No reaction network runs here. The path on the chart is the time-integrated net reaction flow of Cyburt et al. (2016), read from the vector drawing of their figure, and the ashes and the model light curves are theirs too. The way the flow front advances with burst time, the speed of the sparks and the spreading of the flame over the star are drawn, not computed.
The live numbers are the masses and what follows from them (Sp, the proton drip line, the equilibrium along an isotone), the half-lives, and the closed form for the hot CNO cycle. The equilibrium only tells how matter shares out between a waiting point and the next isotones while (p,γ) and (γ,p) are both fast. It does not give how much matter leaks past by a second proton capture, which needs the capture rates. Half-lives are terrestrial (NUBASE2020); Meisel et al. (2018) note that uncertainties remain in the corrections needed for high temperature and density.