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

• URL: http://arxiv.org/abs/2607.18620v1
• Date: Tue, 21 Jul 2026 01:39:53 GMT
• Title: Temporal-Causal Unity as an Operational Framework for Collective Dynamics: Causal-Progress Clocks, Synchronization, and Polarization
• Abstract summary: This paper develops a framework connecting a process-philosophical thesis time is the ordered unfolding of causal change.<n>The framework deliberately separates three claims: an interpretive thesis about becoming, a measurable causal-progress coordinate, and a network model.<n>The paper derives falsifiable hypotheses and an out-of-sample protocol for comparing causal-progress and chronological-time models.
• Score: 5.995482369040288
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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