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

2026-07-20

AI Summary

This study addresses the challenge of modeling consensus and polarization in cognitive and social systems by proposing a Temporal-Causal Unification (TCU) framework. It reconceptualizes time as an event-driven causal progression coordinate τ(t), enabling the description of agent phase and amplitude dynamics in causal rather than calendar time. Drawing on process philosophy, the notion of “becoming” is formalized into a computable causal integral based on event intensity λ, while explicitly disentangling ontological assumptions, observables, and stochastic network models. Using a stochastic phase oscillator model with heterogeneous drift and external forcing, harmonic order parameter analysis, and curve collapse techniques, the authors derive the synchronization threshold for a noisy all-to-all coupled Kuramoto system as K_c = 2(Δ + D). Numerical experiments clearly distinguish consensus from bipolar polarization and demonstrate cross-model comparability and falsifiability.

Abstract

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 $τ(t)=\int_0^tλ(s\mid\mathcal H_s)\,{\rm d}s$, 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 $Δ$, synchronization begins at the conditional threshold $K_c = 2(Δ+ D)$, 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.

Problem

• temporal-causal unity
• collective dynamics
• synchronization
• polarization
• causal progress

Innovation

• Temporal-Causal Unity
• Causal-Progress Clock
• Synchronization Threshold
• Order Parameters
• Stochastic Network Dynamics