Stabilisation Dynamics II: Correlation Geometry in Coupled Systems

This paper extends the stabilisation dynamics framework to joint outcome statistics, showing that correlations arise from geometric deformation of shared attraction basins. In the weak-noise regime, outcome statistics are determined by basin measures. When systems are coupled, interaction modifies the underlying stabilisation landscape, deforming basin geometry and inducing non-factorisable statistics. This work forms part of the “Stabilisation Dynamics” series, which develops a geometric framework for probability, correlation and dynamical behaviour in stabilisation systems. Subsequent papers extend this framework to spatial propagation, continuum limits and domain growth, and further derive resolution…