How to Prove Your Dimensions Are Right: Finite Decomposition for Multi-Criteria Analysis

This paper establishes the mathematical foundations of the EAGLES_EYE framework, unifying Dominance-Geometry-Dynamics (DGD) analysis, the Principle of Finite Decomposition (PFD), and Cartesian coordinate emergence. We position DGD within the multi-criteria decision analysis (MCDA) landscape, demonstrating how existing methods (TOPSIS, AHP, PROMETHEE) emerge as special cases under specific conditions. The framework introduces 11 distance metrics, diagnostic protocols for detecting geometric failures, and dual-mode dynamics (positive prediction + normative optimization). We propose five testable hypotheses (H1-H5) spanning decomposition validity, visibility thresholds, Cartesian emergence, curvature detection, and dynamic decision superiority-all with pre-specified statistical thresholds to prevent post-hoc rationalization. Empirical and axiomatic validation is deferred to Episode 2 (2026-Q3). This is Episode 1 of a 3-episode SEASON.