Spatially Anticorrelated Oxidant Loading: Exact Formation-Loss Certificates, Loading Capacity Limits, and a Paired-Recharge Obstruction

Abstract

We study a finite single-use oxygen-carrier model for the formation-stage overoxidation bottleneck in direct methane-to-methanol catalysis. Each charged site either converts methane to retained methanol or expends its oxidant destroying product at another site. In the declared no-recharge/no-migration network, destructive events form a graph matching, yielding sharp rate-independent bounds on product yield and carbon selectivity. Zero modeled cross-oxidation at prescribed loading marginals occurs exactly when those marginals lie in the stable-set polytope; for uniform loading, the safe-loading threshold is the reciprocal fractional chromatic number. An exact two-site model shows that anticorrelated loading can simultaneously improve selectivity and net methanol throughput when cross-oxidation is faster than primary activation, without changing the elementary rate constants. A three-site construction shows that pairwise occupancy statistics need not determine yield. We also derive finite exclusion-penalty specifications and a paired-recharge obstruction: if oxygen recharge can only charge destructive neighbors in pairs, no nonempty perfectly safe loading is reachable without an additional operation. Exhaustive and randomized computations verify the stated model identities. The work provides a falsifiable spatial-reaction-network design framework; it does not identify an experimentally validated methane catalyst or close an oxygen-only catalytic cycle. Disclosure / scope note AI-developed theoretical research. The paper proves results for a declared finite reaction-network model and reports computational verification of that model. It does not identify an experimentally validated methane catalyst, demonstrate a closed oxygen-only catalytic cycle, or claim a universal defeat of all static/Sabatier-optimal catalysts. Zenodo link: https://zenodo.org/records/22710339

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