do not expect the system to follow the corresponding law of mass action. However, earlier studies on nucleated self-assembly have shown that in the context of the early time kinetics we focus attention on, polymer recombination does not play a significant role and hence can be ignored as in fact we shall also make plausible below. [@knowles_two_stage] Indeed, by identifying the most dominant terms in the dynamical equations for the polymerisation kinetics, the predicted lag phase has been shown to be in a quantitative agreement with theoretical models, at least in the absence of *body evaporation and addition*. [@tuomas_science; @knowles_two_stage; @hong; @hong_moment_closure; @subramaniam] This motivates us to do the same for our reaction pathway, despite it potentially being inaccurate in the long-time limit.

The steady-state solution of Eqs. \[eq6\] and \[eq7\] sheds some light on the role of molecular pathways and how our approximations, i.e., $k_n^+ \rightarrow 0$ and $k_f^+ P^2=0$, impact upon the long-time behaviour. In the steady state, the time derivatives of the two moments are zero and we are left with algebraic equations. If we define $K_f=\kpf/\kmf$ to be the fragmentation equilibrium constant, we can switch off the effect of *scission and recombination*, at least in equilibrium, 