Why Rosenzweig–Porter? Evanescent Coupling and a Random Matrix Hypothesis for Intermediate Statistics in Freely Vibrating Plates

López-González et al. discovered that the spectral statistics of freely vibrating rectangular thin plates follow the Rosenzweig–Porter (RP) model of random matrix theory—an intermediate statistics model originally formulated for quantum systems. No first-principles explanation has been proposed for why RP appears in a classical system, why free boundary conditions produce it while simply supported conditions do not, or why the same statistics arise across different physical substrates. We propose a testable hypothesis: within each symmetry sector (ℤ₂ × ℤ₂), the eigenfrequencies are the eigenvalues of a random matrix H = H₀ + λV, where H₀ contains the uncoupled frequencies, V represents evanescent-wave coupling at free boundaries, and λ is the coupling strength. Since the plate system has time-reversal symmetry, V is real symmetric (orthogonal class), and the RP model is the natural interpolation between Poisson (λ=0, simply supported) and GOE (λ→∞, fully irregular boundaries). The hypothesis explains why RP specifically—not Brody or semi-Poisson—governs these systems and generates five testable predictions. We identify the specific calculations and experiments needed to verify or refute the hypothesis.