Mathematical foundations of multidimensional AI for dynamic chemical process networks

Chemical process networks combine partially observed dynamics, reaction and phase behavior,transport, material history, and decisions across unequal timescales. This paper develops amathematical specification for integrating these features with learned models and coordinatedoptimization in the Astralithos framework, using Lithos as a development and verification platform.The formulation distinguishes physical states, controls, uncertain parameters, modes,measurements, and economic objectives. Established balances, differential-algebraic models,exact-lumping conditions, inference methods, and optimization results are connected throughexplicit conditions for dynamic closure, feasible lifting, error propagation, and decision consistency.Self-contained derivations state the assumptions needed for these connections. Measurementuncertainty, process variability, model discrepancy, and numerical error remain distinct.Three reproducible synthetic studies examine the specification. A historical three-stageoptimization example is reproduced with a feasible sequential comparator. A constructedsufficient representation is compared with raw coordinates on the same physical problem andevaluation budget. A coupled reaction, filtration, and drying model illustrates state memory andevolving conditional response surfaces. These studies establish case-specific numerical results;they do not establish a general low-dimensional representation, real-time industrial performance, oradded value from a learned reasoning model. The resulting framework supplies explicitmathematical and evidential conditions for testing those claims.