Static Vibrational Reality (SVR): Two Papers on ΛCDM Equivalence and Empirical Separation

This upload contains two complementary papers on Static Vibrational Reality (SVR), presenting both the theoretical framework and the first empirical evidence beyond the ΛCDM paradigm. Empirical Separation of SVR from ΛCDM via Global Phase Coherence at 31 nHz (main paper): Presents the first cross-domain phase analysis at the fundamental frequency Ω ≈ 31 nHz, combining pulsar timing residuals (PTA), gravitational-wave ringdowns (GW), and baryon acoustic oscillations (BAO). All three independent datasets exhibit phase coherence at Ω. A Rayleigh test yields R ≈ 0.24 with p ~ 10⁻⁴, establishing statistically significant global phase-locking. This constitutes the first empirical evidence for SVR as a physically testable alternative to ΛCDM. Linear Perturbations in SVR and Equivalence to ΛCDM (companion paper): Develops the full linear perturbation framework of SVR. By introducing an effective phase-dependent scale factor a_eff, the SVR perturbation equations map one-to-one onto those of ΛCDM. All linear observables (CMB anisotropies, matter power spectrum, weak lensing, BAO, ISW) are indistinguishable from ΛCDM. This establishes the theoretical equivalence at linear order. Together, these two works provide both the mathematical foundation and the first empirical separation of SVR from ΛCDM, pointing toward a universal vibrational order of the cosmos at Ω ≈ 31 nHz.