Relational Emergence Model (REM 5.12): Variational Selection of Tensor-Product Structure in Quantum Systems

Quantum theory does not uniquely determine subsystem structure. This paper proposes a variational principle on factorization space to select preferred tensor-product structure. The optimization objective balances informational articulation (mutual information across subsystem boundaries) and dynamical separability (interaction coupling across the partition). The framework is formulated on the coset manifold F ≅ U(N)/(U(n_A)⊗U(n_B)) and provides a generative extension of relational quantum mechanics (Rovelli 1996), in which subsystem structure itself is treated as a variational degree of freedom rather than a primitive assumption. A three-qubit illustration demonstrates regime competition with crossover at λ* ≈ 0.28, consistent with results in the REM series (REM2–REM4). This paper is the fifth in the Relational Emergence Model (REM) series.