Cognitive Phase Transitions in Subjective Physics: Modeling Synchronization and Order Parameters with Reproducible Simulations

This work provides a reproducible computational framework for studying cognitive phase transitions within Subjective Physics. Using an adaptive network of $N=40$ agents, it distinguishes local pairwise coherence (MPC) from global order (Kuramoto mean-field amplitude) and demonstrates a non-monotonic critical transition characterized by cluster reorganization, a transient desynchronization valley, and stabilization into a high-coherence phase. Python simulations with explicit parameter control enable transparent, reproducible experiments, offering a practical platform for exploring emergent collective dynamics and observer-state reorganization in cognitive systems.