Topology-Aware Discrete Structural Annealing (TA-DSA) and the Daopology Engine: A Foundation for Neuro-Symbolic AI

The dominance of continuous gradient-based optimization in modern machine learning faces severe limitations when navigating non-convex, discontinuous, or highly constrained spaces. Large Language Models (LLMs), despite their generative prowess, suffer from probabilistic hallucinations and a lack of grounded physical constraints. In this position paper, we introduce Topology-Aware Discrete Structural Annealing (TA-DSA), a gradient-free paradigm that abandons continuous calculus to operate directly on discrete topological grids. Built upon this foundation, we propose the Daopology Engine, a novel Neuro-Symbolic AI architecture that integrates four core modules: LLMs for noisy generation, Symbolic Systems for rigid physical constraints, TA-DSA as the white-box World Model for state transitions, and CSI (Correctable Structural Intelligence) for auditing and local graph rewriting. We demonstrate the cross-domain viability of this paradigm in signal analysis, peptide conformational sampling, VLSI routing, and battery material discovery. This "minimalist physicalism" paradigm shifts AI from a black-box statistical generator to a fully explainable and auditable white-box physical engine, offering a highly cost-effective pathway toward the next generation of reliable, reasoning AI.