A nontrivial critical window for RAF emergence in the binary polymer model
Hordijk and Steel (https://arxiv.org/abs/1605.03919, Section 7, Eq. (21)) conjectured a zero-one threshold for RAF emergence at linear mean catalysis. In the uniform reversible binary-polymer model with split-position reaction identities and food consisting of monomers and dimers, a nontrivial limiting law is established. Each molecule independently catalyzes each reaction, with one catalysis coordinate shared by both directions. If the mean catalysis parameter f(n) satisfies f(n)/n → λ > 0, the probability of a reflexively autocatalytic and food-generated (RAF) set converges to L(λ). The…
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