Ordinal numbers, oracle Turing machines, and decentralized consensus: a new path to computational completeness In the depths of 20th century mathematics and logic, G ö del's incompleteness theorem revealed that any sufficiently powerful and consistent formal arithmetic system is inevitably incomplete, meaning that we cannot capture all mathematical truths within a single, finite axiomatic system. This discovery challenged Hilbert's grand vision of establishing an absolutely complete foundation for mathematics. However, if we expand our perspective from the closed nature of a single system to the open dynamic structure constructed by ordinal based super poor induction techniques and relatively computable oracle Turing machines, we may be able to find a path that allows partially incomplete systems to approach global completeness through continuous, super limited iterations and interactions. The theoretical intersection of ultra poor induction and oracle Turing machines Ordinal numbers, as a tool for measuring the "length" of well ordered sets in mathematics, provide us with powerful means beyond finite hyperfine induction and hyperfine recursion. This technique of 'pushing the infinite from the finite' allows for the definition and exploration of larger mathematical structures through a progressive and infinitely extended construction process when dealing with infinity. When G ö del proved the consistency of the continuum hypothesis, he cleverly utilized the superpoor construction based on ordinal numbers to construct a constructible set (L), demonstrating the extraordinary ability of this technique. Meanwhile, Turing's exploration of Oracle Turing Machine (OTM) and Relative Computability in his doctoral thesis "Ordinal Logic Systems" provides another key dimension for our understanding of this "near completeness" mechanism. The oracle Turing machine extends its computing power by accessing an "oracle" that can answer specific complex questions (even if these questions themselves are not computable for a standard Turing machine). In this framework, a problem can be seen as "relatively computable" to a certain oracle. By combining these two, we can conceive a theoretical framework: when a single formal system cannot be complete on its own due to G ö del's incompleteness theorem, if a series of relatively computable oracle Turing machines can be introduced - these "oracles" can be external, independently existing information sources or computational results - and these oracles can be mutually judged and verified, then through ordinal based super poor iteration, the system can continuously and cumulatively increase its knowledge and certainty, thereby infinitely approaching the completeness of the whole. The term 'super poor iteration' here is no longer just a mathematical abstraction, but refers to a system that, with infinite time and computing resources, continuously integrates information provided by the 'oracle' and tends towards an irreversible and stable state. Bitcoin: Early Application of the Theory Bitcoin, a complex adaptive system that implements fully decentralized dual flower arbitration under the UTXO structure, can be seen as an early and successful practical implementation of the aforementioned theoretical framework. In the Bitcoin network: The UTXO structure represents its basic formal rules and local states. The miners in the Proof of Work (PoW) mechanism can be cleverly likened to the "Oracle Turing Machine" that provides * * "relative computability". Every time a miner finds a block that meets the difficulty level, it is an "oracle" that provides an unforgeable "answer" or "proof" to the current global state. The principle of longest chain is the core technique of "mutual judgment" and super poor induction between these "oracles". All nodes in the network follow the longest chain relatively computably, constantly stacking new, PoW validated blocks on top of it. The continuous growth of this chain is an approximate process of super poor iteration * * - although not mathematically infinite, its accumulated workload and computational input make the irreversibility of historical transactions exponentially increase, infinitely approaching the completeness in practical sense. In this decentralized environment, no central authority can provide absolute "arbitration" and "completeness" guarantees. However, through the input of miners' "oracles" and the super poor iterative growth of the longest chain, the Bitcoin network has successfully achieved a trustless consensus under the condition of absolute individual sovereignty, making the double spending problem economically unfeasible and achieving extremely high security and transaction finality. This is precisely an example of how an incomplete tool for local approximation can enter a "approaching complete global system" through dynamic and cumulative interactions. Outlook: The Implementation of Precision Theoretical Philosophy The success of Bitcoin may also confirm the implementation of G ö del's predicted "exact theoretical philosophy". This philosophy does not pursue a centralized and absolutely complete axiomatic system in the traditional sense, but rather constructs a system that can operate efficiently and reach consensus in a decentralized and complex adaptive environment through precise calculations, probability, and game theory design, while acknowledging the inherent limitations of the system. Through finite steps (block generation) and ordinal super poor induction (the continuous growth of blockchain and the determinacy revealed from it), we are able to construct a whole (longest chain) containing infinite potential history from locally approximate incomplete tools (individual blocks or short chains), thus achieving reliable and nearly complete systems in practice. This theory not only explains the success of Bitcoin, but also provides a new theoretical foundation for us to expand various complex adaptive systems similar to Bitcoin that operate in decentralized environments based on it. Future decentralized technologies may draw on the essence of mathematics and logical philosophy at a deeper level, constructing a more robust, consistent, and nearly 'complete' digital ecosystem.