THE FUNCTIONAL-PROJECTION DIVERGENCE PRINCIPLE (FPDP): A Medium-General and Criterion-Explicit Framework for Analyzing Divergence Between Functional Reality and Its Projected or Evaluated Representation.

This paper proposes the Functional-Projection Divergence Principle (FPDP), a conditional analytical framework for examining discrepancies between a system's actual functional state or activity and a representation, projection, label, or evaluation constructed about that system. The framework does not define projection as exclusively temporal, cognitive, political, or predictive. Instead, it treats projection as a transformation process that may operate through temporal, informational, communicative, representational, institutional, computational, social, comparative, or multimodal settings. The relevant criterion and reference relation must be explicitly specified for each application.
The primary motivating case is the Reciprocal Regime Projection-Function Divergence Case (RRPFDC): opposing political groups may evaluate a former governing period more favorably after losing power or while facing difficulties under a successor regime, even when the earlier period also contained substantial problems. The case illustrates a possible divergence between historical functional performance and subsequent representation; it does not establish that such divergence always occurs or that any political group necessarily exhibits it.
The paper develops a three-layer research architecture: philosophical-epistemological, systems-functional, and mathematical-computational-empirical. It defines functional state, activity, projection, representation, criterion, reference, evaluation, and divergence; presents a domain-conditional mathematical schema; distinguishes functional change from representational change; and identifies boundary conditions, counterexamples, falsifiability requirements, alternative explanations, and validation strategies. Thirty analytical case templates and a fourteen-step integrity protocol are provided. Numerical illustrations are explicitly hypothetical, and no empirical validation or completed simulation is claimed. FPDP is therefore presented as a research proposal whose originality, explanatory value, portability, and empirical adequacy remain to be established through literature review and systematic testing.