Stabilisation Dynamics V: Absence of Critical Behaviour in Stabilisation Lattice Dynamics

This paper investigates whether stabilisation lattice dynamics exhibit conventional critical behaviour. Using numerical diagnostics including correlation length scaling, finite-size analysis, susceptibility and Binder cumulants, we find no evidence of a critical transition. Although correlation lengths increase with coupling, they remain finite and do not exhibit scale-invariant behaviour. Susceptibility does not show a sharp, size-independent peak and Binder cumulants do not exhibit a common intersection point across system sizes. These results indicate that stabilisation dynamics generate structured but intrinsically bounded spatial behaviour. Within the geometric stabilisation framework, propagation arises from deformation of basin structure and remains finite, rather than exhibiting critical divergence. This work further reinforces the geometric framework governing probability, correlation and spatial propagation in stabilisation dynamics.