I. From Formal Systems to the Problem of Trust

The decidability problems in traditional formal systems have inherent boundaries. Turing, in his dissertation “Systems of Logic Based on Ordinals,” proposed the concepts of transfinite iterative logic and the oracle Turing machine, offering a theoretical framework to overcome the internal incompleteness of formal systems.

The core ideas of this theory include:

• Using transfinite ordinal iterations to construct external extensions of formal systems;
• Employing oracle machines to handle problems undecidable within the system;
• Introducing an irreversible structural process through continuous “upward evolution” of the system—this structure exhibits time-like characteristics: irreversible, non-cyclic, and verifiable.
  

This provides the theoretical foundation for constructing “trust in time” within computational systems.

II. Bitcoin: Physicalizing the Structure of “Irreversible Time”

Bitcoin is an example of turning the logical structure of “trust in time” into a physical process. Its core mechanisms are:

• Double Hashing + Proof-of-Work (PoW): Together form a resource competition system, where miners search for valid blocks through hash computation in a highly unpredictable search space;
• This process simulates the “entropy increase” described in the second law of thermodynamics: computational resources are continuously consumed, and the process is irreversible;
• Anyone, at any time, can participate by contributing computing power. The system has no centralized entry point or permissions, reflecting an infinitely open evolutionary structure;
• The “block time” generated by PoW is not physical clock time, but system time defined by real-world resource expenditure and physical cost.
  

Thus, Bitcoin’s consensus mechanism is fundamentally built on an irreversible structure generated by the maximum hash power humans can invest at any given moment. This structure is not only difficult to forge but also irreversible—serving as the foundation of trust in the network.

III. Consensus Mechanisms That Construct “Trust in Time” Are Not Limited to Bitcoin‍

Bitcoin is not the only system capable of constructing “trust in time.” More generally, any resource system that approximates a thermodynamically irreversible process, is verifiable, and is competitive, can build a similar “time-evolution structure.” This paradigm can be termed:Time-Trust Consensus Paradigm. Its essential characteristics are:

• Utilizing real-world resources (computation, storage, energy, sensing, etc.) to participate in irreversible processes;
• Constructing a one-way time structure driven by resource competition;
• Using this structure as the foundation for all internal judgments, confirmations, and consensus in the system.
  

This structure generally takes the following form:

IV. Generalizing Decentralized Trust Structures: From Currency to Autonomous Driving

If Bitcoin represents a decentralized currency system entirely based on “trust in time,” then similar trust structures can be applied to broader domains.

For example, in autonomous driving scenarios:

• Each car acts as a “self-sufficient node,” participating in irreversible processes through computation, sensing, route planning, and other resources;
• Every decision is based on its own “time trajectory” of perception and resource processing;
• No reliance on central servers; decisions are unforgeable and irreversible.
  

This forms an “autonomous time-based judgment structure” that can build a trustless safety system for autonomous driving. System safety doesn’t come from centralized control, but from each node’s own mastery of irreversible time.

This is precisely the extension path of the core idea of “building trust through time” in non-financial domains.

V. Conclusion: From Turing’s Time Evolution Logic to Real-World Decentralized Trust Structures

By mapping Turing’s “transfinite evolution” in ordinal logic to physical-world resource consumption, Bitcoin has pioneered a time-trust structure driven by real thermodynamics. This structure can be generalized into a universal paradigm:

Any irreversible, competition-driven, and globally verifiable time-evolution mechanism can serve as the foundation for building trust systems.

In the future, every system that requires “trustlessness”—from digital assets to autonomous driving, from public governance to scientific consensus—can construct its own “trust in time” to replace traditional centralized trust mechanisms.