A Thermodynamically Consistent Macroscopic Framework for Planetary Engineering: Part I – Invariant Manifold Structure and Control-Theoretic Admissibility

The proposed framework formulates the planetary macrosystem as a thermodynamically constrained Index-1 Differential-Algebraic Equation (DAE) system. To guarantee absolute compliance with mass, energy, and stoichiometric invariants across highly nonlinear regimes, the dynamic vector field is embedded with an orthogonal constraint projection operator.Non-equilibrium thermodynamic limits and geomechanical failure thresholds are operationalized exclusively via a Control-Theoretic Trajectory Admissibility Filter, strictly separating generative physical dynamics from technological boundary conditions.