The Relational Emergence Model: Generative Differentiation via Variational Selection on Factorization Manifold

The Relational Emergence Model (REM) is a generative framework for the articulation of relational structure in quantum theory. While Relational Quantum Mechanics (RQM) defines physical states relative to other systems, it does not specify how subsystem structure itself becomes determined. REM addresses this gap by modeling subsystem differentiation as a variational selection process over candidate tensor-product factorizations of Hilbert space. The model introduces a three-layer architecture: Layer 0 — a pre-relational Hilbert space without a privileged tensor-product structureLayer 1 — differentiation as relational articulationLayer 2 — decoherence as stabilization of articulated structure Differentiation is formulated as an optimization problem on a factorization manifold, F ≅ U(N)/(U(n_A) ⊗ U(n_B)), with selection governed by a variational functional Φ = Φ_S + λ Φ_H, combining informational articulation (mutual information) and dynamical stability (boundary Hamiltonian contribution). The parameter λ controls the balance between informational correlation and dynamical coherence, admitting interpretations analogous to inverse temperature, timescale ratio, or renormalization-scale dependence. A three-qubit toy model demonstrates nontrivial factorization selection and a crossover between informationally favored and dynamically stabilized regimes. The framework connects relational quantum mechanics, decoherence theory, information geometry, subsystem structure in gauge theory, and variational optimization on quotient manifolds. The present work is not proposed as a complete physical theory but as a mathematically structured foundational proposal for studying how relational structure itself may become selected, stabilized, and rendered physically meaningful. The REM framework aims to clarify the generative layer underlying relational description and provides a basis for further development including continuous factorization flow, tensor-network formulations, categorical structure, and operational implementations.