Dust Theory Vol. 4: Self-Bootstrapping AGI Engine: A Delta-Driven Two-Level Endogenous Evolution Closure (Gradient Cosmos Research Series)

The unification of neural and symbolic systems remains a core challenge in cognitive science and artificial intelligence. Symbolism and connectionism have long been locked in a binary opposition. Most existing neuro-symbolic integration schemes are engineering-level dual-system splicings, lacking a native unified foundation at the ontological level. They have consistently failed to explain how discrete symbols emerge endogenously from distributed neural activity. Based on the axiomatic framework of Gradient-Relational Ontology, this paper takes the gradient relation network as the sole cognitive substrate and realizes the ontological unification of neural and symbolic systems through the path-rule duality principle: distributed neural activation corresponds to the path-state level of the network, while discrete symbolic rules correspond to the rule-state level. The two are manifestations of the same gradient system at different degrees of condensation, rather than two independent cognitive modules. The study proves that concepts and logical rules can emerge spontaneously from distributed conduction through the path condensation mechanism, without external implantation of symbolic axioms. The cognitive dual system is not two parallel modules, but a continuous switch of the same network between a parallel low-condensation mode and a serial high-condensation mode. This framework provides a unified mechanistic explanation for core cognitive phenomena such as categorization, conceptual combination, and insight transition, and offers an ontological foundation of endogenous evolution for neuro-symbolic artificial intelligence.