Domain-agnostic multiplicative stress framework for systemic collapse

Complex systems rarely collapse from a single perturbation; however, no framework has formalized the coincidence mechanism across domains. Here, we introduce a multiplicative stress integral, S(t) = ρ(t) × Ψ(t) × Ω(t), which decomposes systemic stress into external pressure (ρ), internal amplification (Ψ), and structural degradation (Ω). The multiplicative structure drives the stress toward zero when any channel is quiescent, thereby creating a coincidence filter. The cumulative index Π(t) integrates the joint stress with a fixed equal weighting (1:1:1) and no weight optimization. Applied to five major crises, the 2008 financial crisis, Terra–Luna collapse, Fukushima disaster, COVID-19 pandemic, and global supply-chain disruption, the crisis periods separate from controls (1.9× to 3,627×; Fisher p = 1.66 × 10⁻¹¹), with the multiplicative formulation matching or outperforming alternative models in all cases. When the channels are redundant, the filter dilutes rather than amplifies the signal, which is a falsifiable prediction that is empirically confirmed. Analysis of Π accumulation dynamics reveals three failure modes, ductile, brittle, and preloaded, suggesting that co-occurrence of independent stresses is a shared structural feature of systemic collapse.