Projection Insufficiency and Trajectory Realization - A Unified Constraint-Based Framework for Bounded Systems

Foundational paper of the Global Admissibility Filtering (GAF) research program. The Projection Insufficiency Theorem isolates a structural obstruction shared by bounded information systems, lossy records, forward-local decision procedures, and closed-interval dynamical models — and is the result that the remainder of the program specializes, extends, and applies. Abstract This paper isolates a structural limitation shared by bounded information systems, lossy records, forward-local decision procedures, and closed-interval dynamical models: any property that depends on a complete trajectory cannot, in general, be recovered from a non-injective projection of that trajectory. The obstruction is…