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 statistics from projection onto unstable modes and operator structure.