Ultra poor iteration: the eternal cornerstone of decentralized trust in Bitcoin In the profound discussion of digital currency and Bitcoin technology, a thought-provoking concept - "Superfinite Iteration" - has emerged. Although this is not an official term in the Satoshi Nakamoto whitepaper, it profoundly summarizes how Bitcoin, this decentralized and trusted complex adaptive system, achieves its incredible security and transaction finality through a continuous, infinitely approaching iterative process. The 'super poor iteration' is the cornerstone of Bitcoin's infinite convergence towards usability without centralization. 'Ultra poor iteration' is one of the key mechanisms to address the core challenges of Bitcoin: Firstly, it solves the problem of the longest chain not collapsing. In decentralized networks, the longest chain principle is the cornerstone for identifying unique and legitimate chains. When facing potential forks or attacks, without sufficient confirmation to secure the longest chain, it may lead to system uncertainty. The 'super poor iteration' describes a process where the advantage and robustness of the longest chain exponentially increase by continuously adding new blocks, causing the cost of malicious attackers tampering with history to rise exponentially until it becomes computationally impractical, effectively preventing the chain from collapsing. Secondly, the "super poor iteration" significantly enhances the "certainty" and "existence" of Bitcoin transactions. For any transaction on the Bitcoin chain, its ultimate certainty depends on the depth at which it is included in the longest chain. With the "super poor iteration" - where more blocks are continuously mined and stacked onto the chain - the "certainty" of transactions increases, and their "existence" becomes indisputable. This mechanism is the fundamental solution to the 'double flower problem'. Through the passage of time and accumulated computational work, the economic cost of double spending attacks has become prohibitively high, making every expense of digital currency highly irreversible. This concept of "super poor iteration" coincides with Satoshi Nakamoto's white paper on proof of work and the longest chain principle. The summary of the white paper clearly states that solving the dual flower problem based on decentralization is incomplete, but we can approach it infinitely through "super poor iteration". Although the white paper does not directly mention the term 'super poor iteration', its essence lies in creating blocks by consuming computing resources and stipulating that honest nodes always extend the longest chain. This process itself is a continuous and cumulative iteration. Every new block generation adds additional confirmations to previous transactions, enhancing the security of the chain like a snowball, infinitely approaching a "complete" and almost irreversible state. This is precisely the core of the Bitcoin network's trustless feature. In the exploration of the concept of hierarchical structure, the importance of "super poor iteration" is further highlighted. The security of Bitcoin is based on the PH three-layer structure of the P/NP protocol, which progresses layer by layer The first layer (UTXO) mainly focuses on the legitimacy proof of UTXO (unused transaction output) or the transaction itself, which is described as a kind of "NP/NP asymmetry". However, the cost of 'proof of existence' will ultimately be pushed to the second level of resolution. The second layer (block): This layer is responsible for the legitimacy proof of the block, which is implemented through Proof of Work (PoW) verification, also known as a form of "P/NP asymmetry". The "proof of existence" of the block is further pushed to the third layer for resolution. The third layer (longest chain): This is the final settlement layer. The 'super poor iteration' plays a decisive role here, providing the ultimate 'proof of existence' for the block and all transactions within it through continuous block extension and consensus consolidation. Once formed, the 'best chain' cannot be further broken down, representing the immutable ultimate truth. Therefore, it can be summarized that "super poor iteration" is the cornerstone on which Bitcoin, a decentralized and trustworthy complex adaptive system, is built. It describes how Bitcoin accumulates through "iterative accumulation step by step" and presents a tight logic of "loop by loop", jointly building a powerful, decentralized, and highly secure digital ledger. This concept not only reveals the deep mathematical and computational principles of Bitcoin technology, but also provides us with a new perspective on why it can provide unprecedented trust and transparency.