Temporal Coherence as a Universal Safety Metric - A Kappa-Based Synthesis Across Physical - Infrastructural and Planetary Systems

Temporal Coherence as a Universal Safety Metric presents a cross-domain synthesis of the Kappa framework, reframing safety, stability, and resilience as properties of temporal coherence rather than static thresholds or probabilistic failure events. Across physical systems, critical infrastructure, energy networks, and planetary-scale dynamics, catastrophic collapse is rarely abrupt. Instead, failure is preceded by a prolonged erosion of a system’s ability to absorb perturbations, damp oscillations, and recover within viable temporal margins. This work formalizes that pattern by treating safety as a temporal process sustained through continuous correction under stochastic disturbance. Kappa is introduced as a coherence-based safety metric, defined as the minimal stochastic cost required to preserve functional identity over time. Rather than representing a force or stored resource, Kappa quantifies temporal margin: the time available for corrective action before perturbations become irreversible. Loss of safety corresponds to the degradation of this margin, not the violation of design limits. The paper integrates evidence from mechanical systems, structural infrastructure, electrical grids, climate dynamics, and large-scale containment systems, demonstrating that diverse failure modes converge on a common temporal precursor: increased variance, delayed recovery, loss of damping, and amplification of low-energy disturbances. These signals consistently emerge well before conventional safety alarms are triggered. By shifting the focus from failure prediction to temporal governance, this framework supports earlier, less disruptive intervention strategies and provides a unified physical grammar for safety assessment across domains. The approach is applicable wherever systems must persist under noise and variability, offering a foundation for resilience analysis, infrastructure governance, and sustainability planning.