Two consecutive productive windows in random polymer reactors: startup, resource bounds, and selection by successful operation

A reflexively autocatalytic and food-generated set certifies that a reaction network can regenerate its catalysts from food. It does not say when the first catalyst molecule appears in a reactor started from food alone, how much material leaves the reactor, or whether stock remains after an operating interval. We study these questions in one explicit random model: the reversible binary polymer model with ordered split identities, the capped, shifted Zipf catalysis law, independent kinetic marks, and a fed, diluted count process with falling-factorial propensities. The operating requirement is a joint event on one uninterrupted trajectory: measured stock at times $1$, $100$ and $199$, nonfood monomer export above $V/10$ in each of the windows $(1,100]$ and $(100,199]$, a mass corridor, and a gross supply allowance, where $V$ is the count scale. We prove a positive lower bound for its probability, constructive on an exactly counted source class with arbitrary nonfood background, and a converse; both hold for every Zipf exponent $a>1$ and every polymer length $n\ge4$ at a sufficient count scale. Along the critical sequence $a_n=2-2/n$ the probability is $\Theta(2^{-n})$, the limiting prefactors relative to the incidence probability lie between $(6/\pi^2)^6$ and $224$, where $224$ is the exact number of productive one-channel incidences, and conditioning on success selects such an incidence with probability tending to one. The same estimates bound the fraction of highly reliable environments, the cost of independent screening, and the effect of deleting all catalysis. For every fixed exponent the rarity order is computed exactly; singleton dominance persists for $a\ge2$ and the argument identifies why heavier tails need a different converse. A stopped first-birth argument gives a necessary startup scale: in food-silent environments the success probability is at most $1-\exp[-(484/3)\varepsilon V]$, so $99\%$ reliability needs $V\ge1.43\times10^7$, while the sufficient scale of the constructive proof, even after an explicit tolerance optimisation, remains near $5\times10^{49}$; we explain which single tolerance sets it. Material identities show that the export is net internal synthesis and recover at least $1/12000$ of the supplied monomer. The loss envelopes, potential, startup, interval and noise lemmas are stated with complete hypotheses; the finite core is machine-checked in Lean 4 and every conventional step is labelled.