Stabilisation Dynamics IV: A Continuum Field Theory of Stabilisation Dynamics (A Unified Framework for Basin Capture, Correlation and Propagation)

This paper presents a continuum field formulation of stabilisation dynamics, providing a unified theoretical framework for probability, correlation and spatial propagation. The resulting stabilisation field equation has the structure of a relaxational gradient-flow system with local nonlinear stabilisation and diffusive coupling. Within this framework, outcome selection arises from basin geometry, correlations emerge from deformation of shared stabilisation structure and propagation is governed by a finite correlation length. This work unifies the geometric stabilisation framework developed in earlier papers, showing that discrete and lattice models arise as specific realisations of an underlying continuum theory. Subsequent work further develops this framework through domain growth dynamics and operator-based resolution structure.