcoming new version of the white paper will further elaborate on how the GEB project inherits the core principles of BEVM (λ) and delves into the practical implementation strategies of these concepts, heralding a future that goes beyond the traditional blockchain paradigm.