Stabilisation Dynamics I: The Basin Capture Principle

This paper introduces the Basin Capture Principle establishing that, in the weak-noise regime, outcome probabilities in stabilisation dynamics are determined by the geometry of deterministic attraction basins. 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 correlated systems, spatial propagation, continuum limits and domain growth, and further derive resolution statistics from projection onto unstable modes and operator structure.