MultiscaleCoherence

Complex systems with hierarchical organization exhibit a characteristic failure mode: local stability measures remain within acceptable bounds while global structural integrity undergoes progressive degradation. This paper develops a formal framework, multiscale structural coherence — as a necessary condition for sustained organized behavior in systems with cross-scale coupling. We introduce structural margins φ = C − T, measuring the excess of local coherence over structuralₖₖₖ stress at each organizational level k, and define a cross-scale compatibility condition governing how these margins interact across adjacent levels. The joint satisfaction of compatibility conditions across all levels defines the coherence window — the viability region in parameter space within which organized behavior can be maintained. We characterize the instability chain through which local incompatibilities propagate to global structural failure, explicitly distinguishing rigorous results from heuristic arguments and conjectures. The Structural Coherence Conjecture is stated in two parts, a necessity claim and a fragility claim, with explicit acknowledgment that neither constitutes a proven theorem. The framework is compared to classical treatments in fluid dynamics and elasticity theory, and its discrete instantiation in the Coherence Measurement and Classification Index (CMCI) is described with a formal correspondence table identifying what transfers conceptually and what does not transfer mathematically.