Structural Depth Definition of Reality: Constrained Observational Functors and Invariant Core Structure

This work proposes a structural framework in which reality is defined as an invariant class emerging from a constrained family of observational functors. We consider an inaccessible latent source structure S, together with a family of observational functors F_i : S → O_i mapping into observational categories O_i. Each functor represents a structure-reducing, non-invertible projection of the underlying system. To avoid trivial collapse and ensure structural consistency, we introduce an Admissibility Constraint Layer defined by three axiomatic conditions: Structural Non-Triviality, Refinement Consistency, and Bounded Information Collapse. Within this layered architecture, reality R is defined not as a primitive object or a substructure of S, but as the constraint-stabilized invariance class across all admissible observational reductions. Category-theoretic constructions (such as limits) and sheaf-theoretic representations (global sections) are treated strictly as formal encoding mechanisms rather than ontological commitments. The framework is intended as a minimal structural ontology applicable across different domains of structured observation, including systems theory and information-based modeling, without committing to domain-specific physical assumptions.