Symmetry and Asymmetry in Fe(II)–Salen Speciation Networks: A Category-Theoretic and Bayesian Framework

Fe(II)–salen chemistry is often summarized by a single synthetic arrow, although ligand condensation, hydrolysis, oxidation, axial coordination, and formation of unanticipated products can coexist under realistic conditions. We develop a compositional framework in which chemically distinguishable Fe–salen states are objects, admissible transformations are morphisms, independent components combine through a symmetric monoidal product, and experimental techniques act as partial observation maps. The framework makes the connection to symmetry explicit by separating structural symmetry from condition-induced asymmetry in branch weights and by introducing explicit asymmetry indices on measured outcome distributions. Quantitative examples are grounded in published experimental and computational data rather than unsupported illustrative energies or arbitrary optimization updates. A complete worked application uses published iron–salen/dioxygen data: for 1 M cyclohexene, 1 mM iron–salen catalyst, 24 h at 23 ± 1 °C, ketone/alcohol/epoxide concentrations of 53.6/26.1/0.9 mM under air and 27.8/12.6/0.4 mM under dioxygen yield normalized branch weights and reproducible asymmetry measures. Independent electrochemical and structural studies provide constraints on Fe(III)/Fe(II), Fe(II)/Fe(I), oxidation, racemization, and N2O2 coordination. Bayesian conditioning is retained as an evidence-integration architecture, but numerical posteriors are reported only when likelihoods are calibrated from data. This evidence-constrained formulation preserves the mathematical contribution while making chemical assumptions, data provenance, and limits of inference explicit.