RS1/RS2 AND DYNAMIC LOCALIZATION OF GRAVITY. THE SOLUTION TO THE HIERARCHY PROBLEM IN THE ELASTIC MODEL OF A TWISTING BULK (SBM)

ABSTRACT This work proposes an extension of the elastic cosmology model (Snap-Buckling Model, SBM), which reinterprets the brane structure not as a static geometry but as a dynamic equilibrium in a pre-stressed higher-dimensional medium. The model resolves the hierarchy of forces problem through the kinematics of the near-relativistic rotation of a multi-dimensional "roll", stabilizes the radion through gravitational interaction between layers, and ensures the fulf i llment of Israel junction conditions through a coherent pre-stressed state. The key achievement of this work is the formulation of fi ve falsif i able predictions, two of which have already been conf i rmed by observational astrophysics (the elongated structure of the Eridanus supervoid and the existence of the Dipole Repeller), one is a retrodiction (antipodal symmetry), and two are testable in the near future (the spiral pattern of B-modes and the global chirality dipole). LIMITATIONS AND OPEN TASKS: The author openly acknowledges having reached the limit of his physical intuition and lacking the advanced mathematical capabilities to solve the following fundamental problems: (1) Rigorous derivation of the background metric from the Lagrangian of an elastic medium with a non-zero shear modulus — the metric in Section 2 is presented as an ansatz motivated by analogy with Solid Inflation models and the theory of relativistic p-branes, but is not derived from first principles. (2) Specification of the full energy-momentum tensor T_MN of the twisted medium, including normal and shear components, and the rigorous derivation of the phenomenological parameters a, b, n in the effective radion potential (Section 3). (3) Rigorous analytical solution of the radial balance equation for an arbitrary T_MN — the present work only qualitatively demonstrates that when the centrifugal term dominates, the metric prof i le approaches an exponential one, but full numerical integration has not been performed. (4) Complete stability analysis, including the consideration of tensor and shear perturbations of the metric, not only the radial mode. (5) Microscopic justification of the discrete structure of the bulk (quantization of the brane area or topological defects), which would turn the interpretation of kY as the number of turns from a model assumption into a rigorous derivation. These problems go beyond the scope of the present work and are the subject of a separate study. The author leaves these questions open and hopes that the researcher who finds their solution will receive well-deserved recognition from the scientif i c community, regardless of whether the SBM model itself is ultimately conf i rmed or requires substantial modif i cation. The present work is not a completed theory but a research program offering a new geometric language for describing fundamental problems in physics.