Quantitative analysis of critical-window profiles for autocatalytic emergence
The critical-window law for reflexively autocatalytic and food-generated (RAF) sets in the reversible binary-polymer model states that, when the mean number of reactions catalysed per molecule grows like $\lambda n$, the RAF probability converges to $S_\nu(1-\mathrm{e}^{-\lambda})$, where $S_\nu$ is the probability that ordinary reversible closure of the food set is unbounded in an infinite field of independently open reaction channels. The law is known for the ordered split-position catalogue ($\nu=\mathrm{sp}$) and for the commuting-factor quotient catalogue ($\nu=\mathrm{qt}$). It is an…
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