The Relational Emergence Model (REM) extends Relational Quantum Mechanics (RQM) by treating relational structure as *generated* rather than assumed. This companion paper addresses the central open question left in the main REM framework: what selects the differentiation map 𝒟 that articulates a specific tensor-product decomposition out of the pre-relational Hilbert space (Layer 0 → Layer 1). We introduce a variational formulation over candidate factorizations ℱ, with functionals based on von Neumann entropy maximization (ΦS), mutual-information maximization (ΦI), and energetic stability (ΦH). A combined functional Φ = ΦS + λ ΦH allows continuous interpolation between purely informational and dynamically stabilized regimes. A concrete 3-qubit numerical example (with entropy landscape visualization) demonstrates that informational extremization induces nontrivial bipartition selection. The framework is further embedded in three mathematical structures: information geometry on factorization space, categorical quantum mechanics (Frobenius algebra selection), and gauge-theoretic subsystem construction (boundary degrees of freedom analogy). Connections to recent integrated-information approaches in relational quantum dynamics (Zaghi 2025) are discussed as natural extensions. This work complements the main REM paper by supplying the missing selection mechanism, transforming REM from a conceptual proposal into a mathematically structured generative model of relational quantum reality. Related publication: "Relational Emergence Model: A Generative Extension of Relational Quantum Mechanics" (Maruko 2026, Zenodo DOI: https: //doi. org/10. 5281/zenodo. 19123314) This is the companion paper providing the selection mechanism for the differentiation map 𝒟 introduced in the main REM framework.
Yoshifumi Maruko (Sun,) studied this question.