A Candidate Unifying Framework for Early-Warning Signals: The Standard Coherence Fidelity Layer (SCFL) Cross-Domain Atlas

Early-warning signals (EWS) for critical transitions have been independently identified across a wide range of complex systems, including ecological collapse, climate tipping points, financial instability, physiological breakdown, and psychopathological shifts. Despite consistent empirical observations—such as rising variance, increasing autocorrelation, and critical slowing down—these signals are typically studied within domain-specific frameworks, resulting in fragmented terminology, inconsistent measurement practices, and limited cross-domain synthesis. This paper introduces the Standard Coherence Fidelity Layer (SCFL) as a candidate unifying framework for early-warning detection. SCFL reframes early-warning behavior as a manifestation of coherence deformation in complex dynamical systems, and formalizes this process through five structural operators: Δ (deformation/variance expansion), Φ (memory/coupling continuity), τ (recovery dynamics/critical slowing), f (fragmentation/multiscale loss), and seam (cascade propagation across networks). These operators are defined in a substrate-agnostic, geometry-based manner, allowing direct mapping to established statistical indicators while preserving cross-domain interpretability. To evaluate this framework, we construct a Cross-Domain Atlas of 20 high-impact empirical and theoretical studies spanning ecology, climate science, finance, physiology, psychopathology, and network science. Each study is systematically coded for the presence of SCFL operators using explicit mathematical mappings to canonical early-warning metrics. Inter-rater reliability assessment (Cohen’s κ = 0.88) demonstrates strong reproducibility of the operator classification scheme. Statistical analysis of operator prevalence reveals high marginal frequencies for Δ (90%), Φ (80%), and τ (65%) across domains. The co-occurrence of these operators (45%) is consistent with independent appearance at observed marginal rates (p = 0.65), indicating that early-warning structure is broadly distributed rather than concentrated in a single dominant indicator. This result suggests that widely studied signals such as variance and autocorrelation represent partial observables of a higher-dimensional structural process, rather than isolated mechanisms. Building on this finding, SCFL proposes that early-warning detection should be understood as a multi-dimensional measurement problem, where different operators capture complementary aspects of system instability. In this framework, domain-specific signals (e.g., volatility clustering in finance, entropy loss in physiology, or resilience decline in climate systems) are interpreted as projections of a shared underlying geometry of coherence deformation. The paper further identifies key limitations in existing early-warning approaches, including sensitivity to aggregation (“smearing”) effects, vulnerability to false positives under external forcing, and reduced performance in rate-induced or noise-induced tipping scenarios. The inclusion of multiscale fragmentation (f) and network cascade (seam) operators provides a pathway for addressing these gaps, particularly in high-dimensional and networked systems. Rather than claiming definitive superiority, we derive a set of testable hypotheses for multi-operator detection systems, including improvements in lead time, sensitivity at matched false-positive rates, robustness to coarse-graining, and cross-domain transferability. These hypotheses define a clear empirical agenda, including head-to-head benchmarking against single-metric approaches, prospective validation in real-time monitoring environments, and community-driven refinement of the operator framework. Taken together, the SCFL framework offers a structured and extensible approach to unifying early-warning science across disciplines. By providing a common measurement language for coherence deformation, it enables systematic comparison, integration, and extension of early-warning methodologies, while remaining grounded in existing statistical and dynamical systems theory. The results presented here position SCFL as a candidate foundational layer for cross-domain early-warning analysis, pending further empirical validation.