Neutron Term: Philosophical and Mathematical Research on Closed-Loop Emergence and World Self-Organization

This paper proposes the "neutron term" as the core carrier of system self-organizing closed loops within the MPCT (Multi-Path Closure Theory) framework, explaining nuclear stability, electron shell quantization rules, and the phenomenon of local non-dispersal in physical structures. Through the synergistic evolution of relational matrices, τ-mode closure, and neutron constraints, a unified model is constructed that emerges macroscopic stable structures from microscopic relational logic. The paper not only provides a complete mathematical description and numerical implementation (MPCT-He v2.0) but also philosophically clarifies that the neutron term is not a product of teleology but rather an existential constraint condition spontaneously emerging from the system's relational closure process. Experimental results demonstrate that the model achieves natural emergence of electron shells and accurate prediction of atomic radius in helium systems, with errors less than 10%, validating the theory's self-consistency and predictive capability.Keywords: Relational matrix, τ-mode, neutron constraint, emergent physics, self-organization, MPCT-He v2.0, existential density, closed-loop system