THEORY OF VIBRATIONAL-ENERGETIC RESONANT CONTINUUM (TVERC)

The persistence of fundamental paradoxes in modern physics—including the dark matter hypothesis, spacetime singularities, and quantum non-locality—indicates the mathematical limits of the geometric vacuum paradigm. This monograph introduces the Theory of Vibrational-Energetic Resonant Continuum (TVERC), which reformulates the universe as a physical, highly elastic 3D continuum with Planck-scale energy density. In this framework, matter is modeled not as point particles, but as spatially extended topological solitons (volume deficits) whose phase interactions generate continuous acoustic and optical gradients. By applying continuum mechanics, nonlinear acoustics, and analogue gravity, macroscopic and microscopic phenomena are analytically derived from first principles. It is demonstrated that the flat rotation curves of 175 galaxies from the SPARC database can be accurately modeled (with an average convergence of ~15.6%) using a single universal set of continuum parameters without invoking hypothetical dark matter. Furthermore, the proposed model redefines black holes as stratified elastic macro-objects, replacing the central singularity with a finite Topological Monolith, and calculates the expected gravitational-wave resonance for Cygnus X-1 with 0.18% accuracy against observational data. The TVERC framework provides rigorous mechanical derivations for Newton's law of universal gravitation, special relativity kinematics, the Shapiro delay, and the Eddington limit. Ultimately, this approach offers a deterministic, hydrodynamic resolution to quantum tunneling and entanglement, successfully bridging the theoretical gap between thermodynamics, general relativity, and quantum mechanics.