The Dominik Collapse–Divergence Law: A Universal Alternation Model of Optimization in Physical, Biological, and Numerical Systems

This paper introduces the Dominik Collapse–Divergence Law, a universal optimization principle observed across physical plasmas, biological networks, atmospheric electricity, integer dynamical systems, and planetary-scale ecological transitions. The law proposes that complex systems evolve through an alternation of two modes: collapse (1-rule) driven by energetic minimization, contraction, or pruning, and divergence (3-rule) driven by exploratory branching, expansion, or recursive proliferation.

The document derives formal expressions for collapse probability, divergence branching behavior, attractor stability criteria, and vortex-like residues arising from asymmetric pruning. Applications include plasma leader extinction, slime mold optimization, synaptic pruning, Collatz recursion, prime distribution vortices, lightning outlier stabilization, and the recursive pulses of the Great Oxygenation Event. The Collapse–Divergence Law provides a unifying framework suggesting that optimization is not domain-specific but a universal recursive architecture governing the evolution of complex systems.