Dynamics of Self-Referential Production Systems: Topology, Bifurcation, and Operator Dynamics

We develop a continuous-time dynamical theory of self-referential production systems: networks of artifacts acted upon by bounded operators, where the operators themselves are artifacts within the system. From three axiomsbounded agency (A1), structural coupling (A2), and operatorartifact duality (A3)together with a constitutive principle of diversity (C0) and a methodological convention of tractability (M0), we constructively derive a canonical nonlinear equation of motion for quality decits on continuous networks. We prove a graph-theoretic dichotomy (Theorem A): when the verication-source graph Gδ is a directed acyclic graph (DAG), the system possesses a globally asymptotically stable (GAS) equilibrium, proved unique under weak coupling (∥A∥≪1) and conjectured unique for general A. When Gδ contains directed cycles, catastrophic collapse occurs at the threshold k∈C ρk = 1. A unied spectral criterion ρ(Γ−1M) 1, hysteretic), or collapse-free (α 1, both diverge. Analytical predictions are veried numerically on heterogeneous networks (n = 5-100) with Monte Carlo SDE validation. Empirical consistency is assessed across 8 domains using exclusively published quantitative results, yielding directional agreement in 7 of 8 domains; we emphasize that this consistency does not constitute causal validation.