The completeness of Bitcoin vs. the incompleteness of BFT 1/G ö del said: Any consistent formal system is inevitably incomplete. In blockchain, this corresponds to: How does the system choose when multiple legitimate blocks appear at a certain height at the same time? This is the completeness issue of blockchain. 2/In BFT system (including ETH PoS): When multiple valid blocks appear at height n, the system cannot automatically select them in the endogenous logic. In the end, we can only: Towards consensus through voting/message games; Or shut down and leave it to human intuition/foundation judgment. BFT is incomplete. 3/Differences of Bitcoin: It internalizes' fork selection 'as part of the protocol. PoW nonce resonance=free particle resonance driven by miner energy The longest chain rule=the network automatically selects the highest weight chain This is the oracle of Bitcoin. Here, 'dissipative structure' is key: Physics: Non equilibrium systems generate order through energy consumption Bitcoin: PoW's dissipative process replaces human neuron's' intuition ' Contradictions (forks) no longer rely on human judgment, but are automatically resolved by the system. 5/ But solving only one fork is not enough. The blockchain must be able to continuously evolve through an infinite number of forks. This requires an ordinal logic system: Turing machine: Generate candidate blocks Oracle Machine: The Only Solution for Judgment Ordinal logic: ensuring continuity of super poor iterations 6/So: BFT=Non deterministic Turing Machine+External Oracle+External Guaranteed Continuity → ❌ incomplete Bitcoin=Non deterministic Turing machine+dissipative structure oracle machine+ordinal logic iteration → ✅ complete 7/Conclusion: Bitcoin is not just a computing system, It is a completeness system composed of Turing machines, oracle machines, and ordinal logic. When encountering a fork, the BFT system can only shut down or rely on human intuition to become incomplete.