= Solution
In this <polymerization Brownian ratchet> model, a gap of width $\delta$ immediately accommodates one <monomer>. That event advances the tip by $\delta$ and resets the gap to zero. The threshold is therefore an <absorbing boundary condition for a diffusion>,
$$
\boxed{p(\delta)=0.}
$$
All waiting-time <probability> lies within $0\leq x<\delta$, so the steady occupation <probability density> satisfies
$$
\boxed{\int_0^\delta p(x)\,dx=1.}
$$
There is a reinjection flux $j_0$ at $x=0$ equal to the absorption flux at $x=\delta$. The nonpenetration constraint at zero is a <reflecting boundary condition for a diffusion> during each individual waiting episode. For the stationary reset process it must not be confused with setting the net current $J(0^+)$ to zero: the source at reset supplies $J(0^+)=j_0$. This is how a normalized steady density can coexist with a nonzero exit flux.
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