Temporal-Causal Unity as an Operational Framework for Collective Dynamics: Causal-Progress Clocks, Synchronization, and Polarization

This paper develops temporal-causal unity (TCU), a framework connecting a process-philosophical thesis -- time is the ordered unfolding of causal change -- to an operational model of cognitive and social dynamics. The framework deliberately separates three claims: an interpretive thesis about becoming, a measurable causal-progress coordinate, and a stochastic network model. Causal progress is defined by τ(t)=int0tλ(smidmathcal Hs),rm ds, where the nonnegative event intensity λ must be specified independently of the outcome. Agents carry an orientation phase and an activation amplitude; weighted interaction, heterogeneous drift, external input, anchoring, and diffusion govern their evolution in τ. First- and second-harmonic order parameters separate consensus from bipolar polarization. For the all-to-all noisy Kuramoto special case with Lorentzian drift width Delta, synchronization begins at the conditional threshold Kc = 2(Delta + D), not at a universal constant. Reproducible numerical illustrations illustrate (not empirically demonstrate) this threshold, causal-clock curve collapse, and the consensus-polarization distinction. Six historical episodes are treated as scope probes rather than validation data. The paper derives falsifiable hypotheses and an out-of-sample protocol for comparing causal-progress and chronological-time models. TCU is therefore offered as a disciplined bridge between process ontology and complex-systems modeling, not as a replacement for spacetime physics or as an empirically established identity between time and causation.