Behind the Turing-incomplete Bitcoin system lies a profound structural logic: how to transform an undecidable business problem, adjudicate it via an oracle system, and finally embed it into time through a dissipative physical structure—ultimately forming a decentralized, globally consistent, and irreversible time order.

This article attempts to use a three-layer system structure, corresponding to Turing's three classic papers, to clearly deconstruct the philosophical and computational mechanisms of Bitcoin.

I. Overview of the Three-Layer System: From Undecidability to Time Consensus

II. Transformation Path of Undecidable Problems

The ingenuity of Bitcoin’s design lies in how it “transforms” undecidable problems layer by layer, and engraves the adjudication result of each layer physically into time. The double-spending problem (TX layer) is essentially a self-referential paradox within a formal system, which cannot be resolved by a Turing machine alone.

It is elevated to the fork selection problem at the Block layer, belonging to the Π₂ structure — a problem structure of “∀x∃y”, a typical unconstructible proposition. With the aid of an oracle system constructed via transfinite iteration logic, a Block branch is selected externally.

Finally, the selected branch is embedded as the “one true history” into the system through the irreversible dissipative structure of the physical world (hash power + time + thermodynamics).

III. One-to-One Correspondence Between Turing’s Three Papers and Bitcoin’s Three Systems

These three papers respectively laid the foundation for:

• The formal system of the Turing Machine,
• The solution to completeness and oracle judgment via transfinite iteration,
• The physicalization of logical forms through time structures (dissipative structures).

IV. The Relationship Between Dissipative Structures and Axiomatized Time Systems

-Transfinite Iteration System: Provides a “temporal deductive framework” for completeness
By recursively introducing new ordinals, this system attempts to approach an “ideal adjudication” of all Π₂ structures.

- Dissipative Structure System: Provides a physical axiomatic foundation for each layer constructed by transfinite iteration
Bitcoin uses the PoW mechanism to generate one block every ten minutes. Each block is essentially a marker of an irreversible thermodynamic process. It physically embeds the result of adjudication, making the system history irreversible and tamper-proof.

In short: Transfinite iteration answers “how to decide,” while dissipative structure answers “how to make it real history.”

V. How Does Bitcoin Construct a "Decidable Irreversible Time"?

Bitcoin constructs a stunning structure: unifying computational logic, adjudication, and physical time into a complete path from formal systems to physical reality.

The three systems collaborate as follows:

1. Turing Machine Layer (TX): The place for running business logic. When facing an undecidable problem (e.g., double-spending), it is elevated.
2. Oracle System Layer (Block): The system selects among multiple possible Block branches—making the adjudication.
3. Dissipative Structure Layer (Time): Each selected Block is embedded into physical time through hash power + thermodynamics, forming an irreversible time sequence.

This structure truly solves long-standing problems in computing systems:

• How can subjective business logic become objective consensus?
• How can undecidable problems reach consistent adjudication within the system?
• Can time become a mathematically and physically valid foundation?

VI. Summary: Bitcoin as an Example of a “Meta-Formal System”

Bitcoin is not a Turing-complete system, yet through its three-layer structure, it approaches a Meta-Formal System: By adjudicating undecidable problems through an oracle system, and physically embedding the result via dissipative structure, it ultimately constructs a time consensus network that is both decidable and irreversible.

In this sense, Bitcoin is the first computational entity that truly realizes the unification of: Formal system + External oracle + Irreversible time. This is precisely the kind of question that Turing, Gödel, and Prigogine tried to answer from different dimensions: How can we build a worldview that is logical, physically embedded, and executable?