Abstract

When does a chemical reactor retain useful operation after it is coupled to other reactors and an effective reaction is replaced by an explicit intermediate mechanism? For a specified reversible autocatalytic exporter, we prove a finite-mission guarantee that includes recovery after molecular withdrawal, loss and refill, collected product, food input and gross reaction service. On a symmetric exchange graph with nn reactors, weighted degree at most Δ\Delta and integer count scale V104V\ge10^4, the seven-species refinement completes mm cycles with probability at least max{0,129nmexp[V/(21012(1+Δ)3)]}\max\{0,1-29nm\exp[-V/(2\cdot10^{12}(1+\Delta)^3)]\}. Policies may use the complete history of returned states and physical counters. An exact material-forced reduction of the six-species donor explains which information can be removed; an explicit witness shows why simply deleting the intermediate is not an exact reduction. The proof controls material, stock and phase separately, then composes from actual random endpoints. An augmented-inventory identity shows that every successful mission of at least 55 cycles necessarily produces net new inventory beyond depletion of its initial supply. A connected two-reactor, 100-cycle instance has certified success probability above 99%99\%. The refined operational results have Lean-checked proofs; the donor theorem and the additional accounting consequences are proved conventionally. The count scale is sufficient, not optimized or experimentally calibrated.