How do we understand Bitcoin as a decentralized “temporal order generating system”? What kind of internal logical structure does it operate on?

In Turing’s doctoral thesis “Systems of Logic Based on Ordinals”, he proposed a new approach to addressing the incompleteness of formal systems: using oracle Turing machines + transfinite ordinal evolution mechanisms to handle problems that conventional Turing machines cannot decide. This article adopts that theoretical framework to construct a five-layer structural model of Bitcoin, revealing its underlying computational philosophy:

1. Business Layer: The Formalized Entry of Human Intention

• Structure: User-initiated transactions (TX)
• Characteristics: Openness, subjectivity, incompleteness
• Example: Alice wants to send 1 BTC to Bob — this is an expression of intent that first enters the business layer.
  

Each transaction in this layer originates from real-world intent. It has not yet been validated and merely exists as a potential input awaiting processing.

2. Computable Layer: Deterministic Processing at the Turing Machine Level

• Structure: Bitcoin scripting language + block construction computations
• Characteristics: Formally processable, unambiguous, locally verifiable
• Example: Signature validation, UTXO checks, block header hash verification
  

At this level, Bitcoin relies on Turing machine theory to process the legitimacy of transactions — computations that are deterministic and terminating.

3. Undecidable Layer: Double-Spend Resolution and Π₂ Structure Judgments

• Structure: Involves competitive transaction state perspectives
• Characteristics: Requires arbitration by external reality, cannot be internally decided
• Example: Is a TX a double-spend? Has it already been confirmed?
  

This type of problem has the form (∀x)(∃y)R(x,y) — i.e., for all historical states, does there exist some “retrospective” confirmation path? This is precisely the Π₂ structure Turing referred to as “undecidable”.

Note: Judgment at this level cannot be handled by a Turing machine and must introduce a structure like an “oracle Turing machine” — for instance, real-world PoW temporal ordering.

4. Consensus Layer: Selection Mechanism under Multi-Perspective Conflict

• Structure: Longest chain rule + miner selection behavior
• Characteristics: Relative judgments from local perspectives; subjective and temporary
• Example: A miner facing two valid blocks can only choose one
  

This represents an “adjudication” behavior — selecting one among branches that cannot both be true. This adjudication itself cannot be internally validated for correctness, but the system allows for global convergence within finite time.

5. Temporal Order Layer: Irreversible Thermodynamic Time + Ordinal Evolution

• Structure: Block height, cumulative global PoW difficulty, longest chain construction
• Characteristics: Globally consistent, irreversible, stable historical construction
• Example: Every block in the blockchain has a unique ancestor; every second energy is consumed to construct order
  

This layer fuses two dimensions:

• Thermodynamic dissipative time: The irreversible energy consumed during mining forms Bitcoin’s “arrow of time”.
• Ordinal logical evolution: As block height increases, the system evolves its understanding of truth values, eventually reaching locally stable solutions to undecidable problems.
  

At this layer, Bitcoin becomes a real-world oracle system, granting the entire business process a final and irreversible temporal order.

Summary: A Five-Layer Structure of Bitcoin as a Hyper-Formal System — From Intention to Order

Insight: Bitcoin is not a database. It is a temporal order generator.

Bitcoin is not merely a ledger system. It is a real structure that transcends the limits of formal systems, completing the loop from:

→ Intent input→ Computable validation→ Undecidable arbitration→ Multi-perspective consensus→ Global temporal order

It uses real, unforgeable “thermodynamic time” as the oracle, constructing a future-facing, irreversible history-generating system. As you can see, this is Turing’s unfinished dream of formal systems — realized through an engineering path in Bitcoin.