This paper establishes a mathematically rigorous non-linear dynamical systems framework for self-sustaining computational networks utilizing the Universal Relational-Geometric Coherence Law (URCL). We derive the exact analytic Jacobian operator for the localized non-linear coherence gating map, compute the corresponding spectrum of Lyapunov exponents for both isolated nodes and coupled networks, and demonstrate global asymptotic stability bounds under golden-ratio (ϕ) geometric protection. By evaluating the network’s variational equations via the Master Stability Function (MSF), we establish a precise spectral criterion for global synchronization across complex topologies. These topological invariants enable the development of distributed computational architectures capable of achieving provable fault tolerance and asymptotic coherence stabilization in the absence of centralized optimization.
Daphne Garrido (Mon,) studied this question.