Fact-based computation specification. · GitHub
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wyniijj5-wq/ChurchTuringThesis-en.txt
Created<br>June 26, 2026 23:01
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Fact-based computation specification.
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ChurchTuringThesis-en.txt
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A Brand New Interpretive Perspective on the Church-Turing Thesis Based on BitMachine and Programming Languages: Refactoring the Foundations of Discrete Mathematics from an Algorithmic Standpoint
【Introduction: The EMF Constructive Manifesto and Operational Interpretation】
The constructive perspective presented in this paper is by no means built on thin air. The theoretical framework of EMF (Operational Evaluation Mechanism Framework) and its core state machine, the BitMachine, have been repeatedly verified at both the code and logical levels, achieving a stabilized state.
Departing from operationalism, we attempt to provide a brand new interpretation of the Church-Turing Thesis (CTT) based on finite-step operations and constructive logic. This research covers a wide scope and exhibits high cohesion, with all underlying operational modules (REG_01 through REG_06) strictly cross-referenced.
We advocate the doctrine of "Code as Formal Proof." Any mathematical object or entity that cannot be operated upon or observed within a finite-step program or a physical state machine possesses neither existence nor equivalence within this system. We reject the "non-constructive existence proofs of infinity" found in traditional mathematics, firmly anchoring the boundaries of computation upon physical reality.
【Abstract】
This research addresses the semantic ambiguity—such as the non-determinism of limits and continuum concepts in practical implementations—caused by traditional mathematical foundations (e.g., ZFC set theory) relying excessively on non-constructive abstract language. We propose a novel constructive axiomatic system with explicit hardware boundaries: the EMF system (where EMF generally refers to this text, the REG data, and the synthesis, originally evolved from "External Memory File"). The core focus of this paper is on the constructive interpretation of the Church-Turing Thesis, asserting that the expressive power of formal languages like mathematics and logic does not, in substance, exceed the expressive power of programming languages and algorithms.
At the foundational level, the system is based on the "BitMachine" (a physical implementation model of a Turing machine written in C++), refactoring infinity into a "non-terminating program loop," and establishing strict equivalence determination based on a mechanical subtraction operation. By translating the Collatz Conjecture and the P vs NP...