In the design of cryptographic systems, security is never the result of language completeness or contract complexity, but rather whether the “determinacy structure” is reasonable and clear. This article attempts to re-examine the core philosophical issue of “determinacy” from the perspective of Turing logic, and clarify the key principles of secure design through an analysis of #Bitcoin’s architecture.

I. Determinacy is the Problem of Trust

We can start with a simple proposition: any formal system has at least one problem that it cannot determine from within itself. This is precisely the limitation of formal systems revealed by Gödel and Turing. The principle of secure system design is: Only retain this one internally undecidable problem, and clearly delegate it to an “external” trusted mechanism for handling.

II. Taking Bitcoin as an Example: How to Structure Determinacy

The design of #Bitcoin’s system architecture strictly follows the above logical principle:

1. Transaction (TX) Layer

All transaction logic falls within the Turing machine’s computable domain—fully decidable, deterministic, and unambiguous.

2. Translation of the Self-referential Problem

Whether a transaction is valid (e.g., double-spending) cannot be determined by the transaction itself. Therefore, through “computational equivalence” translation, this problem is handed over to the system’s Block layer.

3. Uniqueness Judgment in the Block Layer

The Block layer retains only one internally undecidable problem: The “existence” of the block itself (i.e., which block is ultimately accepted as real).

The judgment of this problem does not rely on any person, code, or organization, but is based on the method proposed by Turing in “Ordinal Logics”:

Turing Oracle Machine + Transfinite Iteration + Real-time Drive

Through the game played by all nodes in the network over real physical time (PoW), the “existence” of the block is probabilistically determined. This constructs a temporal oracle structure that does not rely on trust in any individual subject.

III. How Do Other Systems Judge?

We can use a simple comparison table to show the “determinacy mechanisms” and trust structures of different systems:

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A crucial judgment: if the core determinacy of a Token still relies on human judgment, its trustworthiness is even lower than that of an audited and regulated stock system.

IV. Security Comes from the Proper Delegation of the “Only Undecidable Problem”

To design a truly secure system, one must follow the structural logic below:

1. Separate business logic (TX) from system judgment logic (Block)
2. Use computational equivalence to elevate all “locally undecidable problems”
3. Ensure that only one “self-referential” determinacy problem remains within the system
4. Choose a clear external mechanism to determine that problem:
   

Three Determinacy Mechanism Options:

✅ Trust “Time + Oracle” → Bitcoin’s method

✅ Trust “Code + Limited Group” → PoS & Contract Consensus Agents

✅ Trust “Human Organization” → Stocks, Centralized Tokens

V. Turing-Completeness ≠ Security-Completeness

Many mistakenly believe that a Turing-complete smart contract language implies system security. In reality: Turing-completeness provides expressiveness and transparency, but does not solve the problem of system determinacy.

True security is when you can clearly tell yourself and your users:

• What problem in the system cannot be self-determined?
• Who is assigned to determine that problem?
• Why do we trust them?

VI. Final Words

The future of cryptographic systems is not just an art of programming, but the coherence of logic. The reason Bitcoin is solid is not because its code is complex or frequently updated, but because it structurally achieves perfect separation and translation of the determinacy problem: Trust in physical time, not in anyone

This is the most restrained structure in cryptographic systems, bringing the strongest trust extrapolation.

Security ≠ Technical Flashiness

Security = Clear Determinacy Structure + Clear Determinacy Agent

This is a first principle that every designer should remember.