Dynamic Harmony Structural Stress-Test Series. This paper evaluates Ilya Prigogine’s theory of dissipative structures as a proposed mechanism for the emergence of ordered organization in nonequilibrium thermodynamic systems. The analysis examines whether far-from-equilibrium self-organization satisfies the structural conditions required for genuine emergence within the Dynamic Harmony framework. Using the Phase Non-Substitutability Test introduced in Paper 0 and the architectural boundary criterion developed in Paper 0B, the paper analyzes whether dissipative structures represent a true architectural redefinition of system organization or remain configurational rearrangements within an existing thermodynamic state space. The analysis clarifies the relationship between instability, energy throughput, and the structural conditions required for the emergence of persistent organized systems. This paper forms part of the Dynamic Harmony Structural Stress-Test Series, a research program that evaluates major theories of emergence across physics, biology, and complex systems through adversarial structural analysis.