The GammaThreshold Law

Wepresent the Gamma Threshold Law, a universal, falsifiable criterion for the emergence of persistent order, memory, and structure in complex systems—from networks and materials to the cosmos itself. Our central finding is that global, sustained order only arises when the fraction of “dark” (non-binary, unlinked, or superposed) states exceeds a critical threshold, γc ∼ 0.3–0.4. Below this Gamma point (“Gemma state”), systems are fragmented, memoryless, and unstable; above, a robust, synchronized backbone of order emerges. This law reframes dark matter—not simply as missing mass, but as the essential, irreducible enabler of cosmic order and memory, operating at the threshold of emergence. The Gamma Law is validated across extensive simulations and counterexample challenges, and makes clear, falsifiable predictions for physical, biological, and computational systems. Any system that sustains global order below the critical Gamma threshold would refute the law—yet no such system has been found. This principle unifies the mathematics of phase transitions, network science, and cosmology, opening new directions for research in physics, biology, AI, and beyond.