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. Because the flexural operator is real and self-adjoint, V is real symmetric (orthogonal class), consistent with the system's time-reversal invariance, and the RP model is the natural interpolation between Poisson (λ=0, simply supported) and GOE (λ→∞, fully irregular boundaries). The hypothesis explains why the Rosenzweig–Porter mechanism — rather than a purely phenomenological interpolation such as the Brody distribution — is the natural description of these systems, and generates eight testable predictions. This version corrects the time-reversal prediction (uniform rotation retains an antiunitary protector and remains orthogonal; reaching the unitary class requires additionally breaking every vertical mirror through chiral mistuning), extends the program along the Hermitian→non-Hermitian axis (dissipation; symmetry class AI†) and along a constructive axis (coupling matrices designed via point contacts), and pre-registers a falsifiable value for the plate's eigenvector fractal dimension, D2 = 0.76 ± 0.15. We identify the specific calculations and experiments needed to verify or refute the hypothesis. This version also adds: the full free disk as an executed zero-coupling (Poisson) control; a material-dependence prediction with an executed ν-trend; a faithful-basis computation of the coupling matrix V (dense; power-law banded and low-rank alternatives excluded for the idealized operator); explicit rival exclusion for power-law banded criticality via Dq-flatness and long-range statistics; a declared measurement protocol with bias-transported falsification bands; and an error-budget section for finite resolution and missing levels. All executed pre-tests are included as seeded, reproducible scripts in the supplementary material.
J. Arturo Ornelas Brand (Sat,) studied this question.