Higher-Order Materials Synthesis: From Provenance Completion to Resource-Constrained Planning

Materials-synthesis workflows increasingly rely on literature-derived provenance for knowledge recovery and experimental decision making. These records are often incomplete, while synthesis activities jointly involve materials, tools, roles, and process conditions, and executable routes require complete precursor sets. Pairwise reductions can lose joint-event identity when activities overlap, so we evaluate when complete-event information matters. We represent synthesis provenance as a hypergraph and evaluate 2,367 MatProv procedures across prediction and resource-constrained planning. Hyper-SAGNN gives the strongest event-validity performance under pairwise-matched negatives (AUC 0.663), while downstream missing-link gains are selective and strongest for jointly constrained information such as tool identity. We then formulate precursor selection as a resource-constrained portfolio with an OR-of-ANDs objective over alternative routes; pairwise surrogates realize lower true portfolio value on 24-59% of exactly solved instances. Complete-route feasibility induces higher-degree products and therefore a natural Higher-Order Unconstrained Binary Optimization (HUBO) formulation, linking synthesis planning to quantum optimization; a representative instance uses 8 native HUBO variables versus 14 qubits after QUBO quadratization. Together, these results support hypergraph provenance for retaining joint-event information when it affects prediction, executable planning, and higher-order optimization.