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 a
mathematical specification for integrating these features with learned models and coordinated
optimization 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 through
explicit conditions for dynamic closure, feasible lifting, error propagation, and decision consistency.
Self-contained derivations state the assumptions needed for these connections. Measurement
uncertainty, process variability, model discrepancy, and numerical error remain distinct.
Three reproducible synthetic studies examine the specification. A historical three-stage
optimization example is reproduced with a feasible sequential comparator. A constructed
sufficient representation is compared with raw coordinates on the same physical problem and
evaluation budget. A coupled reaction, filtration, and drying model illustrates state memory and
evolving conditional response surfaces. These studies establish case-specific numerical results;
they do not establish a general low-dimensional representation, real-time industrial performance, or
added value from a learned reasoning model. The resulting framework supplies explicit
mathematical and evidential conditions for testing those claims.