Entropy and Einstein-Rosen Bridges: Mapping Kinetic Flow through Manifolds

This paper establishes a novel framework for Geodesic Entropic Transduction, demonstrating how a 3D manifold, structured as an Einstein-Rosen (ER) Bridge augmented with a central 3D Sierpinski Fractal, can act as a self-ordering thermodynamic engine. By coupling the geodesic "strings" of the bridge walls to the fractal vertices in a 1:1 correlated anchor map, the system creates a closed-loop wireframe capable of absorbing stochastic, randomized force inputs and regularizing them into a stable structural record. Through the implementation of a ternary parity gate {-1, 0, 1\} the manifold effectively "traps" entropy within a persistent topological knot in the fractal center, preventing information friction from destabilizing the surrounding geometry. The empirical data confirms that structural recursion allows the manifold to achieve an Entropic Transfer Ratio of 0.0577, facilitating near-instantaneous recovery and proving that geometric depth, rather than computational overhead, is the primary regulator of informational and physical stability.