RTEBT Geometry, Cosmic Boundaries, and Elastic Spacetime

This paper examines the foundational geometric and continuum mechanics of the Resilient Thermodynamic Elastic Boundary Theory (RTEBT), modeling spacetime as an elastic 3-brane boundary embedded within a higher-dimensional Bulk. By establishing the mathematical necessity of dimensional localization to preserve inverse-square force laws, the framework details how standard model fields, topological variations, and amorphous metric deformations operate without singularities. The analysis presents the Master Lagrangian and variational action governing boundary surface tension, volumetric vacuum pressure, extrinsic curvature tensors, and bending stiffness moduli.