Temporal Dynamics of Structural Value in Tension-Based Systems: Trajectories V(t) in the ZTH Model

In tension-based systems, static assessments of structural value may hide important temporal patterns. Building on the ZTH model introduced in previous articles, this paper examines the temporal evolution of structural value V(t) generated by time-varying tension vectors τ(t). Structural value trajectories are defined by applying the same multiplicative formulation as in the static case at each time step, using intrinsic value Vi = 1 as a neutral reference. We characterize typical temporal regimes, including transient excursions around the intrinsic state, progressive drift towards degraded or amplified configurations, and oscillatory behaviors. Simple dynamic indicators such as time spent below Vi, excursion depth and recovery time are introduced to summarize these regimes. Stylized scenarios illustrate how different patterns of tension change produce distinct trajectories V(t) despite similar initial and final values. This dynamic perspective extends the ZTH framework beyond static snapshots and prepares the ground for analyzing perceived value trajectories Vp(t). This paper is part of the ZTH research series.Part I: https://doi.org/10.5281/zenodo.18671741Part II: https://doi.org/10.5281/zenodo.18684678