Turing Completeness via Kernelization: The Computational Universality of Discrete Topological Search and Corrigible Structural Intelligence
Year: 2026
Type: preprint
Abstract: The Church-Turing thesis posits that any effective computation can be performed by a Turing machine. However, modern computational paradigms often struggle to bridge continuous mathematical constraints with discrete logical operations. This paper formally proves that the Daopology Engine—a discrete topological framework based on structural kernels K = (G, Σ, B, Θ)—is Turing complete. We define "Kernelization" as the process of mapping any computable problem into a discrete topological state space. By mapping the Turing machine's infinite tape to a dynamically expandable directed graph, and its transition function to stochastic topological operators (Swap, Reverse, Mutation) governed by deterministic CSI (Corrigible Structural Intelligence) control flow, we demonstrate that the engine can exactly simulate any Turing machine. Furthermore, we discuss how multi-stage spatial kernelization allows this paradigm to achieve high-precision local optimization without relying on continuous calculus. This proof mathematically liberates AI computation from the energy barrier of continuous tensor calculus, establishing a rigorous foundation for Corrigible Structural Intelligence and pointing toward a new era of ultra-low-power structural intelligence.
Author: Zhang, Baoyuan
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225036602