Structural Projection Principle (SPP 1.4): Operator Reconstruction and Structural Validation

This work presents a structural framework for reconstructing, classifying, and validating operators from mathematical distinctions, residuals, and incomplete representations. It develops procedures for identifying operator origins, evaluating structural necessity, distinguishing genuine reconstruction from numerical fitting, and testing consistency across representations and resolutions. Particular attention is given to candidate admission, structural non-closure, zero and limiting structures, operator dependencies, and the separation of hypothesis generation from validation. The framework includes formal definitions, conditional constructions, verification criteria, and open research questions intended to support further mathematical investigation.