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This paper presents a research project entitled The Theory of Cosmic Differentiation for Black Holes, aiming to develop a theoretical framework for investigating quantum–spacetime behavior in regimes of extreme curvature, without claiming a complete theory or definitive results. The work is grounded in black hole physics as described by General Relativity and in the central role of Hawking radiation in linking quantum mechanics with curved spacetime. It proposes that quantum effects near the event horizon may give rise to effective patterns of energy differentiation that can be described within a phenomenological field-theoretic framework. In this context, we explore a reinterpretation of the proposed differentiation field as an effective entity emerging from quantum pair production processes, with vacuum expectation values evaluated in the Unruh vacuum, which is the physically appropriate quantum state for an evaporating black hole. This connection embeds the project within semiclassical gravity and provides a more well-defined physical interpretation compared to earlier formulations.The proposed mathematical structure indicates that admissible solutions may allow mechanisms of transformation or reorganization among energy components or field species emitted from the horizon. This behavior is interpreted as an effective differentiation driven by the extreme curvature of spacetime, without postulating new fundamental forces or violating the core principles of General Relativity or quantum theory. At the same time, the framework remains phenomenological in nature and requires further development, particularly regarding derivation from first principles, determination of free parameters, and consistency with existing observational constraints. Accordingly, this work represents an advanced stage within an ongoing research program initiated by earlier studies on the Theory of Cosmic Differentiation. It seeks to provide a more mature formulation that is more closely connected to established physics while retaining a constructive exploratory character. In this spirit, we invite researchers in quantum gravity, quantum field theory in curved spacetime, and theoretical astrophysics to engage in critical scientific discussion and international collaboration to further develop this research project, through analytical, numerical, or observational approaches, in order to assess its long-term physical viability and relevance.