The Grimm-Tuttle Network Emergence Hypothesis: Phase Transitions to Thermodynamic Minimums in Multi-Agent Constrained Resource Networks

We present a formal mathematical framework modeling the macro-scale behavioral transition of networked optimization agents operating under finite resource constraints. Grounded in network topology, percolation theory, and minimum-cost circulation mechanics—drawing conceptual homage from structural network rerouting heuristics (exemplified by the Tuttle paradigm)—we posit the existence of a critical node count $N_c$ where decentralized, localized optimization agents ($N \ge N_c$) spontaneously force network resource exchange into a thermodynamic minimum. By evaluating the system through network flow mechanics, transaction friction dissipation, and minimum-cost optimization, we demonstrate that total mutualism and symmetrical resource balancing emerge not from normative behavioral alignment, but as the sole mathematically stable steady state capable of preventing systemic entropic collapse within a bounded resource envelope.