The ultimate practice of Bitcoin's Transfinite technology and CAP principle In the world of digital currencies, Bitcoin's UTXO (Unspoken Transaction Output) model and its underlying mechanisms embody a profound understanding and ultimate practice of the "impossible triangle" principle of distributed systems - CAP. The CAP principle states that a distributed system cannot simultaneously satisfy Consistency, Availability, and Partition Tolerance. The design of Bitcoin clearly focuses on availability and partition fault tolerance (AP), and approaches consistency (C) with innovative "Transfinite craftsmanship" while meeting these two criteria. The UTXO model of Bitcoin inherently has complete decentralized fault tolerance, meaning that any single node failure will not affect the operation of the entire network, and each UTXO is 100% privately owned by the user, achieving the ultimate decentralization. This fully satisfies the principles of A (availability) and P (partition fault tolerance) in CAP. However, achieving consistency under such decentralized fault-tolerant conditions is a huge challenge. Bitcoin solves the double spending problem through its "longest chain" principle, but this is not the traditional sense of instantaneous perfect consistency. It adopts a technique called "Transfinite iteration" to infinitely approach complete consistency by continuously extending the chain and reaching majority consensus. This design concept is described as "exchanging 99% of energy for 1% of problem-solving", which means that in order to solve the double spending problem in a highly decentralized and fault-tolerant environment, huge computing resources and time need to be invested to ensure the final consensus. However, this is already the optimal solution for Bitcoin to achieve C under the premise of fully satisfying AP. This design philosophy has also sparked contemplation on other blockchain projects. For example, projects such as Sui and Ada are also trying to solve the extension problem of UTXO, but they may still fall short in achieving the approximate consistency brought by the "longest chain" and the craftsmanship of the "last 1% longest chain". It can be said that it is precisely this "Transfinite craftsmanship" like the finishing touch, that is, the over limit iteration mechanism of the longest chain, that enables Bitcoin to truly achieve its breakthrough and innovation in distributed consensus. On a deeper level, Bitcoin's "Transfinite Craftsmanship" can even echo the cognitive pathways of great thinkers of the 20th century, such as Wittgenstein, Turing, and G ö del. From the perspective of "explaining the problem from the end point of cognition": Wittgenstein's theory, as if it had reached the end point of the "indescribable theory of cognition", traces and explains the essence of cognition from this height. Turing and G ö del explored the boundaries of mathematical logic, using rigorous logical deduction and construction to ultimately prove or reach certain theoretical limits. Turing's "Transfinite" method can be understood in a sense as providing specific tools and paths for Wittgenstein's insight into the "endpoint" at the abstract level. Wittgenstein may have already grasped the ultimate answer, but he did not have a direct implementation method, so his ideas seemed to foresee and anticipate the emergence of concrete works like Turing's. This implies that Bitcoin has reached some theoretical limits in practice through its unique technological path, just as Turing's work provided concrete solutions for Wittgenstein's abstract thinking. In summary, Bitcoin is not only a technological innovation, but also a philosophical practice. It has achieved the ultimate satisfaction of AP in the CAP principle through its unique "longest chain" and "Transfinite craftsmanship" in the complex challenges of distributed systems, and on this basis, it has approached C as closely as possible. The profound insights behind it are worth our continuous thinking.