Reliable finite-time output from stochastic autocatalytic reactors: retained rewards, uncertain background catalysis, and quantitative startup

A reflexively autocatalytic and food-generated (RAF) set certifies that a reaction network could regenerate its catalysts from food. It supplies no deadline, stock, export quota or reliability for a finite reactor started from food, and the surrounding chemistry that may destroy a selected autocatalyst is usually unknown. We prove a finite-time output certificate for marked jump processes that uses this disturbance. A one-sided logarithmic reward retains every adverse fluctuation of a selected count and only its designated self-catalytic birth; a drift inequality charges all other catalytic activity to nonfood occupation, the compensator of collected output; and a continuous-time Bernstein bound controls the reward without paying for favourable births. In a fed, diluted, reversible binary-polymer reactor with falling-factorial propensities, for every maximum length $n\ge4$, count scale $V\ge\max\{2\times10^{22},10^{8}n\}$, arbitrary nonfood catalytic background and arbitrary food catalysis of strength at most $10^{-5}$, a self-catalytic witness started from food meets two export quotas, three stock observations, a mass corridor and a food budget on one trajectory with probability above $1-10^{-10}$. Every time window receives a quota on one event. For fixed $n$ the failure bound tends to zero, and averaging over a capped-Zipf source gives success probability $\Omega(2^{-n})$ along the critical sequence. The internal chemistry is detailed-balanced for every admitted assignment. An earlier food-silent theorem at $V\ge\max\{10^{24},10^{13}n\}$ with reliability $0.9989$ is machine-checked in Lean 4, as are the new algebraic and scalar components; the new stochastic theorems are proved conventionally. The sufficient scale remains fifteen orders of magnitude above a necessary first-birth scale, and we isolate the establishment estimate that controls the gap. The model is schematic and the output is aggregate material, not a functional product.