A Reproducible Bayesian Framework for Collective Trust Dynamics in Human AI Symbiosis: Postphenomenological Mediation as a Network Coupled Stochastic Process

Human AI collaboration is typically theorized qualitatively, through postphenomenological accounts of technological mediation, or modeled quantitatively, through control theoretic and Bayesian formalisms, rarely both, and rarely with a numerically validated implementation. This paper closes that gap by formalizing postphenomenological mediation as a bounded, network coupled term in a multi agent stochastic differential system, embedding the resulting collective trust dynamics in a Bayesian graphical model, and analyzing agents' beliefs about that dynamics with a variational free energy (active inference theoretic) inference layer. Every quantitative result reported, including trust trajectories, a Saltelli/Jansen Sobol global sensitivity analysis with an explicit convergence study and a multi seed robustness check across independent stochastic realizations, a Kraskov Stögbauer Grassberger (KSG) mutual information estimate, a Bayesian posterior update, a two regime Kolmogorov Smirnov/Welch test of the mediation effect on the mean, and a Brown Forsythe/bootstrap test of the mediation effect on variance, is produced by an open, self contained, seeded (seed equals 42) Python implementation (Appendix B) and is exactly reproducible under the software environment specified there. All inputs are synthetic, and no proprietary or restricted dataset is used or required. Validating the numerical integrator against closed form Ornstein Uhlenbeck moments, we show that network mediated coupling measurably shifts the mean of collective trust, an effect that is robust across independent stochastic realizations and across two network topologies (Erdős Rényi and Barabási Albert), while idiosyncratic volatility, not mediation strength, dominates the sensitivity of trust variance to model parameters. A direct variance test finds the corresponding reduction in variance hypothesis not statistically supported at this sample size, a result we report rather than obscure. The paper further contributes an explicit falsifiability and uncertainty quantification framework, a scientific and technical risk assessment, and a staged experimental validation roadmap linking the model to testable human subjects protocols. We discuss applications in social robotics, medical and surgical robotics, clinical AI decision support, and smart city infrastructure, grounding each in current peer reviewed evidence.