Causal symmetrization as an empirical signature of operational autonomy in complex systems

TL;DR

This study empirically investigates the signature of operational autonomy in artificial sociotechnical systems by analyzing structural persistence, causal coupling, and a viability index across large-scale collaborative software ecosystems.

Contribution

It introduces a statistical framework to detect operational autonomy in non-biological systems, demonstrating core principles of self-organizing autonomy in artificial environments.

Findings

Identification of a phase transition in structural persistence

Emergence of causal symmetrization at system maturity

A viability index improves activity prediction accuracy

Abstract

Theoretical biology has long proposed that autonomous systems sustain their identity through reciprocal constraints between structure and activity, a dynamical regime underlying concepts such as closure to efficient causation and autopoiesis. Despite their influence, these principles have resisted direct empirical assessment outside biological systems. Here, we empirically assess this framework in artificial sociotechnical systems by identifying a statistical signature consistent with operational autonomy. Analyzing 50 large-scale collaborative software ecosystems spanning 11,042 system-months, we develop an order parameter ($\Gamma$) quantifying structural persistence under component turnover and use Granger causality to characterize directional coupling between organizational architecture and collective activity. $\Gamma$ exhibits a bimodal distribution (Hartigan's dip test $p = 0.0126$; $\Delta$BIC = 2000), revealing a sharp phase transition between an exploratory regime of high variance and a mature regime characterized by a 1.77-fold variance collapse. At maturity, causal symmetrization emerges, with the structure--activity coupling ratio shifting from 0.71 (activity-driven) to 0.94 (bidirectional). A composite viability index combining activity and structural persistence outperforms activity-based prediction alone (AUC = 0.88 vs. 0.81), identifying ``structural zombie'' systems in which sustained activity masks architectural decay. Together, these results show that causal symmetrization functions as a necessary statistical signature consistent with theoretical notions of operational closure, without implying biological life or mechanistic closure. They demonstrate that core principles of autonomy can be empirically probed in artificial collaborative systems, supporting substrate-independent dynamical signatures of self-organizing autonomy across complex adaptive systems.